a portfolio management decision support system for transit …815/fulltext.pdf · a portfolio...

A Portfolio Management Decision Support System for Transit Projects

A Dissertation Presented

by

Ye Zhang

to

The Department of Civil and Environmental Engineering

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in the field of

Civil Engineering

Northeastern University Boston, Massachusetts

(July 2013)

i

ABSTRACT

Cost overruns and schedule delays have long been problems for transit projects. The lengthy

development process and large capital investment needed for transit projects have further

increased the complexity of accurately estimating time and cost requirements. Much effort

has been made to achieve more accurate estimates for project’s schedule and cost, for

example using probabilistic approach, yet the overruns still haunts many of the projects and

causes problems for agencies. For those agencies who manage concurrent projects, ensuring

that all their projects remain on target becomes a major challenge. Agencies usually allocate

contingency to a project cost estimate to cope with uncertainties. Adding too large a

contingency to a project will reduce the number of projects that can receive funding, while

an underestimated contingency may cause projects to overrun their budgets. The agencies

would also need to mitigate ongoing projects that are already experiencing cost overruns and

schedule delays. Original estimates prepared at early project development stage are usually

based on historical data and limited information. As projects progress, more information

becomes available and this should allow the owner agencies to improve the cost and

duration requirements.

This research is based on the premise that project cost and schedule are fraught with

uncertainty, and in order to estimate these, an approach is needed that considers this

uncertainty explicitly. In this research, three aspects of transit projects have been examined:

Schedule, Cost, and Escalation. The escalation is examined here mainly due to the long

duration and large capital investment of transit projects. In this research, a new probabilistic

analysis system: Portfolio Management Decision Support System (PMDSS) has been

ii

developed. The system consists of four modules, allowing users to perform (1) expenditure

and contingency planning, (2) escalation analysis, (3) portfolio ranking and (4) Bayesian

updating. The expenditure or cash flow planning will allow users to obtain periodic

expenditures for all individual projects as well as the portfolio, while considering cost and

duration uncertainties. For contingency planning, singularity functions have been applied to

project cost and schedule, resulting in an efficient model for contingency draw-down

throughout project’s life cycle. Because of the major impact of cost escalation on transit

projects, a new: Integrated Transit Index (ITI) has been developed and introduced. This is

different from other cost indices currently available because it specifically uses components

that are related to transit construction. In managing a portfolio of projects, often times

several projects are competing for resources and management attention. Because of this, the

management can benefit from a consistent and logical methodology for ranking projects in

the portfolio. In order to rank the projects within a portfolio, a ranking system is developed

in this research using the PROMETHEE-GAIA method. Finally, a Bayesian updating

procedure is developed and utilized to update cost and schedule estimates at various phases

to provide users with most recent updated estimate and help with making timely decisions.

While Bayesian updating has been used in construction project management, it is believed

that this implementation for updating project cost and schedule at individual and portfolio

levels is new.

The major contribution of this research is to develop a framework for developing a decision

support system, which can be used as a planning tool as early as planning phase, while can

also serve as a managing and control tool throughout the project’s life cycle. It provides both

micro-level schedule and cost analysis for individual project as well as schedule, cost, ranking

iii

and updating at portfolio level. The use of the Singularity functions for contingency analysis,

Bayesian updating and the proposed ranking methods are new in the subject area.

The system developed in this dissertation draws upon various methodologies and concepts

to create a framework for managing a portfolio of transit projects while explicitly considering

the uncertainty of the input variables. The framework can be used in advancing current

practices for managing and predicting project performance and set the stage for

implementation of these concepts in commercial decision support systems.

iv

ACKNOWLEDGEMENTS

This PhD thesis is the result of the most challenging journey in my life so far. During the

process, many people contributed and showed their support. It has been a great experience

to spend more than four years in the Department of Civil and Environmental Engineering at

Northeastern University, and all the people I got to know during this journey and all the

memories we had will always be cherished.

Having started as a Master’s student here in Northeastern, I certainly did not expect to finish

my PhD thesis years later. As I spent more time in pursuing my degree in Construction

Management, I became more interested in this topic, which motivated me to continue my

education for Construction Management.

I would like to firstly express my special thanks and gratitude to Prof. Ali Touran. It has

been my privilege to have him as my advisor throughout the whole journey. The knowledge

I have learned from him, in or out of class, within or without the research, is priceless and

valuable for the rest of my life. His visions, advices, encouragements and patience have

guided me throughout my study and research. It would not have been possible to finish this

thesis without the kindly help and support of Prof. Touran.

Special thanks go to my committee, Prof. Clifford Schexnayder, Prof. Matthew J. Eckelman,

and Prof. Payam Bakhshi Khayani for their valuable time and support. I owe them my

sincere gratitude.

I want to thank the Department of Civil and Environmental Engineering at Northeastern

University for the financial support and everything they have done to make my graduate

study experience nothing but a precious one. Also, special thanks to the department chair:

v

Prof. Jerome F. Hajjar, the professors I have worked with: Prof. Peter Furth, Dr. Daniel

Dulaski, and the department staff Dr. David Whelpley and Patricia Michaud. I would like to

thank all my colleagues, especially Payam, Babak, Amol, Arash, Xinan, Wenhua, thank you

all for your help and support.

For my friends in the United States, China and all over the world, we have shared so much

joy and laughter together. Each of you will be remembered and the memories we shared will

not be forgotten.

Last but not least, I would like to thank my parents, Guohua Zhang and Xuhua Nie, my

grandparents, Wuxian Zhang and Liange Wen. Their selfless love has been my driving force.

I wish I could show them just how much I love and appreciate them. I hope this work will

make you proud.

vi

TABLE OF CONTENTS

ABSTRACT ........................................................................................................................................... i

ACKNOWLEDGEMENTS ............................................................................................................ iv

TABLE OF CONTENTS ................................................................................................................. vi

LIST OF FIGURES ............................................................................................................................ x

LIST OF TABLES ........................................................................................................................... xiii

Chapter 1 : INTRODUCTION ........................................................................................................ 1

1.1 Overview .................................................................................................................................... 1

1.2 Purpose ....................................................................................................................................... 1

1.3 Methodology .............................................................................................................................. 2

1.4 Contributions ............................................................................................................................. 3

Index ............................................................................................................................................. 3

1.5 The Network of Portfolio Project Management .................................................................. 6

1.5.1 Schedule .............................................................................................................................. 8

1.5.2 Cost ...................................................................................................................................... 9

1.5.3 Escalation .......................................................................................................................... 11

1.5.4 PROMETHEE & GAIA Ranking System .................................................................. 13

1.5.5 Bayesian Updating ........................................................................................................... 15

1.5.6 Decision Support System Procedure ............................................................................ 17

1.5.7 Probability Analysis ......................................................................................................... 18

1.5.8 Software ............................................................................................................................ 19

1.5.9 Future Work ..................................................................................................................... 20

Chapter 2 : Contingency Planning During Project Life Cycle..................................................... 21

2.1 Introduction ............................................................................................................................. 21

2.2 Background .............................................................................................................................. 22

2.3 Methodology ............................................................................................................................ 23

2.3.1 Overview of the developed system ............................................................................... 23

2.3.2 Singularity functions ........................................................................................................ 24

2.3.3 Contingency levels during project life cycle ................................................................ 25

2.3.4 Portfolio of projects ........................................................................................................ 29

2.3.5 Modeling the effect of escalation .................................................................................. 31

vii

2.4 Results ....................................................................................................................................... 31

2.4.1 Deterministic Analysis .................................................................................................... 31

2.4.2 Probabilistic Analysis ...................................................................................................... 35

2.5 Schedule Contingency ............................................................................................................ 36

2.5.1 Singularity Function for Project Schedule Contingency ............................................ 36

2.5.2 Portfolio Schedule Contingency .................................................................................... 39

2.6 Summary ................................................................................................................................... 39

Chapter 3 : The Application of PROMETHEE-GAIA Methodology in Portfolio Project Management for Transit Projects .................................................................................................... 41

3.1 Introduction ............................................................................................................................. 41

3.2 Background .............................................................................................................................. 42

3.3 Mathematics ............................................................................................................................. 43

3.3.1 Preference Degree ........................................................................................................... 43

3.3.2 Preference Functions ...................................................................................................... 44

3.3.3 Multicriteria Preference Degree .................................................................................... 47

3.3.4 Multicriteria Preference Flows ....................................................................................... 48

3.4 Example .................................................................................................................................... 50

3.4.1 Example of Purchasing a Car ........................................................................................ 50

3.4.2 Results ............................................................................................................................... 53

3.5 Application to Portfolio Project Management.................................................................... 59

3.5.1 Criteria and Preference Functions ................................................................................ 60

3.5.2 Using Software to Establish Ranking Based on Original Estimate ......................... 65

3.5.3 Using Software to Update Ranking based on Progress Reports .............................. 72

3.6 Application of PROMOTHEE Ranking in Excel ............................................................. 80

3.6.1 Using Excel to Establish Ranking Based on Original Estimate ............................... 81

3.6.2 Using Excel to Update Ranking based on Progress Reports .................................... 89

3.7 Summary ................................................................................................................................... 94

Chapter 4 : Escalation........................................................................................................................ 95

4.1 Introduction ............................................................................................................................. 95

4.2 Modeling of Escalation Factor .............................................................................................. 96

4.2.1 Background ...................................................................................................................... 96

4.2.2 Background ...................................................................................................................... 98

4.2.3 Methodology .................................................................................................................... 99

4.2.4 Validation of Results ..................................................................................................... 104

4.2.5 Analysis of Results ......................................................................................................... 106

viii

4.2.6 Summary ......................................................................................................................... 110

4.3 Modeling and Forecasting Integrated Transit Index........................................................ 111

4.3.1 Background .................................................................................................................... 111

4.3.2 Standard Cost Categories (SCC) for Capital Projects .............................................. 112

4.3.3 Integrated Transit Index ............................................................................................... 113

4.3.4 Forecast with Time Series Analysis and Neural Network ....................................... 116

4.3.5 Forecasting Integrated Transit Index Results............................................................ 120

4.3.6 Summary ......................................................................................................................... 123

Chapter 5 : Bayesian Updating For Portfolio Projects ............................................................... 124

5.1 Introduction ........................................................................................................................... 124

5.2 Background ............................................................................................................................ 124

5.3 Bayesian Updating Concept and Mathematical Formulations ....................................... 126

5.3.1 Bayesian Updating Concept ......................................................................................... 126

5.4 Bayesian Updating for a Single Transit Project in a Portfolio ........................................ 128

5.4.1 Mathematical Concept .................................................................................................. 128

5.4.2 Application ..................................................................................................................... 131

5.5 Bayesian Updating for a Portfolio of Transit Projects .................................................... 139

5.5.1 Mathematical Concept .................................................................................................. 139

5.5.2 Applications with PMDSS ........................................................................................... 141

5.6 Summary ................................................................................................................................. 155

Chapter 6 : The Portfolio Management decision Support System ........................................... 156

6.1 Introduction ........................................................................................................................... 156

6.1.1 The Four Modules of the PMDSS .............................................................................. 156

6.2 Portfolio Management Decision Support System - General (PMDSS-G) ................... 158

6.2.1 General Information ..................................................................................................... 158

6.2.2 Ranking System .............................................................................................................. 160

6.3 Portfolio Management Decision Support System – Bayesian Updating (PMDSS-B) 163


6.3.2 Updating Projects .......................................................................................................... 166

6.4 Portfolio Management Decision Support System – Contingency (PMDSS-C) ........... 168


6.4.2 Cost and Schedule Contingency .................................................................................. 171

6.5 Portfolio Management Decision Support System – Escalation (PMDSS-E) ............... 173

6.5.1 Integrated Transit Index ............................................................................................... 173

6.5.2 Integrated Transit Index Forecast ............................................................................... 174

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6.6 Summary ................................................................................................................................. 176

Chapter 7 : Application of Portfolio MANAGEMENT decision SUPPORT SYSTEM ..... 177

7.1 Introduction ........................................................................................................................... 177

7.1.1 The Projects ................................................................................................................... 177

7.2 Data ......................................................................................................................................... 182

7.2.1 Expenditures from Quarterly Reports ....................................................................... 183

7.2.2 PMDSS Calculated Expenditure vs. Planned Expenditure from Reports ............ 186

7.2.3 2009 Q3 Update vs. Actual (Bayesian Updating) ..................................................... 189

7.2.4 2010 Q3 Update vs. Actual .......................................................................................... 191

7.2.5 2011 Q3 Update vs. Actual .......................................................................................... 193

7.2.6 Bayesian Updating Summary ....................................................................................... 195

7.3 Ranking of the Projects in the Portfolio ............................................................................ 198

7.3.1 Ranking Based on Original Estimates ........................................................................ 199

7.3.2 Updated Ranking at 2009 Quarter 3 ........................................................................... 202



7.3.5 Ranking Changes ........................................................................................................... 207

7.4 Summary ................................................................................................................................. 209

Chapter 8 : Conclusion .................................................................................................................... 211

8.1 Summary of Completed Work ............................................................................................ 211

8.2 Limitations of the Proposed System .................................................................................. 213

8.3 Recommended Work for Future ........................................................................................ 214

APPENDIX A: References ............................................................................................................ 216

x

LIST OF FIGURES

Figure 1.5.1 The Network of Project Portfolio Management ....................................................... 6

Figure 1.5.2.1 - Beta Distribution with a=0, b=1, α=1.70 and β=1.85 (Touran et al., 2004) . 10

Figure 1.5.5.1 – Gantt Chart for eight projects in Manhattan ..................................................... 16

Figure 1.5.6.1 – Decision Support System Procedure .................................................................. 18

Figure 2.3.1.1 - Bar Chart for 8 Projects in Manhattan ................................................................ 23

Figure 2.3.3.1 - Unit step (left) and unit ramp (right) ................................................................... 27

Figure 2.3.3.2 - Contingency vs. Project Phase when pre-bid contingency is overestimated . 28

Figure 2.3.3.3 - Contingency vs. Project Phase when pre-bid contingency is underestimated .............................................................................................................................................................. 29

Figure 2.4.1.1 - Contingency drawdown for 8 projects in Manhattan ....................................... 34

Figure 2.4.2.1 - Contingency drawdown for eight projects with 25% coefficient of variation to the mean of contingencies ........................................................................................................... 36

Figure 2.5.1.1 - Schedule Contingency vs. Project Phases ........................................................... 37

Figure 3.3.2.1 - Preference Functions (Brans & Mareschal, 2005) ............................................. 45

Figure 3.3.2.2 - The Linear Preference Function (Ishizaka & Nemery, 2011) .......................... 46

Figure 3.4.1.1 - Example of Criteria and Preference Functions .................................................. 52

Figure 3.4.1.2 - Car Evaluation Data and Statistics ....................................................................... 53

Figure 3.4.2.1 - PROMOTHEE I – Partial Ranking .................................................................... 55

Figure 3.4.2.2 - PROMOTHEE I – Complete Ranking .............................................................. 57

Figure 3.4.2.3 - GAIA Plane ............................................................................................................. 58

Figure 3.5.2.1 - Evaluations of Projects Based on Original Estimates....................................... 66

Figure 3.5.2.2 - PROMETHEE I – Partial Ranking ..................................................................... 68

Figure 3.5.2.3 - PROMETHEE II – Complete Ranking ............................................................. 68

Figure 3.5.2.4 - PROMETHEE Rainbow ...................................................................................... 70

Figure 3.5.2.5 - PROMETHEE & GAIA ...................................................................................... 71

Figure 3.5.2.6 - Weight Stability Intervals for Duration ............................................................... 72

Figure 3.5.3.1 - Evaluations of Projects Based on Updates ......................................................... 74

Figure 3.5.3.2 - PROMETHEE I – Partial Ranking for Updates ............................................... 76

Figure 3.5.3.3 - PROMETHEE II – Complete Ranking for Updates ....................................... 77

Figure 3.5.3.4 - PROMETHEE Rainbow for Updates ................................................................ 78

Figure 3.5.3.5 - PROMETHEE GAIA for Updates .................................................................... 79

Figure 3.5.3.6 - Wight Stability Intervals for Updated Percent Complete ................................. 80

Figure 3.6.1.1 - Partial Ranking for Original Estimate ................................................................. 83

Figure 3.6.1.2 - Complete Ranking for Original Estimate ........................................................... 83

Figure 3.6.1.3 - The Ranking Analysis for Projects 2 and 3 Based on Original Estimate ....... 85

Figure 3.6.1.4 - The Ranking Analysis for Projects 9 and 10 Based on Original Estimate ..... 86

Figure 3.6.1.5 - The PROMETHEE Rainbow for the Original Estimate ................................. 87

Figure 3.6.1.6 - Project 2 Profile for Original Estimate ............................................................... 88

Figure 3.6.1.7 - Project 2 Spider Web for Original Estimate ....................................................... 88

Figure 3.6.2.1 - Partial Ranking for Updated Estimate................................................................. 90

Figure 3.6.2.2 - Complete Ranking for Updated Estimate........................................................... 91

Figure 3.6.2.3 - The Ranking Analysis for Projects 2 and 3 Based on Updated Estimate ...... 92

Figure 3.6.2.4 - The Ranking Analysis for Projects 5 and 9 Based on Updated Estimate ...... 93

xi

Figure 4.2.3.1 - (a) Actual percent change per year vs. a normal distribution; (b) Actual percent change per year vs. a Loglogistic distribution ................................................................ 102

Figure 4.2.5.1 - Independent Series vs. Historical Data ............................................................. 107

Figure 4.2.5.2 - Martingale Series vs. Historical Data ................................................................. 109

Figure 4.2.5.3 - Correlated Series vs. Historical Data ................................................................. 110

Figure 4.3.3.1 - Percentage of Each SCC to the Total Cost (Booz Allen & Hamilton, 2003 & 2004) ................................................................................................................................................... 115

Figure 5.3.1.1 - Continuous prior distribution of parameter (Ang & Tang, 2007) ............ 127

Figure 5.4.2.1 - Gantt Chart for 8 Projects in Manhattan .......................................................... 132

Figure 5.4.2.2 - Prior, Likelihood and Posterior Distributions for Schedule .......................... 134

Figure 5.4.2.3 - Schedule Progress Curves for Plan and Forecast Distribution...................... 135

Figure 5.4.2.4 - Duration Range for Project 1 ............................................................................. 136

Figure 5.4.2.5 - Prior, Likelihood and Posterior Distributions for Cost .................................. 137

Figure 5.4.2.6 - Cost S-Curves for Plan and Forecast Distribution .......................................... 138

Figure 5.4.2.7 - Cost Range for Project 1 ..................................................................................... 138

Figure 5.5.2.1 - Flow chart for Contingency Estimate Using PMDSS ..................................... 142

Figure 5.5.2.2 - Cost Contingency Drawdown for All Projects ................................................ 143

Figure 5.5.2.3 - Year Expenditure for the Portfolio ................................................................... 144

Figure 5.5.2.4 - Planned vs. Forecast Schedule Curve for the Portfolio at PE ....................... 147

Figure 5.5.2.5 - Planned vs. Forecast Schedule Curve for the Portfolio at FD ...................... 147

Figure 5.5.2.6 – Portfolio Duration Range at PE ........................................................................ 148

Figure 5.5.2.7 – Portfolio Duration Range at FD ....................................................................... 149

Figure 5.5.2.8 - Prior, Likelihood, and Posterior Curves at PE ................................................ 149

Figure 5.5.2.9 - Prior, Likelihood, and Posterior Cumulative S-Curves at PE ........................ 150

Figure 5.5.2.10 - Prior, Likelihood, and Posterior Curves at FD .............................................. 150

Figure 5.5.2.11 - Prior, Likelihood, and Posterior Curves at FD .............................................. 151

Figure 5.5.2.12 – Key Components on the First Worksheet of the Spreadsheet ................... 153

Figure 5.5.2.13 - Project Schedule for the remainder of the Project (Percentile Values) ...... 153

Figure 6.1.1.1 - Flowchart for PMDSS ......................................................................................... 157

Figure 6.2.1.1 - Project Information Table................................................................................... 158

Figure 6.2.1.2 - Gantt Chart and Escalation Rates ...................................................................... 159

Figure 6.2.1.3 - Yearly and Cumulative Expenditures ................................................................ 160

Figure 6.2.2.1 - Prior Project Ranking Criteria ............................................................................ 161

Figure 6.2.2.2 - PROMETHEE I & II Rankings ........................................................................ 162

Figure 6.3.1.1 - Defining Possible Critical Paths ......................................................................... 164

Figure 6.3.1.2 - Portfolio Total Cost (Probability of Not Exceeding) ..................................... 165

Figure 6.3.1.3 - Portfolio Total Duration (Probability of Not Exceeding) ............................. 165

Figure 6.3.2.1 - Bayesian Updating Table ..................................................................................... 167

Figure 6.4.1.1 - Bayesian Updating Table ..................................................................................... 169

Figure 6.4.1.2 - Defining Contingency at 10% Design ............................................................... 170

Figure 6.4.1.3 - Defining Contingency at Pre-Bid Using Historical Data................................ 171

Figure 6.4.2.1 - Cost Contingency Drawdown for the Portfolio .............................................. 172

Figure 6.4.2.2 - Schedule Contingency Drawdown for the Portfolio ....................................... 173

Figure 6.5.1.1 - Integrated Transit Index ...................................................................................... 174

Figure 6.5.2.1 - Forecasted Integrated Transit Index Using Time-Series Analysis ................ 175

Figure 7.1.1.1 - Planned Improvements of East Side Access (MTA, 2013) ............................ 179

xii

Figure 7.1.1.2 - A History of ESA Budget and Completion Year Estimates from Media and MTA Reports .................................................................................................................................... 180

Figure 7.1.1.3 - Manhattan Contracts Active during 2009 Quarter 3 ....................................... 181

Figure 7.2.6.1 - Bayesian Updating Flowchart for Project Costs Means ................................. 197

Figure 7.3.1.1 - Ranking Input Based on Original Estimates .................................................... 200

Figure 7.3.1.2 - Ranking Orders Based on Original Estimates ................................................. 200

Figure 7.3.1.3 - Ranking Orders Probability Analysis: CM009 vs. CM019 ............................. 201

Figure 7.3.1.4 - Ranking Orders Probability Analysis: FM216 vs. CS790 ............................... 202

Figure 7.3.2.1 - Updated Ranking Orders at 2009 Q3 ................................................................ 203

Figure 7.3.2.2 - Ranking Orders Probability Analysis: CM004 vs. CS790 ............................... 204

Figure 7.3.2.3 - Ranking Orders Probability Analysis: CM008A vs. FM216 ........................... 204



Figure 7.3.5.1 - Ranking Order Changes for Six Selected Projects ........................................... 208

xiii

LIST OF TABLES Table 1.5.3.1 - Five Main Cost Categories ...................................................................................... 12

Table 1.5.4.1 – Eight Criteria for Ranking Projects ...................................................................... 15

Table 1.5.7.1 – Inputs Modeled as Distributions .......................................................................... 19

Table 2.4.1.1 - Cost and Schedule Data for the Eight Projects ................................................... 33

Table 3.3.1.1- Alternatives and Criteria .......................................................................................... 44

Table 3.4.2.1 - PROMOTHEE I – Partial Ranking ...................................................................... 53

Table 3.4.2.2 - PROMOTHEE II – Complete Ranking .............................................................. 56

Table 3.5.2.1 – Ranking Inputs Based on Original Estimates ..................................................... 66

Table 3.5.3.1 – Ranking Inputs Based on Original Estimates ..................................................... 73

Table 3.6.1.1 - PROMETHEE Ranking in Excel for Original Estimate .................................. 82

Table 3.6.2.1 - PROMETHEE Ranking in Excel for Updated Estimate .................................. 89

Table 4.2.3.1 - ENR'S Building Cost Index History (1980-2010) ............................................. 101

Table 4.2.4.1 - Measurement Values for Three Series ................................................................ 106

Table 4.3.2.1 - Standard Cost Categories for Capital Projects (FTA) ...................................... 113

Table 4.3.3.1 - Cost Categories and Percentages ......................................................................... 114

Table 4.3.3.2 - Integrated Transit Index and Percent Changes ................................................. 116

Table 4.3.4.1 - MAPE for BCI Prediction Using Neural Network .......................................... 119

Table 4.3.4.2 - MAPE for BCI Prediction Using Time Series Analysis ................................... 120

Table 4.3.5.1 - ITI Prediction Using Neural Networks .............................................................. 121

Table 4.3.5.2 - ITI Prediction Using Time Series Analysis ........................................................ 122

Table 5.4.1.1 - Standard Deviation Assumptions ........................................................................ 131

Table 5.4.2.1 – Information on the 8 Projects in Manhattan .................................................... 132

Table 5.4.2.2 - Prior and Observations at Different Phases for Project 1 ............................... 133

Table 7.2.1.1 - Planned Expenditure and Actual Expenditure from 2009 Q4 Report .......... 184



Table 7.2.2.1 - PMDSS Calculated Expenditure vs. Planned Expenditure from 2009 Q4 Report ................................................................................................................................................ 187



Table 7.2.2.4 – PMDSS Calculated Expenditure vs. Planned Expenditure Based on Report MAPD................................................................................................................................................ 189

Table 7.2.3.1 - PMDSS 2009 Q3 Updated Expenditure vs. Actual Expenditure Based on Report (at 2009 Q4) ......................................................................................................................... 190



Table 7.2.3.4 - PMDSS 2009 Q3 Updated Expenditure vs. Actual Expenditure Based on Report MAPD .................................................................................................................................. 191


xiv


Table 7.2.4.3 - PMDSS 2010 Q3 Updated Expenditure vs. Actual Expenditure Based on Report MAPD .................................................................................................................................. 193


Table 7.2.5.2 - PMDSS 2011 Q3 Updated Expenditure vs. Actual Expenditure MAPD ..... 195

Table 7.2.6.1 - MAPD Comparisons ............................................................................................. 198

1

CHAPTER 1 : INTRODUCTION

1.1 Overview

In this dissertation, a decision support system for project portfolio management (PPM) is

developed and described for transit projects. The developed tool named Portfolio

Management Decision Support System (PMDSS) may be used for managing cost and

schedule for a portfolio of transit projects. Transit projects were selected because

traditionally they have been plagued with cost and schedule overruns, long development

periods, and escalation. The integrated portfolio project management decision support

system (PMDSS) can be utilized from as early as the conceptual design phase to the end of

construction. Three major aspects of this system are schedule, cost, and escalation. To

analyze and track these three aspects, various concepts and techniques have been used,

including singularity functions, Bayesian updating, time series forecasting, and neural

networks.

1.2 Purpose

The purpose of this research is to develop a decision support system that can be used by

transit agencies that are managing several projects concurrently, to manage the cost and

schedule for these projects. Projects in the portfolio can either be part of a larger program or

2

totally independent from each other. As a planning tool, this system can provide a macro-

level schedule network, yearly expenditure plan, a contingency drawdown curve, and

escalation budget. As a management tool, this system can help project managers to

continually update the progress of projects as more information becomes available.

1.3 Methodology

The PMDSS focuses on three main aspects of the PMDSS that are considered to be

extremely important in PPM in transit projects – schedule, cost and escalation. Schedule

delay has long been a problem for transit projects. According to a database consisting of

information on 24 transit projects published by the FTA, the average schedule delay is about

34% of the original schedule (FTA, 2004). Cost is another major issue in these projects,

where the average cost overrun is about 35% of the original estimated budget (FTA, 2004).

These two major issues have been concerns for not only single projects but also portfolios

of projects, where massive cost overruns and delays can occur due to complex interaction

among projects and the shear scope of the portfolio. The third aspect considered here is

escalation. Since transit projects usually have long development periods, the impact of

escalation must not be overlooked. Moreover, escalation interacts with both schedule and

cost directly, and any effective plan for controlling and tracking cost and schedule should

consider the effects of escalation as well.

3

1.4 Contributions

The contribution of the research is summarized as follows:

The integrated cost index

Project cost and schedule updating

Project ranking within the portfolio

Cost and schedule have long been the concerns of estimators and are closely interrelated.

Escalation is considered to be significant due to the long duration of transit projects and

large capital investments that they require. There is considerable interaction among these

three aspects: budget, funding and expenditures can affect a project’s schedule; delays can

affect project’s cost and make the effect of escalation more significant; and the escalation

rate can affect the project cost estimate and schedule planning.

The integrated cost index

In this work, a new composite index named the ‘Integrated Transit Index’ (ITI) has been

developed to measure the cost escalation for transit projects. This index breaks down the

project capital costs into five main categories. It uses various sources of cost data to come

up with a weighted value for each of these categories. After combining these five categories,

the ITI is obtained. A time series analysis and neural network analysis have been performed

to forecast the index to achieve better accuracy in regard to transit project cost movements.

The ITI improves the accuracy of cost estimates and provides decision-makers with more

information about the risk of escalation.

4

Project cost and schedule updating

In order to track and update cost and schedule throughout the progress of the project, two

phases are identified in this work: the Prior Phase and the Posterior Phase. At the beginning,

cost estimates and schedule plans are prepared for each individual project in the portfolio.

This constitutes the Prior Phase where estimates are based on historical data as well as the

sources that are usually used for estimating the cost and duration of projects. As projects

progress, the original estimates can be updated with newly observed progress information.

This update is implemented using the Bayesian approach. After the update, the projects are

considered to be in their Posterior Phase. Each Posterior Phase will then, in turn, be

considered as the Prior Phase for the next update. Analyzing projects in both phases can

help project managers to better understand the states of the projects and to avoid potential

risks in the future.

Project ranking within the portfolio

Another important contribution of this research is the ranking of projects in the portfolio.

PROMETHEE-GAIA was selected to rank the projects in the portfolio. A comprehensive

report can be obtained to better define and understand the position of each individual

project in the portfolio and provide timely information to decision-makers. Bayesian

updating is another tool that provides a consistent and defensible mathematical approach for

updating project and portfolio schedule and cost status at regular intervals. As original

estimates maybe based on relatively limited data, and newly observed information can be

quite valuable, the updating process can contribute tremendously not only to each individual

5

project but also to the overall PPM. These four analyses are believed to be of great benefit

not for only tranit projects and PPM but also for individual projects and in other fields.

6

1.5 The Network of Portfolio Project Management

An overview of the scope of this research is provided in Figure 1.5.1. All these components

are incorporated into the developed Portfolio Management Decision Support System

(PMDSS).

Figure 1.5.1 The Network of Project Portfolio Management

Prior Posterior

Schedule

Escalation

Cost

Schedule

Cost

Bayesian Updating

Singularity Functions

Schedule Contingency

Singularity Functions

Cost Contingency

Time Series Analysis

Neural Networks

Integrated Transit Index

PROMETHEE-GAIA

Portfolio Ranking Portfolio Ranking

7

The interaction between the three aspects mentioned earlier (i.e., cost, schedule, escalation)

is shown in Figure 1.5.1, and the mathematical tools and techniques used in the research are

highlighted. The long duration of a project, involving uncertainties and risks, can cause an

increase in project budget as well as escalation costs. The larger the project base cost, the

higher the escalation cost. Also, costs can impact project schedule since for some projects

schedule is a primary consideration, while in others schedule is restricted due to budget

limitations. Escalation will surely affect project total costs, while a project’s original schedule

might sometimes be disrupted due to unexpectedly large escalation costs and cash flow

issues. The ITI was developed for modeling and measuring escalation. Both schedule and

cost contingency drawdown curves are modeled by applying singularity functions. The

PROMETHEE-GAIA ranking method (described later in this chapter) is used to rank the

projects in the portfolio. The ranking of projects is an important element in PPM and allows

management to focus on more important projects as time progresses (The Standard for

Portfolio Management, 2008). Bayesian updating will then be applied to the Prior Phase to

obtain updated estimates, which will be utilized for the analyses mentioned above all over

again. For example, as the projects progress, project priorities can change, and through the

use of PROMETHEE-GAIA, projects are ranked on a regular basis according to updated

project progress data. These issues will be discussed in more detail in subsequent chapters,

and the decision support system will work as a planning and management tool to improve

the experience with PPM in transit projects.

8

1.5.1 Schedule

Both cost and schedule planning in this work are based on a simulation-based probabilistic

approach.

To start, the system will generate a precedence network for the portfolio of projects. This

network will model each project in the portfolio as an activity in the precedence network and

identify precedence relationships between projects. Thus, the whole portfolio will then be

considered as a network of projects. All of the project durations will be modeled as normal

distributions. The possibility of having multiple critical paths has also been covered. The

total duration for the portfolio can be obtained, and the distribution for the total duration

can be computed.

When the schedule estimate is prepared for a single project, there are two scenarios. Under

the first scenario, there is sufficient historical data on similar projects, and thus a distribution

can be selected to model the project duration. The schedule delay can be accounted for by

selecting a preferred percentile value from the cumulative distribution of portfolio duration

generated by historical data. Under the alternative scenario, however, when there is an

insufficient amount of similar cases from the past, the schedule contingency can be

calculated as a percentage of base estimates to cover the potential schedule delays. Gurgun,

Zhang and Touran (2013) proposed a model for schedule contingency level throughout

project’s life cycle. Their model used three straight lines (i.e., 0-5% complete, 5-15%

complete, and 15% complete to the end of construction) to model the contingency percent

mean values against project percent completion. Here, for portfolio projects, a singularity

function is used to model schedule contingency level for the portfolio. After the schedule

9

contingency has been established for all projects, the new base estimate for each project can

be applied to those contingency levels to arrive at the new schedule contingency for each

project. By summing up the schedule contingencies for the projects on critical paths, the

portfolio schedule contingency can be obtained.

As more information becomes available, the original schedule may need to be modified. This

process has been considered in the system as well. The Bayesian updating technique has

been used to update project schedule. It should be noted that the total duration only

considers the critical path for projects that are part of a portfolio, or critical projects for

situations when there are independent projects in the portfolio system. The newly obtained

information will contribute to a new distribution (i.e., underlying distribution). By combining

this distribution and the original distribution (i.e., prior distribution) via the Bayesian

updating technique, we can calculate the revised distribution (posterior distribution), which

will be used for planning and management until the next update is implemented.

1.5.2 Cost

In this study, individual project costs have been modeled as normal distributions to perform

risk analysis. The total cost for the portfolio can be obtained by simply adding up all of the

project costs. The project expenditure has been modeled as a beta distribution with shape

factors 1.70 and 1.85 (Fig. 1.5.2.1, Touran et al., 2004). By considering the information

obtained from schedule analysis, we can compute the expenditure for all projects. By

10

summing up the expenditures for all of the projects in the portfolio, we can calculate the

yearly expenditure for the portfolio.

Figure 1.5.2.1 - Beta Distribution with a=0, b=1, α=1.70 and β=1.85 (Touran et al., 2004)

The same procedure that was used for modeling schedule contingency and updating original

distribution has been used to manage the cost aspect as well. The cost singularity function

will be somewhat different from the schedule function, as there is a contingency change at

the bidding time. The project life cycle is broken down into three phases: pre-bid, bidding,

and post-bid. It should be noted that at the time of bid opening, the cost contingency can be

rising instead of falling, which depends on whether the original cost estimate overestimated

or underestimated the contingency amount. The use of a singularity function will facilitate

the modeling of these possible scenarios, and summing up all of the singularity functions for

the projects will provide the total cost contingency for the portfolio.

11

The Bayesian updating procedure also differs from the schedule management approach

described earlier. Instead of using critical projects or a critical path to estimate the total

duration of a portfolio of projects, the total costs would be the sum of all projects in the

portfolio. The posterior distribution will be used for cost management until the next

available cost estimate update becomes available.

1.5.3 Escalation

When preparing a cost estimate, one risk that cannot be overlooked is escalation. Commonly

used sources, such as Engineering News Record (ENR) and R.S. Means, have been

publishing related indices for a long time. For example, ENR has been collecting data from

20 cities in the United States since 1921 and publishing indices such as the Construction

Cost Index (CCI) and Building Cost Index (BCI), which have been used to measure cost

trends (Touran and Lopez, 2006). The lengthy development phase of transit projects, usually

extending over a period of several years, have been known to be a major cause of increase in

transit project costs (Flyvbjerg et al., 2004). For even small transit projects, the time span

from the planning phase to the end of construction may easily exceed five years. Thus, it is

important to understand the crucial role that escalation plays in regard to cost and budget.

As a result, these indices have been critically examined in this research and a new cost index

has been proposed for transit projects – namely, the Integrated Transit Index (ITI).

Since it is important to accurately estimate escalation, it is essential to provide an index with

forecasted values for estimating. In regard to forecasting the index, previous research has

utilized methods such as a time series model, Auto-Regressive Integrated Moving Average

12

(ARIMA), and neural networks. The goal is to model the index in such a way that estimators

can get forecasted index values to estimate escalation for future years. ENR’s BCI has been

selected over CCI due to its representation of skilled labor as opposed to common labor.

Also, the data used in this part of the research has been limited to the past 30 years as it is

believed that this time span would be adequate to capture the variations of construction

costs for the recent years.

Three approaches have been chosen to examine BCI over the past 30 years, and it has been

found that the best results could be achieved by modeling the BCI as an independent series.

The second major part in escalation analysis is to develop an index for transit projects. Based

on the FTA-published Standard Cost Categories (SCC), a cost index system – namely, the

Integrated Transit Index – for modeling escalation in transit projects in the United States is

proposed. The 10 SCC categories have further summarized into 5 main categories. These

categories are presented below and explained in Chapter 4.

Table 1.5.3.1 - Five Main Cost Categories

01 Construction SCC10-SCC40

02 Systems SCC50

03 Real Estate SCC60

04 Vehicles SCC70

05 Soft Cost SCC80

Data to model these five categories have been collected from various sources and, by

combining the weighted values of these five categories, the ITI is obtained.

13

The forecast of the ITI has also been performed using neural network and time series

analysis. The results suggest keeping both neural network and time series analysis as they

outperform each other in certain cases. The forecasted ITI values for the next 10 years have

also been computed. It should be noted that forecasting the escalation for 20 years will be

very challenging and generally unreliable. The results demonstrate that the MAPE values are

quite good compared to previous research. The forecasted index will be applied to the yearly

expenditure; however, if Monte Carlo simulation is required, the escalation should be

modeled using a normal distribution with forecasted index values. Normal distribution is

selected because it provides relatively good statistical test results (Chi-squared test) when

performing distribution fitting, if not the best, in addition to being commonly selected in

statistical analysis by researchers and more familiar to readers.

1.5.4 PROMETHEE & GAIA Ranking System

As the proposed decision support system is designed for agencies that are managing

concurrent projects, it is necessary to provide a ranking system for a portfolio, especially

when resources and funds are limited. After a preliminary research, we selected the

Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE)

and its descriptive complement, Geometrical Analysis for Interactive Aid (GAIA), to

perform the ranking of projects within the portfolio. First introduced in the 1980s, the

methodology has since been improved and refined. It has been applied in various fields,

including business and education, (Behzadiana et al., 2010; Mareschal & De Smet, 2009;

Hayez, 2009; Lv et al., 2011). This methodology belongs to the outranking method family

14

and follows the principle of pairwise comparisons of the alternatives (D-Sight, 2012). It

provides an elaborate analysis of the alternatives, both numerical and graphical, to help

decision-makers achieve better understanding of the portfolio of projects and make a

prudent choice of the alternatives; however, it should be noted that even though the

methodology is chosen, only PROMETHEE I (partial ranking), PROMETHEE II

(complete ranking) and GAIA have been applied to the context of this research. Other

approaches, including the PROMETHEE III (ranking based on intervals), PROMETHEE

IV (continuous case), PROMETHEE V (MCDA including segmentation constraints) and

PROMETHEE VI (representation of human brain) have not be utilized as they are

considered unsuitable for this research.

To apply this method, criteria and preference functions must first be defined. Eight criteria

have been selected for the ranking system (Table 1.5.4.1). These criteria will be explained in

Chapter 3; however, it should be noted here that not all of the criteria are to be applied at

the beginning. Three criteria in particular (i.e., cost overrun, schedule delay and percent

complete, italics in Table 1.5.4.1) are based on project progress, as a result of which, only the

remaining five criteria will be included in the analysis that is prepared at the start of the

portfolio, i.e., the Prior Phase. The ranking system will produce a ranking order of the

projects in the portfolio at the Prior Phase. It is understood, however, that the rank can

change later as projects progress. Once the project has been updated with new observations,

all eight of the criteria will then be utilized again to provide a new ranking order, which is the

most up-to-date and is considered as the ranking at the Posterior Phase. Based on the results

obtained from these reports, project managers can evaluate alternatives and make timely

judgments accordingly.

15

Table 1.5.4.1 – Eight Criteria for Ranking Projects

ID Criteria Type

1 Project Cost Numerical

2 Project Duration Numerical

3 Project Cost Overrun Numerical

4 Project Schedule Delay Numerical

5 Project Criticality Index Categorical

6 Percent Complete Numerical

7 Project Starting Time Numerical

8 Stakeholders Categorical

GAIA is a descriptive approach, offering visualized information on criteria and the

alternatives. As more than a few criteria are involved in this process, the analysis can be

presented in a multi-dimensional space.

1.5.5 Bayesian Updating

While the preparation of the original estimate is based on limited data and assumptions,

Bayesian updating can combine information used for original estimate and newly observed

information during the implementation of the projects, thereby providing the most up-to-

date estimates of project cost and schedule. Since the original estimates are based on many

uncertain inputs, actual observations can be quite valuable. A Bayesian approach helps with

revising project cost and schedule estimates over the course of the lengthy development and

construction phases of transit projects. In this research, Bayesian updating is closely tied to

other aspects, such as updating project cost, updating schedule, updating project contingency

and updating project ranking, as the most recent estimates will determine the expenditure,

the schedule of the portfolio, contingency levels, and the ranking in the portfolio. After

performing all of the necessary analyses in the Prior Phase, applying Bayesian updating

16

makes it possible to perform all of the analyses again in the Posterior Phase. The results

obtained from Posterior Phase can then be compared with those of Prior Phase to assess the

current state of all projects and the portfolio as a whole. Project cost and duration are the

parameters that need to be estimated in this research. Based on historical data, experts’

experiences, and available information, the distribution of project cost and duration can be

established. This is considered as prior probability for the parameters; posterior probability can

be obtained by applying Bayesian updating after observed information has been collected.

Eight projects in Manhattan that were part of the East Side Access Project in New York City

have been selected to demonstrate this methodology. These projects have been considered

as a portfolio even though the East Side Access project is a much larger program. The Gantt

chart for these eight projects can be obtained after entering all of the information into the

decision support system (Fig. 1.5.5.1).

Figure 1.5.5.1 – Gantt Chart for eight projects in Manhattan

After applying the update, one can perform the schedule and cost analysis again in regard to

project budget, duration, yearly expenditure, cost and schedule contingencies, and ranking.

17

Comparing these analyses with the original analysis can help a project manager to understand

where the projects currently stand and make timely decisions.

1.5.6 Decision Support System Procedure

The procedure for utilizing the developed decision support system is shown in the following

flow chart (Fig. 1.5.6.1). It should be noted that Bayesian updating is a repeated process, and

whenever there is an updated schedule or costs report, it must be performed.

18

1.5.7 Probability Analysis

As a significant part of this research as well as an important feature of the developed system,

probability analysis is performed throughout the whole research. Many inputs were

Historical &

Available Data

Prior Estimates for Cost

& Schedule

Index

Sources

Integrated Transit

Index Forecast

Cost & Schedule

Contingencies

Portfolio Ranking

System

Yearly Expenditure and

Cumulative

Bayesian Updating

Posterior Estimates for

Cost & Schedule

Cost & Schedule

Contingencies

Portfolio Ranking

System

Yearly Expenditure and

Cumulative

Prior Phase

Posterior Phase

RE

PE

AT

Figure 1.5.6.1 – Decision Support System Procedure

19

considered as random variables and modeled as distributions. A list of basic inputs being

modeled as distributions is presented in Table 1.5.7.1.

Table 1.5.7.1 – Inputs Modeled as Distributions

Inputs Distributions

Project cost Normal distribution

Project duration Normal distribution

Project contingency Normal distribution (optional)

Integrate Transit Index forecasted values Normal distribution (optional)

Inputs like project contingency and forecasted values of ITI were either modeled as

distributions or used fix numbers in this research. When contingency is known, we used

fixed values in contingency analysis. For escalation analysis, the ITI values for future years

were the fixed results produced by forecast methods. However, one could model the ITI

values as a normal distribution to generate escalation rates for future years.

1.5.8 Software

A number of software programs have been utilized in this research. @Risk 6.0 has been used

throughout the whole process, as it enables users to perform Monte Carlo simulations. Also,

neural network and time series analysis tools within Excel have been used. Visual

PROMETHEE was also selected to perform PROMETHEE-GAIA ranking. It should be

noted that other software programs such as SPSS, Minitab, D-Sight have been used for the

purposes of testing or comparisons but are not included here as they were not essential for

this research.

20

1.5.9 Future Work

For future work, it will be beneficial if more actual portfolio project data is available to

improve the developed system. Also, the ITI is mainly based on the past 6 years’ data, and

the inclusion of more data would result in better escalation forecasts. Moreover, the decision

support system is mainly Excel-based and includes many random variables. It was relatively

time-consuming to simulate all of the random variables in the system. Thus, the use of

another software platform such as MATLAB could possibly accelerate the computation,

although it may diminish the transparency of the proposed system. Lastly, some assumptions

regarding distributions can be improved when more data becomes available.

21

CHAPTER 2 : CONTINGENCY PLANNING DURING PROJECT LIFE CYCLE

2.1 Introduction

In this chapter, a probabilistic method is proposed for contingency planning during the

project design and construction phases to establish project budgets for large transportation

projects. Contingency is the reserve budget that is set aside to cope with uncertainties

during a project design and construction. The main phases for which the contingency

budget is established include pre-bid, bidding and post-bid. The pre-bid phase starts with the

beginning of the project’s conceptual design and lasts to the time right before bidding, and

the post-bid phase can be generally considered as the construction phase. As the project

progresses and more information on scope become available, the level of contingency tends

to reduce. In this thesis, we have used singularity functions to model the contingency level

for a single project. This is the first time that singularity functions have been used in this

context. By combining these singularity functions, the total contingency for a portfolio of

projects can be obtained, and the escalation factor can then be applied. To demonstrate the

methodology, we used cost data from eight large transportation projects that are part of the

East Side Access Project in New York City. As part of the probabilistic analysis, confidence

levels for contingency during project life cycle have been calculated and plotted. It is

believed that this method can help the owner to better understand budget requirements and

22

thereby avoid cost overrun at various phases of project completion; it can also benefit the

project manager by providing timely information about budget shortfall so that proper

actions can be undertaken.

2.2 Background

The issues of cost overrun and schedule delay have long been concerns for professionals in

the construction industry. Previous researchers have examined and reported these issues

extensively (Flyvbjerg et al., 2004; Booz Allen, 2005; Bakhshi & Touran, 2009; Touran & Ye,

2011). Risks and uncertainties, such as unclearly defined project scope and escalation, can all

lead to cost overruns for a project. In order to cover these risks, uncertainties, and potential

cost overruns, a contingency budget is usually established. A contingency budget should be

accurately estimated and well planned, since an overestimated contingency will tie up the

owner’s funds unnecessarily, while an underestimated contingency will result in cost

overruns.

During the design phase, as more information on project scope becomes available, the

contingency budget is expected to be reduced. Part of the contingency will be shifted to the

base estimate. Another phase that will affect contingency is the bidding phase, especially in

fixed-price projects. After the project is awarded, part of the construction risks is transferred

to the contractor. As construction progresses, the contingency is drawn upon and

consumed. By the end of the construction phase, the contingency is expected to be zeroed

out. So, it is clear that the contingency budget is a variable and will change depending on

known and unknown risks. Planning contingency throughout the project life cycle will help

the owner to have better control over project budget and avoid potential cost overruns.

23

2.3 Methodology

2.3.1 Overview of the developed system

In this thesis, we introduce a spreadsheet-based risk assessment tool that can be used to

calculate the levels of contingency needed to cope with uncertainties in a portfolio of

projects. The emphasis here is to show the variability of contingency budget levels during

various phases of project life cycle, including the pre-bid and post-bid phases. A portfolio of

projects is defined as multiple projects under the direction of a single organization. As an

example, at any given time, the US Federal Transit Administration sponsors several transit

projects throughout the country. The general format of the spreadsheet is as shown in

Figure 2.3.1.1, as the pre-bid and post-bid phases have both been defined for each project in

the portfolio.

Figure 2.3.1.1 - Bar Chart for 8 Projects in Manhattan

Since it is considered that all the projects start at the same time as soon as the conceptual

design for the whole program finishes, all of the bars shown in Figure 2.3.1.1 begin at month

24

zero and end when the projects are completed. Users have the option to define the start

time for each project in the portfolio if the projects start at different times. The system also

provides users with the choice of defining the relationships and lags between projects, such

as Start-to-Start, Finish-to-Start with a lag of five days, and so on. For each project, the

contingency budget is established either deterministically or probabilistically. The singularity

function is selected to model project contingency levels throughout the project’s life cycle. It

will be applied to perform deterministic analysis first, in order to obtain the contingency

drawdown curve for the portfolio. After that, the probabilistic analysis is also utilized by

assigning a coefficient of variation to the data, which is assumed to be the mean of the

contingency, to get the percentile values of contingency levels at various phases of the

project life cycle.

2.3.2 Singularity functions

A singularity function is selected to model the contingency level for a single project during

its life cycle. A singularity function was proposed by German civil engineer August Otto

Föppl and British mathematician William Herrick Macaulay (Lucko, 2009), after whom the

function’s mathematical operator was named the Föppl symbol (Föppl, 1927) and Macaulay

brackets, respectively (Macaulay, 1919). As a tool for load analysis on beams, singularity

functions have been referenced in many structural engineering classes (Lahey, 2000;

Assakkaf, 2003; Lubline, 2007). However, this approach had never been applied in the field

of project management until Lucko used singularity functions in cash flow optimization and

scheduling applications (Lucko, 2008; Lucko & Orozco 2009; Lucko, 2011).

25

2.3.3 Contingency levels during project life cycle

The estimated contingency level will be part of the total project budget; an owner is

interested in knowing how much the project will cost and also how much funding to apply

for if those funds are coming from another source (e.g., a federal agency funding

transportation projects). The singularity function developed for this work consists of (1) the

pre-bid phase, (2) the bidding phase and (3) the post-bid phase. The pre-bid phase starts

with the project’s conceptual design and spans to the time right before bidding. During this

phase, the contingency adjusts as more information on the project’s scope becomes available.

The pre-bid phase is usually divided into sub-phases, such as conceptual design, preliminary

engineering, and final design. As more of the design is completed, the amount of

contingency tends to drop. Sometimes, as a result of scope changes, the project gets

expanded, causing the total contingency budget to increase as well. The singularity function

presented in this work will cover all of these scenarios. To simplify the process, a straight

line is used to model the contingency change during the pre-bid phase. It should be noted,

however, that until the end of the pre-bid phase, the owner does not know how accurate the

contingency estimate is.

After the bidding phase, when all of the bids are in, the owner can better assess whether the

contingency estimate is sufficient. At this point, based on the accepted low bid, the owner

can revise the contingency budget knowing that certain risks are not transferred to the

contractor. The model developed in this work is sufficiently flexible to handle cases of

overestimation and underestimation of pre-bid contingency. Also, since the bidding phase is

shorter than the pre-bid and post-bid phases, this change will be represented as a vertical

jump in the chart at that particular point.

26

The post-bid, or construction phase, starts right after the bidding. After the bid, part of the

contingency will become the contractor’s responsibility; however, the owner still needs to

maintain a contingency budget to cope with construction changes. Presumably, this

contingency should be smaller than the pre-bid contingency. As the construction progresses,

the contingency will be drawn upon. The proposed model assumes that by the end of

construction phase, the contingency will reach zero. A straight line is also used here to

model this change.

The singularity function, representing the contingency level y during the project life cycle,

can be calculated using the following equation:

1 2 1 20 1 1 0 13

1 2 3- 0 0I II III IV V

y y y y yy y x x x a y y x a x a

a a b a

(2.3.3.1)

Here, x represents time during the project’s life cycle, which can be days or months

depending on the size of the project. y1, y2 and y3 represent the contingency amounts at the

beginning of the project, the contingency amount right before the bidding, and the

contingency amount right after the bidding, respectively. y4 is the contingency amount at

project completion (Fig. 2.3.3.2), which equals zero and is not used in Eq. (2.3.3.1). a is the

pre-bid phase duration, and b is the total project duration, including both pre-bid and post-

bid phases. The upper indices 0 and 1 represent two basic singularity functions shapes used

in this work: unit step and unit ramp. These two basic functions are shown in Fig. (2.3.3.1)

(Lahey, 2000).

27

Figure 2.3.3.1 - Unit step (left) and unit ramp (right)

While the example in Figure (2.3.1.1) assumes a single starting point for all projects (note

that this is the point of project inception and the construction start time differs for each

project depending on availability of funds and length of design phase), the developed

spreadsheet can easily accommodate various starting points for each project in the portfolio.

The lower indices I to V represent the areas shown in Figures (2.3.3.2) and (2.3.3.3). Figure

(2.3.3.2) shows the case where contingency budget has been overestimated by the owner

during the pre-bid phase. The solid bold line, representing the contingency drawdown line,

can be modeled by the five basic terms in Eq. (2.3.3.1). According to Eq. (2.3.3.1), term 1

( 0

1 -0 Iy x ) represents that addition of a rectangle I, with a length of x and a width of y1;

then, triangle II is subtracted according to term 2, which is ( 1

1 2 / 0 IIy y a x ); term 3,

i.e., ( 1

1 2 / IIIy y a x a ), shows that triangle III is then added; finally, both rectangle IV

and triangle V are subtracted based on term 4, ( 0

2 3 IVy y x a ), and term 5,

( 1

3 / ( ) Vy b a x a ). In order to make these terms easier to remember, positive and

negative signs are added after the area codes (I to V) to show the relations.

28

Figure 2.3.3.2 - Contingency vs. Project Phase when pre-bid contingency is overestimated

The case where the contingency is underestimated by the owner during the pre-bid phase is

shown in Figure (2.3.3.3). In this case, the shape of the bold line is different from that in

Figure (2.3.3.2), as the line jumps up at the bidding phase.

It should be noted that the signs for the areas are not changed in this figure; however, the

sign for the term with (y2 – y3) in Eq. (2.3.3.1) will automatically change, as in this case y2 is

smaller than y3. In other words, Eq. (2.3.3.1) is valid for both Figures (2.3.3.2) and (2.3.3.3).

29

Figure 2.3.3.3 - Contingency vs. Project Phase when pre-bid contingency is underestimated

By using Eq. (2.3.3.1) and Figures (2.3.3.2) and (2.3.3.3), the contingency for each project

can be computed at various phases. It should be noted that the contingency will be

deterministic values if values for y, a, and b are fixed and known. The curve is supposed to

represent the mean values of the contingency due to the uncertainties involved in estimating

contingency.

2.3.4 Portfolio of projects

The singularity function described above can be used to calculate the contingency budget for

any single project. If there are several projects in a portfolio of projects, then the total

contingency can be obtained by summing up all singularity functions for projects in the

portfolio.

It should be noted that the projects in a portfolio or program may have different ending

times. After a project ends, the contingency for that project will remain zero until all

other projects are completed. For this study, a conceptual model is developed in Excel

30

spreadsheet that shows projects in a portfolio in a bar chart format (see Fig. 2.3.1.1).

For each project, contingency budget is estimated over its lifecycle and modeled using the

approach described above (similar to cases illustrated in Figs. 2.3.3.2 and 2.3.3.3). Then,

for each time unit, a summation of contingency budgets is calculated. This sum then

represents the total portfolio (or program) contingency budget. The use of a probabilistic

approach is recommended because there is uncertainty with respect to the calculation of

contingencies. In fact, the contingency budget represents all that is uncertain about a

project; thus, it makes sense to use a probabilistic approach to estimate contingencies. As

a result, Monte Carlo simulation is used to model contingency budgets for various

projects in a portfolio. The simulation approaches used in infrastructure project risk

assessments have been described in some detail by various authors (Parsons et al., 2004;

Molenaar 2005). Parsons et al. (2004) suggested using Monte Carlo (MC) simulation

methods for risk management, and pointed out that the MC simulation is “a probabilistic

simulation approach where distributions of random variables are sampled several times

using a computer,” and with the increase in the number of simulated samples, “the result

approaches theoretical distribution of the objective function (e.g., total project cost).”

Molenaar (2005) reported nine case studies using a cost estimating validation method

designed by Washington State Department of Transportation (WSDOT), and the range

of cost outputs provided by MC simulation made WSDOT’s estimation of project costs

to both management and the public very successful. Using @RiskTM or similar software

can help model the probabilistic aspects of costs and contingency levels at various points

of the portfolio life cycle.

31

2.3.5 Modeling the effect of escalation

After the total contingency level has been established, an escalation factor will be applied to

the total contingency in each year. In this work, Engineering News Record’s (ENR)

Building Cost Index (BCI) has been used to model escalation. The BCI has been widely

used to establish escalated project budget in construction (Touran & Lopez, 2006).

Historical data for BCI from the past 30 years were utilized to test three models:

independent series, Martingale series and correlated series. An extensive statistical analysis

showed that the independent series best predicted the movement of costs in the historical

data. Based on this outcome, contingency calculation was conducted using an independent

normal distribution with a mean of 3.1448% and standard deviation of 2.1734%. Each year,

an escalation factor is sampled from the normal distribution and then applied to the

contingency amount in that year using a MC simulation approach.

2.4 Results

2.4.1 Deterministic Analysis

The deterministic analysis method has been applied to eight construction projects that are

part of East Side Access (ESA) Project in New York City. The purpose of the ESA Project

is to “connect the Long Island Rail Road's (LIRR) Main and Port Washington lines in

Queens to a new LIRR terminal beneath Grand Central Terminal in Manhattan,” resulting in

shorter commuting time and increased capacity (MTA, 2012). While currently the trains

bound for New York City stop at Penn Station, the ESA project when completed will allow

32

a destination of these trains to be in Grand Central Station, hence providing easier access to

the east side of Manhattan. It should be noted that the ESA project is a much larger

program than the eight projects depicted here; however, these eight projects were selected as

a sample to demonstrate the implementation of the work described in this thesis. Based on

the estimates available as of March 2006, we only have y1, y3, a and b for Eq. (2.3.1.1). Cost

data for these eight projects was obtained from the revised project total cost spreadsheet for

ESA, where original estimate, pre-bid contingency, escalation, post-bid contingency, and

2006 estimated start and finish dates were all provided (Table 2.4.1.1). The pre-bid

contingency is assumed to be the amount of contingency at the beginning of the project (y1),

and post-bid contingency as the contingency right after bidding (y3). Also, a and b were

calculated based on the available estimates for project start and finish dates in 2006.

However, the contingency amount right before the bidding (y2) is still required to apply Eq.

(2.3.1.1). In order to get y2, which is the contingency amount before the bid opening, 31

Massachusetts DOT projects were used to calculate the mean and standard deviation for the

differences between y2 and y3 as a percentage of y3. These projects are all transportation

projects ranging from bridges to highway projects. Due to the lack of actual transit project

data, it was decided to look into relatively similar projects like transportation projects. Even

though they are not transit projects, they should still provide some general sense of the

percentage to be calculated. After applying statistical analysis to these 31 Massachusetts

DOT projects, an average of 17.8 was used to model the differences between y2 and y3 as a

percentage of y3, and as a result, the y2 values for these 8 projects in Manhattan were

obtained (Table 2.4.1.1).

33

The method was then applied to all data for the eight projects, and a total contingency

drawdown curve is shown in Figure (2.4.1.1).

Table 2.4.1.1 - Cost and Schedule Data for the Eight Projects

Project ID y1 (Mil. $) y2 (Mil. $) y3 (Mil. $) y4 ($) a (Months) b (Months)

1 32.590 25.372 21.529 0 32 73

2 36.543 28.235 23.959 0 22 68

3 60.724 28.874 24.501 0 67 103

4 4.749 3.042 2.581 0 39 61

5 2.407 1.541 1.308 0 39 61

6 11.821 7.545 6.402 0 39 61

7 27.824 16.638 14.119 0 72 114

8 12.922 5.131 4.354 0 68 107

34

Figure 2.4.1.1 - Contingency drawdown for 8 projects in Manhattan

Figure 2.4.1.1 presents the total contingency drawdown curve for these eight projects in

Manhattan. Even though the contingency drawdown curve for a single project is modeled as

three straight-line segments (Figs. 2.3.3.2 and 2.3.3.3), the total contingency drawdown curve

for the portfolio looks much smoother. The total contingency started at about $190M and

was consumed completely throughout the portfolio duration of almost 10 years. The curve

has a larger slope in the middle section as the projects were awarded to contractors and the

construction phases began. It should be noted that if all of the values in Table 2.4.1.1 are

readily available, then these total contingency levels will be fixed numbers and the trends of

the total contingency levels for the eight projects throughout the project life cycle can be

observed in Figure (2.4.1.1). However, due to the inevitable uncertainties in contingency

estimates, the curve in Figure (2.4.1.1) is actually considered as the mean value for the

contingency at various phases.

35

2.4.2 Probabilistic Analysis

In order to capture the uncertainties involved in contingency estimates and apply MC

simulation to this model, a sensitivity analysis is also performed by assuming uncertainty in

the estimated values of y1, y2 and y3. Assuming that these estimates in Table (2.4.1.1) are

means of y’s, and assuming 5%, 10% and 25% coefficient of variation for y1, y2 and y3,

respectively, we can use distributions instead of fixed numbers, for y1, y2 and y3 to obtain a

confidence level for the contingency throughout the project’s life cycle. By comparing

different confidence levels, we can calculate a margin for the contingency, and consequently

the owner can determine how much of the contingency has been consumed, and whether

the contingency budget is sufficient to complete the rest of the project. Figure (2.4.2.1)

shows the total contingency with 75% and 85% confidence level if the y values have a 25%

coefficient of variation and are modeled as normal distributions. The margin between these

two lines will represent the extra contingency amounts needed for increasing confidence by

10% for the portfolio of projects from 75% to 85%. It is found that with more variability

for y1, y2 and y3, this margin becomes larger.

36

Figure 2.4.2.1 - Contingency drawdown for eight projects with 25% coefficient of variation to the mean of contingencies

2.5 Schedule Contingency

Schedule contingency analysis has also been performed. The main idea is to establish a

contingency level for project duration to cover potential schedule delays. Gurgun et al. (2013)

examined schedule contingency to a certain extent, and developed a model to calculate

schedule contingency mean values at three phases of the project’s life cycle: Preliminary

Engineering / Final Environmental Impact Statement (PE/FEIS) phase, Final Design (FD)

phase, and Construction phase. Utilizing the Joint Confidence Level Probabilistic Calculator

(JCL-PC) method, the schedule contingency confidence levels can be obtained.

2.5.1 Singularity Function for Project Schedule Contingency

Inspired by the research experience with Gurgun (2014), and the applications of singularity

functions in cost contingency estimates, it was decided that singularity functions can also be

implemented in schedule contingency analysis; however, the shape of the contingency

drawdown curve will differ from those in Figures 2.3.3.2 and 2.3.3.3. A suggested by Gurgun

et al. (2013), three straight lines have been selected to model the schedule contingency means

based on 28 transit projects, and a singularity function has been created to model the shape

of the curve.

37

Figure 2.5.1.1 - Schedule Contingency vs. Project Phases

d

s2

s3

s4

Contingency

Duration

s1

c b

I +

II -

IV -

III +

V+

VI -

38

Figure 2.5.1.1 shows the contingency drawdown curve for schedule contingency analysis

with the x-axis representing the duration, and the y-axis representing the contingency levels.

Based on Figure 2.5.1.1, the singularity function can be created (Eq. 2.5.1.1); c, d and b

represent the end of project PE phase, FD phase, and Construction phase, respectively.

According to Gurgun et al. (2013), c and d were defined as 5% and 15% of project total

duration (b), respectively.

1 2 1 2 2 3 2 30 1 1 1 1 13

1 -0 0( ) ( )

I II III IV V VI

s s s s s s s s ss s x x x c x c x d x d

c c d c d c b d

Equation (2.5.1.1)

Similar to the cost singularity functions, the lower indices I to VI represent the areas shown

in Figure (2.5.1.1). The solid bold line, representing the contingency drawdown line for

project schedule, can be modeled by the six basic terms in Eq. (2.5.1.1). Term 1

( 0

1 -0 Is x ) represents the addition of a rectangle I, with a length of x and width of s1;

then, triangle II is subtracted according to term 2, which is ( 1 2 10 II

s sx

c

); term 3,

i.e., ( 1 2 1

III

s sx c

c

), shows that triangle III is then added; term 4,

( 2 3 1

( )IV

s sx c

d c

), shows that triangle IV is then subtracted; with rectangle V being

added and triangle VI being subtracted based on term 5, ( 2 3 1

( )V

s sx d

d c

), and term 6,

(

13VI

sx d

b d

), the shape of the contingency drawdown curve can be obtained.

Positive and negative signs are added after the area codes, making them easier to remember.

39

2.5.2 Portfolio Schedule Contingency

The difference in portfolio contingency analysis between project cost and schedule is that,

for cost, the total portfolio cost contingency will simply be the summation of all projects’

cost contingency in that portfolio; the total portfolio schedule contingency, however, will be

the summation of the schedule contingency for projects falling on the critical path. While the

MC simulation creates more than one possible critical path, a system is developed in this

study for users to identify possible critical paths and calculate total portfolio schedule

contingency levels.

The calculation of portfolio schedule contingency has been integrated into Chapter 5, and

the system will be introduced in Chapter 6. Due to the similarity of this analysis to the cost

contingency analysis, it is not repeated here.

2.6 Summary

A probabilistic approach is presented for modeling contingency and its variabilities during

the lifecycle of a portfolio of projects. The approach is based upon current risk assessment

methodologies that model uncertain cost items as random variables and use MC simulation

to calculate the distribution of cost or contingencies. For project cost, a singularity function

model is presented for contingency planning during the project design and construction

phases to establish project budget for large transportation projects. The main phases, which

includes pre-bid, bidding and post-bid phases, have been provided with contingency budgets

by using this method. Singularity functions are used to model the contingency level for a

single project, and the total contingency level will be the sum of these singularity functions.

40

A 75% and 85% confidence interval is also presented for contingency with a 25% coefficient

of variation, which can be used to check against actual contingency level to see if potential

cost overruns might be encountered. For project schedule, a singularity function model is

also proposed to establish project schedule contingency levels at three main phases:

PE/FEIS, FD and Construction. It is believed that this method can help the owner to better

understand budget requirements and thereby avoid cost overrun, and reserve the amount of

time needed to cover potential schedule delays at various phases of project completion; it

can also benefit the project manager by providing timely information regarding budget

shortfall and schedule issues so that proper action can be undertaken.

41

CHAPTER 3 : THE APPLICATION OF PROMETHEE-GAIA METHODOLOGY IN PORTFOLIO PROJECT

MANAGEMENT FOR TRANSIT PROJECTS

3.1 Introduction

In this chapter, the Preference Ranking Organization Method for Enrichment Evaluations

(PROMETHEE) and its descriptive complement, Geometrical Analysis for Interactive Aid

(GAIA), are proposed as a way to rank projects in a portfolio of transit projects. A ranking

system consisting of eight criteria considered to have significant impact on the preference of

projects was developed. The eight criteria are (1) Project Cost, (2) Project Duration, (3)

Project Cost Overrun, (4) Project Schedule Delay, (5) Project Criticality Index, (6) Percent

Complete, (7) Project Start Time, and (8) Stakeholders. One of the advantages of this system

over the Analytic Hierarchy Process (AHP) is that these criteria include both objective and

subjective factors. Also, since the ranking can change from time to time, the ranking analysis

should be performed throughout the portfolio’s life cycle. In order to make this system

ready for probabilistic analysis and easily accessible to users, it was integrated into Excel. Six

projects selected from a much larger program (i.e., the East Side Access Project) were used

to show the application of the ranking system. The ranking updating procedure was also

demonstrated. It is believed that this method can help project managers to make timely

decisions and give preference to projects that require greater attention, possibly resulting in

cost and time savings for the portfolio.

42

3.2 Background

The PROMETHEE and its descriptive complement GAIA are decision-making tools that

have been applied in many fields such as business and education (Behzadiana et al., 2010;

Mareschal & De Smet, 2009; Hayez, 2009; Lv et al., 2011). This methodology was first

introduced in the early 1980s, and the methodology has been improved and refined by

researchers ever since (Mareschal, 2012). This methodology provides a rigorous analysis for

alternatives instead of providing a “final decision”, which helps the decision-makers to

achieve a better understanding and thus make better choices. As a member of the

outranking methods family, PROMETHHE and GAIA follow the principle of pairwise

comparisons of alternatives (D-Sight, 2012).

Developed by Jean-Pierre Brans in 1982, the PROMETHEE method was further expanded

through the contributions of Professor Bertrand Mareschal (2012). According to Mareschal

(2012), PROMETHEE is a prescriptive approach that provides complete and partial ranking

analysis, whereas GAIA is a descriptive approach, offering visualized information on criteria

and alternatives. It works best when a team consists of members with various specialties

working together on a complex problem that involves multiple criteria and requires human

interaction (e.g., judgment). The advantages of PROMETHEE and GAIA over AHP are

many. According to Tavakolijou (2009), AHP, based on the principle of pair-wise

comparison, requires users to evaluate alternatives for every criterion on a scale from 1 to 9.

It requires users to perform numerous comparisons and to be consistent with the

comparisons. Compared to AHP, PROMETHEE is mainly computed as an evaluation table

containing both quantitative criteria and qualitative criteria. Instead of performing so many

comparisons, users directly input the data into the evaluation table. Moreover, the

43

descriptive analysis provided by GAIA is very powerful, as a complement to PROMETHEE

rankings, which helps decision-makers to better assess the alternatives (Mareschal, 2009).

According to Brans and Mareschal (2005), J.P. Brans first introduced PROMETHEE I

(partial ranking) and II (complete ranking) in 1982, and the methodology was applied in

healthcare that same year. PROMETHEE III (ranking based on intervals) and IV

(continuous case) were developed by Brans and Mareschal later, and the visual interactive

module GAIA was proposed in 1988. Two more extensions: PROMETHEE V (MCDA,

including segmentation constraints) and VI (representation of human brain) were introduced

in 1992 and 1994, respectively.

Possible situations suitable for this methodology include: finding the best alternative from

the options based on multiple criteria; selecting alternatives that need to be prioritized;

ranking alternatives based on preference; planning resources and allocation.

3.3 Mathematics

3.3.1 Preference Degree

In order to rank the alternatives in a set, we calculate the preference degree, based on

selected criteria, to establish the levels of preference for the alternatives.

Assuming a set of n alternatives 1, , nA a a and a set of q criteria 1, , qF f f to be

optimized, the alternatives and criteria matrix is presented in Table 3.3.1.1.

44

Table 3.3.1.1- Alternatives and Criteria

1( )f 2 ( )f 3( )f ( )jf ( )qf

1a 1 1( )f a 2 1( )f a 3 3( )f a 1( )jf a

1( )qf a

2a 1 2( )f a 2 2( )f a 3 2( )f a 2( )jf a

2( )qf a

3a 1 3( )f a 2 3( )f a 3 3( )f a 3( )jf a

3( )qf a

ia 1( )if a 2 ( )if a 3( )if a ( )j if a ( )q if a

na 1( )nf a 2 ( )nf a 3( )nf a ( )j nf a ( )q nf a

For pairwise comparisons between the alternatives for a certain criterion k, the difference

can be calculated using Equation (3.3.1).

( , ) ( ) ( )k i j k i k jd a a f a f a (3.3.1)

The difference can be translated into a Preference Degree ( ) by applying selected

preference function P :

( , ) [ ( , )]k i j k k i ja a P d a a (3.3.2)

where : [0,1]kP is the preference function with non-decreasing positive values.

3.3.2 Preference Functions

Preference functions are used to compute the degree of preference for each of the

alternatives. After the inputs are introduced to the ranking system, the preference functions

will be applied to the inputs to obtain the preference degrees, which in turn will be used to

establish the ranking of the alternatives. Six different types of preference functions are

introduced by the original PROMETHEE methods (Fig. 3.3.2.1).

45

Figure 3.3.2.1 - Preference Functions (Brans & Mareschal, 2005)

It is believed that the V-shaped and linear preference functions are good choices for

quantitative criteria such as prices and costs (Mareschal, 2012). As a special case for linear,

the V-shaped function differs from the linear in that it lacks an indifference threshold q (Fig.

3.3.2.1).

The Usual and Level preference functions are favored for qualitative criteria where the

criteria can be evaluated on a basis of a scale, such as yes/no or 5-point scale (Mareschal,

2012). If there are large differences between the scales, then the Usual function works better;

however, when the difference is not that significant, then the Level function is more suitable

(Mareschal, 2012). The U-shaped preference function, a special case of the Level function, is

less commonly used.

46

The Gaussian preference function is also selected less often since the parameters are more

difficult to estimate. The threshold value s falls between the q indifference threshold and

the p preference threshold. According to Jean-Pierre Brans, the indifference threshold q

represents the largest deviation that the decision-maker thinks to be negligible, while the

preference threshold p is the smallest deviation adequate to produce a preference. s is an

intermediate value falling in between q and p (Fig. 3.3.2.1).

Taking the linear preference function as an example (Fig. 3.3.2.2), it is defined as:

0,

( ) ,

1,

k

kk k k

k k

k

if x q

x qP x if q x p

p q

if x p

(3.3.2.1)

Figure 3.3.2.2 - The Linear Preference Function (Ishizaka & Nemery, 2011)

For criterion kf , when difference values are smaller than the indifference threshold kq , then

the difference between two alternatives is considered to be negligible. When the differences

exceed the preference threshold kp , the differences will be considered as significant. For

47

values between the two threshold values, the preference function can be applied to obtain an

intermediate value.

Other preference functions are as follows:

Usual: 0, 0

( )1, 0

k

if xP x

if x

(3.3.2.2)

U-Shaped: 0, | |

( )1, | |

k

k

k

if x qP x

if x q

(3.3.2.3)

V-Shaped:

| |, | |

( )

1, | |

k

kk

k

xif x p

pP x

if x p

(3.3.2.4)

Level:

0, | |

1( ) , | |

2

1, | |

k

k k k

k

if x q

P x if q x p

if x p

(3.3.2.5)

Gaussian:

2

22( ) 1 k

xs

kP x e

(3.3.26)

3.3.3 Multicriteria Preference Degree

Equation 3.3.2.1 can be used when the decision-maker is dealing with a simple criterion;

however, in reality, decision-makers are faced with multicriteria problems. By assigning

weight to each criterion if , we can obtain the multicriteria preference degree using Equation

(3.3.3.1):

1

( , ) ( , )q

i j k i j k

k

a a P a a w

(3.3.3.1)

48

where kw is the weight for criterion kf ; 0kw and 1

1q

k

k

w

. As a result, we have:

( , ) 0i ja a (3.3.3.2)

( , ) ( , ) 1i j j ia a a a (3.3.3.3)

Usually, the analysts start with equal weights if a limited amount of information is available.

After that, sensitivity analysis could be performed and the weights can be changed to see the

difference in results; however, with input from experts, this process can be shortened.

3.3.4 Multicriteria Preference Flows

The ranking method is usually applied to a set of alternatives. When comparing one

alternative ia with other alternatives, the positive preference flow ( )ia (outflow), which

indicates the global preference for ia over all other alternatives, and the negative preference

flow ( )ia (inflow), which shows how other alternatives are preferred to ia , can be

computed using Eqs. (3.3.4.1) and (3.3.4.2).

1( ) ( , )

1i i

x A

a a xn

(3.3.4.1)

1( ) ( , )

1i i

x A

a x an

(3.3.4.2)

In order for alternative ia to achieve the highest preference, the ideal flow values should be

( )ia equaling to 1 and ( )ia

equaling to 0.

49

3.3.4.1 PROMETHEE I – Partial Ranking

Two sets of ranking could be obtained by applying Eqs. (3.3.4.1) and (3.3.4.2); while the

former ranks the positive preference flows from largest to smallest, the latter ranks the

negative preference flows according to increasing orders of value. As a result, only if

( ) ( )i ja a and ( ) ( )i ja a can we say that ia is globally preferred to ja or

equally important; however, if ( ) ( )i ja a but ( ) ( )i ja a , then ia and ja will be

considered to be incomparable.

3.3.4.2 PROMETHEE II – Complete Ranking

The net preference flow ( )ia for alternative ia can be computed using Eq. (3.3.4.2.1):

( ) ( ) ( )i i ia a a (3.3.4.2.1)

where ( ) [ 1;1]ia and ( ) 0i

i

a A

a

.

By ranking the net preference flow in descending order, the complete ranking for all the

alternatives can be obtained. It should be noted that when using complete ranking, the

scenario where two alternatives could be incomparable is eliminated. Since the partial

ranking will use two sets of values – namely, the positive preference flow and negative

preference flow – to decide the ranks, it might result in conflicting results and thus

incomparable cases. When applying the complete ranking method, however, only one set of

values – namely, the net preference flow – will be utilized for ranking the alternatives. As a

result, only one ranking order will be produced, and the incomparability is no longer an issue,

in exchange for the loss of some information.

50

It is recommended to use both methodologies for ranking the alternatives. Though

PROMETHEE II provides a ranking without any issue of incomparability, some

information regarding the preference for an individual project relative to the rest of the

projects in the portfolio might be lost in the process of finding the difference between the

positive preference flow and the negative preference flow. PROMETHEE I will provide

more detailed information for ranking, even though incomparable cases will arise.

3.4 Example

Over the past 30 years, PROMETHEE and GAIA methods have been implemented in

various software programs. One of the first software programs based on outranking

methods was the MS-DOS program PROMCALC, developed in Université Libre de

Bruxelles at the end of 1980s. Decision Lab, developed by a joint venture of the Université

Libre de Bruxelles and the Canadian company Visual Decision was introduced at the end of

1990s. For this research, the more recent Visual PROMETHEE software program was

selected (Mareschal, 2013). Developed by Bertrand Mareschal (2012), Université Libre de

Bruxelles, this is an easily accessible software program free of charge for academic users,

with a user-friendly interface.

3.4.1 Example of Purchasing a Car

As an example, the Visual PROMETHEE software explains how to use the PROMETHEE

and GAIA methodology to facilitate decision-making. When someone considers buying a car

from a dealer, he has five concerns regarding the car: price, power, consumption, habitability

51

(i.e., car passenger and spatial capacity), and comfort. In regard to price, the lower it is, the

more preferable the car will be. The preference function is selected to be V-shaped and the

preference threshold is set to $15,000. In regard to power, it is preferable to have a higher-

powered car. For power, the preference function is linear with an indifference threshold of

5kW and a preference threshold of 30kW. Consumption is preferred to be lower, and a V-

shaped function is chosen with a preference threshold of 2L/100km. Habitability has a 5-

point scale: very bad, bad, average, good and very good. The buyer prefers to have a car with

better habitability. The preference function is Level with an indifference threshold set to 1

and a preference threshold set to 2.5. The weights are all set to 1, considering all the criteria

to be equally important (Fig. 3.4.1.1). Sinha et al. (2009) examined past studies on

establishing relative weights for performance criteria of transportation projects, and

indicated the common approaches usually included a questionnaire survey. Methods such as

direct weighting method, asking the survey respondents to directly assign numerical weight

values on a scale to the criteria, and observer-derived weights method, estimating relative

weights using regression analysis were discussed. Sinha et al. (2009) also concluded that:

“weighting methods that ask decision makers to choose weights directly do not guarantee

that the weights are theoretically valid; on the other hand, methods that derive weights by

ensuring that the decision rule is consistent with tradeoffs expressed by decision makers are

more likely to yield valid weights but generally are more difficult to apply”. Since it would be

very challenge to perform the weight questionnaire survey as a student and the weighting

methods alone require a deep investigation, it was decided to assume equal weights for all

selected criteria in this research. However, if suggestions from sources such as project

personnel can be obtained, one can take the average of their inputs to calculate the weighting

sets for selected criteria.

52

It should also be noted that for subjective criteria such as habitability and comfort, the rating

is usually based on either experience or experts’ opinions. A selected function, usually Level,

is then applied to these ratings to obtain degrees of preference. The system supports both

objective and subjective criteria, which is one of its advantages compared to AHP.

Figure 3.4.1.1 - Example of Criteria and Preference Functions

Then, the dealer offers 6 options for the buyer, including car types of economy, tourism,

luxury, and sports. All of these 6 cars have been evaluated according to the five criteria listed

in Figure (3.4.1.1), and the data is shown in Figure (3.4.1.2).

53

Figure 3.4.1.2 - Car Evaluation Data and Statistics

3.4.2 Results

By using Visual PROMETHEE software, we can obtain the values of positive preference

flow and negative preference flow for PROMETHEE I – Partial ranking (Table 3.4.2.1).

Table 3.4.2.1 - PROMOTHEE I – Partial Ranking

Car

1 Tourism B 0.3573 0.1000

2 Luxury 1 0.2760 0.2213

3 Tourism A 0.2060 0.1927

4 Luxury 2 0.2560 0.2573

5 Economic 0.2647 0.4220

6 Sport 0.2280 0.3947

Based on positive preference flow f +, the ranking would be 1-2-5-4-6-3, which indicates

that Tourism B is the best choice and Luxury 1 and Economic are better options than the

rest; however, according to negative preference flow

, the ranking would be 1-3-2-4-6-5.

54

This suggests that Tourism B is still the best option, while Tourism A, Luxury 1 and Luxury

2 are better than Economic and Sport. These results are presented in Figure (3.3.2.1). Results

for f +are on the left side while results for ϕ

- are on the right. The options are based on the

portion’s positive preference flow and negative flow. It should be noted that the axis for ϕ+

and ϕ- follows different directions. For positive preference flow, the larger the value is, the

more optimized it is; while for negative preference flow, the smaller the better. The reason

lies in the definition of the flows, as the positive preference flow represents the global

preference of the selected alternative over other alternatives, whereas the negative preference

flow shows how all other alternatives are preferred to the selected alternative. The option’s

position in Figure (3.4.2.1) shows the preference order of the options based on its positive

flow and negative flow separately. For example, Tourism B is the most preferred based on

both ϕ+ and ϕ-, while Tourism A ranked at the bottom based on ϕ+ but second according to

ϕ-.

55

Figure 3.4.2.1 - PROMOTHEE I – Partial Ranking

However, it is noticeable that some options are incomparable if considering both positive

preference flow

and negative preference flow

. For example, Luxury 1 has a

of

0.2760, higher than Tourism A’s 0.2060, while its

0.2213 is also larger than Tourism A’s

0.1927. As a result, it is hard to decide which one is better by using Partial Ranking.

56

PROMETHEE II – Complete ranking can be used to solve this issue. As shown in Table

(3.4.2.2), by taking the difference between the positive preference flow

and negative

preference flow

, we can obtain a new ranking – the complete ranking.

Table 3.4.2.2 - PROMOTHEE II – Complete Ranking

Car Phi

1 Tourism B 0.2573

2 Luxury 1 0.0547

3 Tourism A 0.0133

4 Luxury 2 -0.0013

5 Economic -0.1573

6 Sport -0.1667

According to Table (3.4.2.2), the ranking would be 1-2-3-4-5-6 as Tourism B is still on top

and Economic and Sport at the bottom. Figure (3.4.2.2) also presents the ranking results.

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Figure 3.4.2.2 - PROMOTHEE I – Complete Ranking

The GAIA method is capable of visualizing multicriteria decision aid (MCDA) problems.

After the data has been analyzed by the PROMETHEE methods, the GAIA plane can be

obtained through Principal Component Analysis (PCA). The GAIA plane helps decision-

makers to understand the problem structure and explain the selected option. With 5 criteria,

the decision-making problem can be represented in a 5-dimensional space. By projecting all

of this information onto one plane, the GAIA plane is obtained with the loss of only some

information.

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Figure 3.4.2.3 - GAIA Plane

As indicated in Figure (3.4.2.3), the alternatives are shown as points and the criteria are

presented as axes. If some points are oriented in the same direction as certain criteria, then

these alternatives are more preferred for that criterion than those that are oriented otherwise.

For example, when considering the criterion of Price, Economic is most preferred and

Luxury 1 and 2 are the least favorite. However, for the criteria of Habitability and Comfort,

Luxury 1 and 2 are better options than the others. The red axis is the PROMETHEE

decision axis , which can be used to indicate the compromise results for all the criteria

based on assigned weights. It should be noted that when the weights are modified, the

59

positions for criteria axis and the alternative points remain the same, but the PROMETHEE

decision axis changes accordingly. In order to rank the alternatives, the users need to first

project all alternatives onto the decision axis . Based on the projection length along the

decision axis , the ranking for all alternatives can be obtained. Right now, when equal

weights are assigned to these criteria, Luxury 1 and 2 as well as Tourism B and A are among

the preference list. This software also provides a sensitivity analysis tool that allows users to

change weights and see results. Again, in order to obtain this plane, some information is

believed to be inevitably lost; however, according to the results provided by the software, for

this particular plane, as much as 90% of the information is still captured.

3.5 Application to Portfolio Project Management

In the context of PPM for transit projects, the PROMETHEE and GAIA methodology can

also be applied. When managing more than one transit project, it is necessary to know which

project should be prioritized since some projects have higher budget, longer duration and

the involvement of more stakeholders. Also, projects that lie along the critical path can play

a vital role in preventing schedule delays, and projects starting in the relatively distant future

involve uncertainties like escalation and inflation. Moreover, after projects start, the

prioritization might need to be modified as some projects could encounter cost overruns and

schedule delays, and some might not have achieved their earned value goals. Using

PROMETHEE and GAIA methodology helps decision-makers to evaluate all of the

projects by considering all relevant factors and prioritizing them in a consistent and

defensible way.

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3.5.1 Criteria and Preference Functions

After some consideration, we selected the following 8 criteria for prioritizing the transit

projects:

1. Project Cost

Rowland (1981) and Hinze et al. (1992) suggested the contract size, complexity, and

the number of change orders may possibly cause an increase in cost overrun. Jahren

and Ashe (1990) also indicated that the median cost overrun rate rises as the project

size increases, and Rowland (1981) proposed that the change-order rate will increase

as project size increases. Accordingly, project size or project cost has been selected as

a criterion in this study, based on project dollar value; however, another option for

this criterion is to divide projects into three categories of size – large, medium and

small – where large includes projects with budgets of $200M and over, medium

includes projects $26–199M; and small includes projects with budgets of less than

$25M (American Association of State Highway and Transportation Officials, 2012).

As for the preference function, linear is selected with a q indifference threshold of

$25M and a p preference threshold of $200M. If a project has a larger budget, the

project is considered to be more significant than the others as a slight cost overrun

might be a huge amount.

2. Project Duration

Project duration is closely tied to escalation cost. Touran and Lopez (2006) suggested

that one of the main contributors to cost variation is “the uncertainty in the value of

escalation factor, especially in multi-year projects”. Pakkala (2002) states that most

transportation projects in the United States use the design-bid-build (DBB) delivery

method, a linear process that does not optimize innovation and causes disputes

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between parties. It is also indicated that delaying project completion and

encountering cost overruns are among the main criticisms of this delivery method.

Shane et al. (2009) also acknowledged the issue of escalation, pointing out that two

factors – the inflation rate and the timing of the expenditure – must be understood

so that funding will be sufficient for all projects. As a result, project duration is also

selected as a criterion for prioritizing transit projects.

Project duration will be expressed in years. The longer the duration, the more

priority should be given to the projects since risks such as escalation can have a more

significant impact on such projects. A linear preference function is also selected. The

indifference threshold q is 0.50 years, and the preference threshold p is set to 5

years.

3. Project Cost Overrun

Flyvbjerg et al. (2002) indicated that the average cost escalation for rail projects is

44.7% worldwide and 40.8% for North America, which is worse than the escalation

for road and bridge projects. In an examination of six major high-speed rail projects

in the European Union, Chevroulet et al. (2012) found an average project overrun of

15–20%. Jahren and Ashe (1990) and Love et al. (2013) examined cost overrun

issues and identified possible reasons for project cost overruns. Thus, it is believed

this criterion should not be overlooked.

Cost overrun will be calculated by comparing the most recent updated estimate with

the original estimate. The G7 report (Booz Allen et al., 2005) indicates a mean of

35.27% and standard deviation of 39.26% cost overrun for 28 transit projects. The

modeling of the cost overrun distribution has been based on these projects. The

value of the mean plus that of 3 standard deviations is used for the linear function’s

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preference threshold value, and the indifference threshold value has been selected as

0 ( q =0, p = 153.05%). If the difference between the cost overruns of two projects

exceeds 153.05%, then the preference degree will be 1.

4. Project Schedule Delay

Touran and Lopez (2006) identified “delays for each individual project that may have

an impact on total program finish time” as one of the two main contributors to

project cost variation. Flyvbjerg et al. (2003) indicated that the underestimation of

the length and cost of delays is one of the main causes of megaproject overruns.

Shane et al. (2009) also suggested that “project schedule changes, particularly

extensions can cause unanticipated increases in inflation cost effects.”

Schedule delay will be calculated by comparing the most recent updated estimate

with the original estimate. The G7 report indicates a mean of 12.57% and standard

deviation of 16.09% schedule delays for 28 transit projects. The value of the mean

plus that of 3 standard deviations is used for preference threshold value, and 0 has

been selected as the indifferent threshold ( q =0, p =60.84%). As a result, the linear

preference function is chosen and a preference degree of 1 is obtained if the

difference between schedule delays of two projects exceeds 60.84%.

5. Project Criticality Index

The Critical Path Method (CPM), which is a mathematical algorithm for scheduling a

set of project activities, has been widely used in the project management field for

scheduling analysis. Hegazy and Menes (2010) stated that CPM plays an important

role in analyzing final as-built schedules. Chua and Shen (2005) examined CPM with

resource and information (RI) availability constraints to analyze the causes of project

delays and pointed out CPM as a common practice of constraints management. It is

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important for contractors to know that the critical path may change, as Galloway

(2006) states, and to understand exactly which activities have been delayed. The

criticality index is selected to demonstrate the effect of the critical path on projects’

completion.

The criticality index measures the likelihood of a project being on the critical path of

the program or portfolio. The project criticality index is measured on a 5-point scale:

Very High, High, Medium, Low, and Very Low. This scale has been assigned values

from 5 to 1 for the sake of mathematical computation. Software such as @Risk

could be used to help define the criticality. The preference function will be Level,

and the thresholds values are q =1 and p =5, respectively.

6. Percent Complete

McConnell (1985) indicated that “the earned value technique is a proven method to

evaluate work progress in order to identify potential schedule slippage and areas of

budget overruns.” Kim and Reinschmidt (2011) proposed a model to incorporate

project cost forecasts into Earned Value Management (EVM). Project Management

Institute (PMI) (2008) also pointed out that EVM has become the most frequently

used project performance measurement method. As a result, percent complete is

selected as a criterion here.

Percent completion should ideally be assessed using an Earned Value approach. The

values will be calculated by comparing planned percent complete and actual percent

complete. The linear preference function is selected, the indifference threshold q is

set to 0, and the preference threshold p is set to 1.

7. Project Start Time

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It is understood that projects in a portfolio may start at different times, and the start

time of a project clearly affects the ranking results. When a project starts later in the

portfolio, more uncertainties are expected, in regard to aspects such as escalation and

cost estimates.

As cost escalation plays an important role in the successful completion of projects,

project start time is selected here as a criterion. A linear preference function with an

indifference threshold q of 1 year and preference threshold p of 5 years is chosen.

8. Stakeholders

Doloi (2013) performed an in-depth analysis of poor cost performance in project

and construction management, and the roles and responsibilities of three key

stakeholders: clients, consultants, and contractors. Jergeas and Ruwanpura (2010)

found that, for megaprojects of long duration, it is common for customers and other

stakeholders to require change over a project’s life cycle, and “the deviations from

the plan are simply costly.” Chevroulet et al. (2012) pointed out “successful

stakeholder consultations and public inquiries not only diminish impediments to

construction, but may also mobilize untapped potentials.” According to Simpson et

al. (2001), public involvement is a critical successful factor for urban pipeline design

and construction. It has also been suggested that the main objectives of a public

involvement program vary from phase to phase. These objectives include the

following: communicating with the public and “assessing liquidated damages for a

variety of public inconveniences identified as important by the public during project

planning” in the design phase; and “communicating construction activities well in

advance of construction, monitoring and addressing complaints, and keeping the

65

public apprised of all construction activities, such as upcoming road closures, detours,

water outages for tie-ins, and completion milestones.”

Since it is believed that stakeholders play an important role in transit projects, their

effect is included in the list of criteria. A Level preference function with a 5-point

scale is selected here, the indifference threshold q is set to 1, and the preference

threshold p is set to 5. It should be noted, in order to make this rating more

understandable, that the 5-point scale is comprised of the following terms: very low,

low, average, high, very high, which carry values from 1 to 5 for mathematical

computation.

3.5.2 Using Software to Establish Ranking Based on Original Estimate

Six projects from the East Side Access Project in New York City have been selected to

demonstrate the application of this methodology. For the original estimate, criteria Project

Cost Overrun, Project Schedule Delay and Percent Complete are not applicable and only 5

criteria are selected in this analysis (Fig. 3.5.2.1). The cost and schedule information can be

obtained from the original estimates, and the stakeholders are set to average as that

information is unavailable. After obtaining the inputs (Table 3.5.2.1) for the ranking system

and entering all of the costs into Visual PROMETHEE software, we computed the results in

Table (3.5.2.2).

66

Table 3.5.2.1 – Ranking Inputs Based on Original Estimates

Projects Cost

(Million US$) Duration (Years)

Criticality (5 Scale)

Start Time (Years)

Stakeholders (5 Scale)

CM019 449.4 8 High 0.58 Average

CM009 756 9.67 Very low 2.33 Average

CM004 40.9 7.92 Very low 3.25 Average

CM008A 42.8 9.08 Very low 3.75 Average

FM216 14.5 7.67 Very low 2.75 Average

CS719 12.8 7.25 Very low 2.83 Average

Figure 3.5.2.1 - Evaluations of Projects Based on Original Estimates

67

Table 3.5.2.2 - Complete Ranking and Partial Ranking Computation Results

Projects

1 CM019 0.2360 0.2602 0.0242

2 CM009 0.1366 0.2622 0.1257

3 CM004 -0.0421 0.0587 0.1008

4 CM008A -0.0977 0.0192 0.117

5 FM216 -0.1108 0.0117 0.1225

6 CS719 -0.1220 0.0125 0.1345

As indicated in Table (3.5.2.2), the PROMETHEE II Complete Ranking suggests CM019 to

be the most preferred project with the highest value of 0.2360, which in this case means

that it should be prioritized. However, when using PROMETHEE I Partial ranking, CM019

and CM009 are incomparable. If based solely on

, CM019 should be prioritized but not

when considering only

. The incomparability here means that CM019 is preferred to

CM009 according to some criteria, while CM009 is considered to be more important based

on other criteria. Figures (3.5.2.2) and (3.5.2.3) also present the rankings.

68

Figure 3.5.2.2 - PROMETHEE I – Partial Ranking

Figure 3.5.2.3 - PROMETHEE II – Complete Ranking

69

Figure (3.5.2.4) is called the ‘PROMETHEE Rainbow’, and demonstrates which criteria are

considered preferable for each project. It is considered to be another view of the

PROMETHEE II net preference flow, with the order from left to right representing the

PROMETHEE II Complete Ranking. For each alternative, a bar shows up on the rainbow

figure, and each slice of the bar represents the contribution of one criterion to the

computation of alternative net preference flow. By multiplying the net flow for criteria with

the weight of the criteria, the height of the slice can be computed. Summing up all of the

slices computed could lead to the multicriteria net flow. On the top of the rainbow figure,

the important criteria for each alternative are listed, while the bottom slices show criteria

where the alternative did not score well. Taking project CM009, for example, it is considered

preferable in the criteria of cost, criticality, cost overrun, schedule delay, percent complete

and stakeholders, and not preferable in the criteria of duration and start time since it does

not have the longest duration but has the shortest start time. The height of each slice

indicates the degree of preference.

70

Figure 3.5.2.4 - PROMETHEE Rainbow

The PROMETHEE GAIA plane can also be obtained (Fig. 3.5.2.5). For each criterion,

projections of all of the projects on that criterion axis can be obtained. By comparing the

length of the projections along the direction of the criterion axis, we can obtain the ranking

of the projects based on the selected criterion. For example, for cost, CM009 and CM019

ranked at the top. For duration, however, CM019 was the most preferred project. In terms

of criticality, CM009 was the first choice among the projects, and in terms of start time,

CM004 ranked first whereas CM009 ranked the last. Also, as indicated by the

PROMETHEE decision axis , when the weights are set to be equal for all criteria, CM019

becomes the top priority and then CM009. According to the results reported by the software,

this plane captures about 98% of the information.

71

Figure 3.5.2.5 - PROMETHEE & GAIA

Weight sensitivity analysis can also be applied, and the Weight Stability Interval (WSI) can be

computed. The WSI provides the weight range for a criterion, within which the changes of

the weight will not affect the ranking. For example, Figure (3.4.2.6) shows the WSI to be

[0.05%, 56.09%], which means that as long as the weight for the criterion Duration falls

within this interval, the ranking for all six projects will not be changed no matter what the

weight value is; however, the WSI can differ as the stability level changes. The stability level

indicates the number of alternatives to be considered. If one only wants to keep the ranking

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stable for 4 out of the 6 projects, which means a stability level of 4, then the WSI would be

[0.00%, 56.09%].

Figure 3.5.2.6 - Weight Stability Intervals for Duration

3.5.3 Using Software to Update Ranking based on Progress Reports

As the projects progress, it is likely that some of the projects may experience cost overruns

and schedule delays. Some could have spent 30% of the budget and only achieved 25% of

the work. It is possible that some projects that are not considered high-priority will become

more critical. The ranking for these projects might change; thus, it is necessary to keep the

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ranking updated in order to see which projects need the most attention in the current phase.

The PMDSS itself can generate data for the posterior phase in terms of project cost,

duration and so on. Furthermore, all of these data (Table 3.5.3.1) can be input into Visual

PROMETHEE as a new scenario to compare with the analysis based on the original

estimate (Figure 3.5.3.1).

Table 3.5.3.1 – Ranking Inputs Based on Original Estimates

Projects Cost

(US$M) Duration (Years)

Cost Overrun

Schedule Delay

Criticality (5-point Scale)

Percent Complete

Start Time

(Years)

Stakeholders (5-point Scale)

CM019 449.4 8 -0.0002 0.2083 High 0.0080 0.58 Average

CM009 756 9.67 0.0054 0.0000 Very low 0.0005 2.33 Average

CM004 40.9 7.92 0.0000 0.0000 Very low 0.1705 3.25 Average

CM008A 42.8 9.08 0.0350 0.0000 Very low 0.0000 3.75 Average

FM216 14.5 7.67 0.0207 0.0000 Very low 0.1575 2.75 Average

CS719 12.8 7.25 0.0920 0.0000 Very low 0.2000 2.83 Average

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Figure 3.5.3.1 - Evaluations of Projects Based on Updates

After entering the updated information into Visual PROMETHEE, Table (3.5.3.2) can be

obtained. This table consists of information gathered from the 2009 Quarter 3 report for

these 6 projects. It should be noted that even though there are 11 projects in the portfolio,

only those projects that had been started by that time were considered. For project CM009,

58.7% of the projects had been completed. For projects CM008A, FM216 and CS729,

almost half of the work had been completed. Project CM019 had just reached its 15% level

of completion, and project CM004 was just about to start. The table indicates that based on

PROMETHEE II Complete Ranking, project CM009 is now ranked as number one and

CM019, which topped the ranking before, is now in second place. CS719, which was placed

last in the original estimate, now came in third. All of these rankings are based on net

preference flow , and show that some of the projects that were not as critical initially may

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now require more attention. When managing all of these projects in a portfolio, it is difficult

to keep all projects in focus at all times. Changes in ranking can provide the project

management team with timely messages, thereby contributing to effective project

management.

Table 3.5.3.2 - Complete Ranking and Partial Ranking Computation Results

Projects

1 CM009 0.1422 0.2246 0.0824

2 CM019 0.1111 0.1527 0.0415

3 CS719 -0.0475 0.0395 0.087

4 CM004 -0.0571 0.0322 0.0893

5 CM008A -0.0701 0.024 0.0941

6 FM216 -0.0787 0.0202 0.0989

In the new ranking, however, CM009 and CM019 are still incomparable using

PROMETHEE I Partial Ranking as CM009 has not only a higher positive preference flow

value but also a higher negative preference flow

, too. The partial ranking is presented

in Figure (3.5.3.2).

76

Figure 3.5.3.2 - PROMETHEE I – Partial Ranking for Updates

Using the net preference flow, the complete ranking is also obtained (Figure 3.5.3.3).

77

Figure 3.5.3.3 - PROMETHEE II – Complete Ranking for Updates

In order to reveal which criteria are preferred in each project, the PROMETHEE Rainbow

figure could be helpful. Figure 3.5.3.3 shows the rainbow for each individual project. For

example, for the criterion of cost, projects CM009 and CM019 are preferred; furthermore,

the block size for cost is larger for CM019, which means that CM019 is the more preferred

one between the two. The data actually agrees with this conclusion as project CM019 has a

budget of $756M, whereas project CM009 has a budget of about $450M. Also, we can see

that for the criterion of schedule delay, project CS719 is preferred, which actually has a 9%

schedule delay. To see the changes, one can also compare this rainbow with the rainbow for

the original estimate, which might alert project managers to pay more attention to these

projects.

78

Figure 3.5.3.4 - PROMETHEE Rainbow for Updates

PROMETHEE GAIA is also examined in Figure (3.5.3.5). Clearly, some of the axes remain

the same if the date for those criteria is the same as in the original (Fig. 3.5.2.5), such as start

time. If the changes are negligible, then the axis will be almost identical to the original;

however, the duration axis has shifted its position since the progress report indicates that

schedule had changed for certain projects, as a result of which, the input data was modified.

The PROMETHEE decision axis has also moved, and now CM009 has a higher

preference than CM019, which is consistent with the results obtained in Table (3.5.3.1).

When some project points are relatively close to each other, these projects tend to have

more or less the same preference in the portfolio, as is the case for projects FM216,

CM008A and CM004.

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Figure 3.5.3.5 - PROMETHEE GAIA for Updates

Again, the weights have been set to be equal in this analysis. The sensitivity analysis for

weights for the criterion of percent complete are shown in Figure (3.5.3.6). With a stability

level of 6, the WSI is [8.86%, 17.76%]. This shows that the rankings are sensitive to this

criterion because the rankings hold only as long as the weight of this criterion remains within

this relatively narrow range. When the stability level changes to 3, then the WSI is [8.86%,

47.37%], which is much wider than the WSI before.

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Figure 3.5.3.6 - Wight Stability Intervals for Updated Percent Complete

3.6 Application of PROMOTHEE Ranking in Excel

As the software establishes ranking by means of the preference flows, it is believed that the

preference flows can be random variables if the inputs for the ranking system, such as

project cost and duration, are modeled as random variables. Due to the limitations of the

software, probabilistic analysis cannot be achieved. In order to apply probabilistic ranking

analysis and make this system easily accessible to users, the ranking system was integrated

into Excel.

The PROMOTHEE ranking applied in this research consists of two major parts. The first is

the PROMETHEE I Partial Ranking. Based on defined criteria and preference functions,

the positive preference flow and the negative preference flow could be obtained. It should

be noted that there are two values that determine the ranking in partial ranking, and these

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two flows could potentially provide conflicting ranking orders, in which case the two

projects are considered to be incomparable. The second is the PROMOETHEE II

Complete Ranking, and the net preference flow will be the difference between the positive

preference flow and the negative preference flow. Taking the difference will make the

ranking order unique, but some information may be lost in the process. As part of this

research, these two ranking methodologies were implemented into Excel, providing easy

access to the ranking systems for users who lacked either the software or a profound level of

knowledge about PROMETHEE. Another reason for implementing PROMETHEE

ranking in Excel is the randomness of the assumptions made about project cost and duration.

The original software will not be able to run MC simulations; however, by implementing the

PROMETHEE in Excel, we can run MS simulations using @Risk add-in software. This is a

new contribution as it allows random input to PROMETHEE; however, GAIA is not

included in Excel due to the complexity of the problem-solving process, and if needed, the

software is always available for more detailed information and analysis. Even though the

GAIA ranking information is not fully presented in Excel due to its limitations, integrating

part of the PROMETHEE ranking results into Excel may benefit the PPM experience in

multiple ways.

3.6.1 Using Excel to Establish Ranking Based on Original Estimate

For the original portfolio plan, PROMETHEE can provide both the original partial ranking

and the complete ranking for later comparison. For this part, only five criteria have been

selected: project cost, duration, criticality, start time and stakeholders. For each of these

criteria, a value should be decided either by the estimators who prepare the original estimate

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for the project or experts who evaluate the results based on historical data or personal

experience, as explained in previous chapters. After defining the preference functions, the

weight for the criteria, and the optimal orientation, the positive preference flow (Phi+), the

negative preference flow (Phi-), and the net preference flow (Phi) could be obtained (Table

3.6.1.1).

Table 3.6.1.1 - PROMETHEE Ranking in Excel for Original Estimate

Project ID Project Name Phi+ Phi- Phi

i A Portfolio of Projects

1 Start 0.0000 0.0000 0.0000

2 CM009 0.2622 0.1257 0.1366

3 CM019 0.2602 0.0242 0.2360

4 FMM19 0.0000 0.0000 0.0000

5 CM008A 0.0191 0.1170 -0.0979

6 CM002 0.0000 0.0000 0.0000

7 CM004 0.0585 0.1008 -0.0423

8 CM013 0.0000 0.0000 0.0000

9 FM216 0.0117 0.1219 -0.1102

10 CS790 0.0125 0.1347 -0.1222

11 VM014 0.0000 0.0000 0.0000

12 CM014A 0.0000 0.0000 0.0000

As shown in Table (3.6.1.1), project CM009 has a higher Phi+ value and Phi- value than

CM019, as a result of which, these two projects are incomparable according to partial

ranking; however, if we only consider the Phi value, then the complete ranking suggests that

project CM019 has a higher priority than CM009. These values are also presented in graphs

(Figs. 3.6.1.1 and 3.6.2.2).

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Figure 3.6.1.1 - Partial Ranking for Original Estimate

Figure 3.6.1.2 - Complete Ranking for Original Estimate

Figure (3.6.1.1) shows the partial ranking for the original estimate. The x-axis represents the

ID of projects in the portfolio (Table 3.6.1.1), while the y-axis represents the preference flow.

The positive and negative preference flow values will always be non-negative and fall in the

range of 0 to 1. By comparing the length of the vertical bars, we can easily obtain the ranking

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Pre

fere

nce

Po

siti

ve

/Ne

ga

tiv

e F

low

Project ID

Partial Ranking

Phi+

Phi-

-1.0000

-0.8000

-0.6000

-0.4000

-0.2000

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Pre

fere

nce

Ne

t F

low

Project ID

Complete Ranking

Phi

84

for Phi+ and Phi-. If both vertical bars for one project are higher than for the other project,

then these two projects will be incomparable. Figure (3.6.1.2) presents the complete ranking

for the original estimate. By subtracting the negative preference flow from the positive

preference flow, we calculate the net preference flow, which will fall in the range of -1 to 1.

The ranking could also be easily obtained by listing the values from the largest to the

smallest. For example, in this case, the project ranking will be 3, 2, 7, 5, 9, 10.

As discussed earlier, a powerful statistical analysis can also be performed in Excel with the

help of @Risk. Due to the normality assumptions that were made for project cost and

durations, the flow values are actually not fixed numbers but rather the mean values of

distributions. Even though the complete ranking provides a ranking of 3, 2, 7, 5, 9, 10, it

only indicates that the means of the net preference flow will follow this order. In order to

see the probability of the prioritization of project 3 over project 2, we calculated the

difference of the net preference flow between projects 2 and 3. By running the simulation

1,000 times, we obtained Figure (3.6.1.3).

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Figure 3.6.1.3 - The Ranking Analysis for Projects 2 and 3 Based on Original Estimate

As indicated by Figure (3.6.1.3), for more than 95% of the time, the difference between the

net preference flow of Projects 2 and 3 is negative. As a result, Project 3 should be preferred

to Project 2 with more than 95% probability.

Another comparison was made for Project 9 and 10 since these two projects have relatively

close values in regard to both partial ranking and complete ranking.

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Figure 3.6.1.4 - The Ranking Analysis for Projects 9 and 10 Based on Original Estimate

Figure (3.6.1.4) presents a statistical analysis of the comparison in 1,000 iterations: 66.3% of

the time, Project 9 is preferred over Project 10; conversely, there is a 33.7% chance that

Project 9 will not be preferred over 10. This result shows how close these two projects are,

and provides a better understanding for project managers about the two projects.

A PROMETHEE Rainbow is also prepared in Excel (Fig. 3.6.1.5). Even though it is slightly

different from the original software output, which ranks the criteria from the largest to the

smallest values, it still provides a general sense of the projects’ preferences according to

different criteria. As mentioned in previous chapters, criteria on the top of the rainbow are

significant for an alternative, while those on the bottom show where the alternative was

relatively unimportant.

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Figure 3.6.1.5 - The PROMETHEE Rainbow for the Original Estimate

Project profiles and spider webs are also implemented into Excel. Taking Project 2 for

example, Figures (3.6.1.6) and (3.6.1.7) show the values for each criterion and represent the

values visually. It should be noted that the software also prepares spider web figures for each

project; however, those values are the projected values on a GAIA plane, not the raw values

calculated using preference functions. Figure (3.6.1.6) shows the values for each criterion as

columns, with the horizontal axis representing the ID of the criteria, while the vertical axis

represents the values. Figure (3.6.1.7) is another way to show the values for each criterion,

with the five criteria forming the shape of the spider web and the shaded area showing the

preference of the project based on each criterion.

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Figure 3.6.1.6 - Project 2 Profile for Original Estimate

Figure 3.6.1.7 - Project 2 Spider Web for Original Estimate

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3.6.2 Using Excel to Update Ranking based on Progress Reports

The PROMETHEE ranking system is also tied to the Bayesian updating process in this

research. It is believed that, after the projects progress, the new information observed can

affect not only the project cost and duration but also the ranking. After Bayesian updating

has been applied to the original estimate, the project attributes such as costs and durations

are expected to change. In order to capture the effects of these changes on the ranking, the

steps in Chapter 5.1 are performed again with updated values. In addition to the original five

criteria (project cost, duration, criticality, start time and stakeholders), three more criteria

have been introduced in the updating process: (1) cost overrun, (2) schedule delay and (3)

percent complete. Input is then collected from estimators and experts are and, by applying

the preference functions, assigned weight and optimized orientation (i.e., whether the input

value is preferred to be larger or smaller), we can obtain the ranking again for the updated

values.

Table 3.6.2.1 - PROMETHEE Ranking in Excel for Updated Estimate

Project ID Project Name Phi+ Phi- Phi

i A Portfolio of Projects

1 Start 0.0000 0.0000 0.0000

2 CM009 0.1856 0.0737 0.1119

3 CM019 0.1552 0.0410 0.1142

4 FMM19 0.0000 0.0000 0.0000

5 CM008A 0.0302 0.0941 -0.0639

6 CM002 0.0000 0.0000 0.0000

7 CM004 0.0389 0.0893 -0.0504

8 CM013 0.0000 0.0000 0.0000

9 FM216 0.0233 0.0985 -0.0752

10 CS790 0.0291 0.0867 -0.0576

11 VM014 0.0000 0.0000 0.0000

12 CM014A 0.0000 0.0000 0.0000

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Table (3.6.2.1) shows the results for partial ranking and complete ranking after the update.

Notably, some values for the positive preference flow, negative preference flow, and the net

preference flow have changed after the updates. For example, the net preference flow for

Project 2 has changed from 0.1366 to 0.1119, which indicates a decrease in preference

degree in the portfolio, even though its might still rank second. The net preference flow for

Project 10 has increased from -0.1222 to -0.0576, suggesting that the preference degree is

stronger than the original estimate and the rank has shifted as well from last to fourth place.

The complete ranking is now 3, 2, 7, 10, 5, 9.

Figures (3.6.2.1) and (3.6.2.2) presents the partial ranking and complete ranking for the

updated estimate. The lengths of the bars have also changed accordingly. From Figure

(3.6.2.2), it is clear that the preference of Projects 2 and 3 in the portfolio has decreased even

though they are still the top 2 optimizations.

Figure 3.6.2.1 - Partial Ranking for Updated Estimate

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Figure 3.6.2.2 - Complete Ranking for Updated Estimate

In order to identify the changes between Projects 2 and 3, a statistical analysis is applied to

the difference between the net preference flows of Projects 2 and 3. As shown in Figure

(3.6.2.3), almost all values are negative in the 1,000 iterations; this proves the strong

preference of Project 3 over Project 2. The preference has been strengthened after the

updates in comparison to Figure (3.6.1.3) since the probability has increased, and the mean

values have decreased.

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Figure 3.6.2.3 - The Ranking Analysis for Projects 2 and 3 Based on Updated Estimate

Another finding after the update is that Projects 9 and 10 are no longer close in the ranking

system; instead, Project 5 and 9 have very close results in both partial and complete ranking.

Figure (3.6.2.4) shows that, for almost all of the 1,000 iterations, Project 9 is preferred over

Project 5.

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Figure 3.6.2.4 - The Ranking Analysis for Projects 5 and 9 Based on Updated Estimate

PROMETHEE Rainbows, project profiles, and spider webs have also been produced in

Excel and show changes, but are not included here.

The purpose of the applying PROMETHEE ranking in Excel is to simplify the ranking

procedure and thereby enable users with relatively little experience in PROMETHEE and

GAIA software to run the ranking analysis. It also provides a huge advantage over the

original software in terms of statistical analysis, which distinguishes this research from other

previous work related to PROMETHEE. It should be noted that even though some of the

reports generated by the software can be reproduced in Excel, the Excel tool still has some

disadvantages when compared with the software, such as the lack of interaction and weight

sensitivity analysis due to limitation, thereby highlighting the value of the software. As a

result, the utilization of both Excel and the software are strongly recommended.

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3.7 Summary

As a ranking method, PROMETHEE and GAIA provide project managers with a powerful

tool for the prioritization of projects within the portfolio. As a decision-making tool first

introduced in the early 1980s and further developed over the past three decades, it has been

widely applied in many industries. In the context of the ranking of capital projects in

construction, however, it is still a new tool. By applying this methodology to the portfolio,

one can identify the most critical projects with detailed information available according to

the selected criteria. Project managers could take full advantage of all of this information and

make timely judgments and decisions to help them successfully complete projects on time

and within budget. It should be noted that the methodology can also be conveniently

applied to the updated progress reports. This is important because during the execution of

the projects, the ranking can change. Thus, the project management team can use this

methodology to modify the rankings and area of emphasis as needed according to the

updated information about the portfolio.

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CHAPTER 4 : ESCALATION

4.1 Introduction

This chapter includes two sections: Section 4.2 focuses mainly on examining the existing

index BCI and determining how to model it, while Section 4.3 focuses on introducing a new

index – namely, the Integrated Transit Index (ITI) – and performing the forecast of the new

index.

In Section 4.2, a method is proposed for generating escalation factors for cost estimating in

large infrastructure projects with long development periods. Cost escalation is a major risk

factor in any large infrastructure project, and the effect of inflation can best be captured by

explicitly incorporating this uncertainty into the calculation of escalation. Using the

Engineering News Record’s Building Cost Index (BCI), the percent change in construction

costs is modeled as a normal random variable with parameters estimated from historical

index values. After comparing the proposed model with two competing approaches, it is

shown that assuming independence among percent changes in various years will result in the

most accurate prediction of BCI index values. The mean absolute percent error for the

independent case is calculated as 7.6% for the period 1980-2010. All three approaches are

tested using appropriate statistical tests, and the results are analyzed.

As examined in Section 4.3, the use of cost indices is common to account for the effect of

escalation in estimating the cost of long-duration capital projects. Indices published by

Engineering News Record (ENR) or RS Means have been widely accepted in the industry.

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These indices are general construction indices and might not be suitable for certain types of

projects. This research proposes an ITI for transit projects, which usually have long

durations and involve large capital investments. Based on the Standard Cost Categories (SCC)

for Capital Projects published by the US Federal Transit Administration (FTA), the project

cost is broken down into 5 subcategories: construction, systems, right of way (ROW),

vehicle, and professional services. For each category, a suitable and specific index has been

selected to model the cost trend. As an example, ENR’s BCI is used for the subcategory of

construction, and the Bureau of Labor Statistics’ Electric Power Distribution Index is used

for the subcategory of systems. By analyzing these subcategories separately, and combing

them to obtain the ITI, we expect to achieve a more accurate composite index. Using this

index, an average escalation rate of 3.35% per year is observed from 2004 to 2010. To

forecast the value of the index in future years, two approaches have been used: neural

networks and time series analysis. These approaches were applied to the ENR index values,

and the results were compared by using statistic Mean Absolute Percentage Error (MAPE).

It was found that each method has its advantages over the other when the input data

changes; thus, both methods have been retained and applied to forecast the index values. A

methodology is presented for forecasting future values of the proposed ITI.

4.2 Modeling of Escalation Factor

4.2.1 Background

When a cost estimate is prepared for a project with a long development period, one of the

risks commonly confronting the estimator is escalation. One way to account for escalation is

to look up historical values of cost indices reported by sources such as ENR and RS Means.

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For example, ENR has been collecting data from 20 cities throughout the United States

since 1921 (with a benchmark period of 1913) and publishing indices such as the

Construction Cost Index (CCI) and Building Cost Index (BCI), which have long been used

as cost trend measurements (Touran & Lopez, 2006). Both the contractor and the owner

have great interest in estimating the impact of cost escalation on projects where the

construction period exceeds two years (Touran et al., 1994). Especially in regard to long-

duration infrastructure projects, where the time span from the planning phase to the end of

construction can easily exceed 5 years, understanding the crucial role of escalation and these

indices will play a vital role in the success of a project. As an example of the importance of

escalation, Flyvbjerg et al. (2009) report that one of the major cost drivers in large

transportation projects appears to be the length of project development. Reilly et al. (2004)

contend that one of the main reasons behind the large discrepancy between initial estimates

and the final cost of the Boston’s Central Artery Project was the fact that the original

estimate prepared in 1986 dollars was not in accordance with FHWA requirements at the

time since the escalation cost was not included.

One of the issues facing the cost modelers and risk analysts in infrastructure projects is how

to incorporate the effect of escalation in the project estimate. From the review of the

literature, it becomes apparent that the most common approach in estimating escalation cost

is the use of cost indices published by various professional organizations.

In the current research, the main objective is to introduce a probabilistic approach for

adequately modeling the effect of cost escalation on construction budgets. Due to the

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complexity of the predictive model and intractability of closed-form solutions, a simulation

approach is used.

4.2.2 Background

Much work has been done in the area of escalation assessment and measurement. Xu and

Moon (2013) suggest that methods for forecasting construction cost trends can be grouped

into two major categories – the casual methods and the univariate time series models – with

the former emphasizing the relationship between predictive and dependent variables, and the

latter highlighting the behavior of past values.

Causal methods have been utilized by many researchers. Akintoye et al. (1998) pointed out

possible indicators, such as unemployment level, construction output, and industrial

production, for construction costs in the United Kingdom. Ng et al. (2004) suggested a

model to forecast construction tender price index. Shane et al. (2009) have categorized 19

primary cost escalation factors by interviewing more than 20 state highway agencies. Neural

networks have also been proposed as a forecast tool for ENR CCI by Williams (1994),

though the results were not satisfactory. Touran and Lopez (2006) have described the major

problems in developing predictive models for estimating the effect of escalation. Several

recent articles have also examined the problem of estimating the value of the cost index in

future years.

Time series models have also been widely used, with popular approaches like simple moving

average (SMA) exponential smoothing and auto-regressive integrated moving-average

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(ARIMA). While simple moving average is preferred due to its simplicity, more complicated

approaches such as ARIMA are among researchers’ favorites. Ashuri and Lu (2010) assessed

the accuracy of various forecasting methods, such as SMA and ARIMA, as well as these

methods’ ability to predict the ENR’s CCI. Hwang (2011) has also developed two times

series models to predict CCI. Xu and Moon (2013) presented an auto-regression model for

forecasting the construction cost trend. In this work, the authors were again working with

ENR indices.

4.2.3 Methodology

In this research, the goal is to develop guidelines for incorporating the effect of cost

escalation into the budget of large multi-year infrastructure projects. In order to achieve this

objective, one must estimate the escalation factors for each year. We have used the ENR’s

BCI for this purpose. The reason for selecting BCI over CCI is because its representation of

skilled labor instead of common labor is more suitable for structures (Grogan, 2006). The

CCI index contains only common labor, and the amount of common labor (200 hours in the

composition of the cost index) seems excessive given current construction practice. Also, it

is decided to only include the past 30 years’ data in the analysis because this timespan was

deemed adequate for capturing variations of construction costs in recent years.

Three approaches have been selected in this research – Independent series, Martingale series

and Correlated series. The Independent series will be modeled by assigning a unique

probability distribution for the escalation factor, obtained from historical data, for each year

in the future; the escalation factor for each year can then be sampled from the distribution

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and is independent from other years. In the Martingale series, the escalation factor for the

first year is calculated by sampling the basic distribution of the escalation factor. For

subsequent years, the escalation factor will be sampled from a distribution with the mean

being the value sampled for the previous year and the same standard deviation of the basic

distribution. In the last approach, the Correlated series, the distributions for various years

are identical but are correlated. In other words, the escalation factor in consecutive years is

modeled as an auto-correlated series.

4.2.3.1 Basic Distribution for Escalation Changes

As shown in Table (4.1.3.1), the mean and standard deviation for the BCI percent change in

the past 30 years have been calculated (Eq. 4.1.3.1.1), which will be used to model the

distribution for escalation factor in this research.

(4.1.3.1.1)

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Table 4.2.3.1 - ENR'S Building Cost Index History (1980-2010)

Year BCI Percent Change

1980 1941

1981 2097 8.0371%

1982 2234 6.5331%

1983 2384 6.7144%

1984 2417 1.3842%

1985 2428 0.4551%

1986 2483 2.2652%

1987 2541 2.3359%

1988 2598 2.2432%

1989 2634 1.3857%

1990 2702 2.5816%

1991 2751 1.8135%

1992 2834 3.0171%

1993 2996 5.7163%

1994 3111 3.8385%

1995 3112 0.0321%

1996 3203 2.9242%

1997 3364 5.0265%

1998 3391 0.8026%

1999 3456 1.9168%

2000 3539 2.4016%

2001 3574 0.9890%

2002 3623 1.3710%

2003 3693 1.9321%

2004 3984 7.8798%

2005 4205 5.5472%

2006 4369 3.9001%

2007 4485 2.6551%

2008 4691 4.5931%

2009 4769 1.6628%

2010 4883 2.3904%

Mean 3.1448%

Standard Deviation 2.1734%

The data is plotted in Figs. (4.1.3.1.a) and (4.1.3.1.b). The best fit is a Loglogistic distribution

based on goodness of fit tests; however, we decided to use a normal distribution to model

percent change in BCI values from year to year. The use of normal distribution is relatively

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common for modeling the effect of inflation or escalation (Bodie et al., 1993; Touran et al.,

1994; Britton et al., 1998; Touran & Lopez, 2006). While it is understood that there is a skew

in the distribution, the use of the bell-shaped curve was deemed appropriate. In this work,

we applied the Loglogistic and normal distributions for modeling annual percent changes,

and then compared the simulation outcomes with actual values. The use of normal

distribution resulted in smaller errors as will be described in the validation section of this

report.

Figure 4.2.3.1 - (a) Actual percent change per year vs. a normal distribution; (b) Actual percent change per year vs. a Loglogistic distribution

The approach here is to provide guidelines for generating values of escalation to be used for

budgeting of infrastructure projects using a MC simulation approach. A normal distribution

with mean and standard deviation given in Table (4.1.3.1) is then created to model the BCI

percent change each year. It is implied that the model works if it is assumed that the

movements of the escalation factor are similar to its movements in the past. At each year i,

the escalation factor for the following year i+1 can be calculated from Eq. (4.1.3.1.2).

(4.1.3.1.2)

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where ri is the escalation factor for year i and ei+1 is percent change for year i+1. For each

year, the normal distribution will be sampled to represent the percent change e for that

specific year. This factor is either independent or correlated with the previous year’s

escalation rate.

4.2.3.2 Independent Series

For the independent series, the same distribution will be sampled for each year throughout

the project’s life cycle. In order to test the reasonableness of the generated escalation factors,

the sampled percent change values will then be applied to the first period BCI (1980) to

calculate the predicted value for BCI in 1981. In this way, all of the BCI values from 1981 to

2010 will be calculated.

4.2.3.3 Martingale Series

In this approach, the same normal distribution will be used to model the first year’s percent

change; however, the mean value in the next year for the percent change will be the sampled

value obtained in the previous year, as an indication that the BCI percent change in the next

year relates to the percent change in the previous year. This approach has been used in prior

research but was not tested against the actual values.

4.2.3.4 Correlated Series

The third approach is conceptually similar to the Martingale series as we try to consider the

possible correlation between escalation factors in consecutive years. Surprisingly, the

Pearson Correlation Coefficient between escalation factors in consecutive years is calculated

as 0.38. The correlation coefficient between each year and the year prior to the immediate

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previous year was calculated as -0.06. This shows that the correlation between consecutive

years is not strong. It should be noted that BCI values are highly correlated between

consecutive years. For example, the correlation coefficient between BCIs for the period

1980-2010 is calculated as 0.99, but the correlation between percent changes (which is used

in this research) is relatively weak.

The simulated escalation factors in this approach were generated by sampling the same basic

normal distribution; however, correlation coefficients were defined between each period and

two prior periods utilizing a correlation matrix of rank correlations. This was done using

@Risk simulation software. The process of generating correlated random variables in a

simulation setting has been explained in several references (@Risk User’s Manual 2008;

Touran & Wiser, 1992).

4.2.4 Validation of Results

In order to test the three approaches proposed above, the basic distribution (i.e., the normal

distribution with mean and standard deviation calculated from historical data 1980-2010,

given in Table 1) was sampled. Using Eq. (4.1.4.1), the BCI for the following year was

estimated and compared with the actual BCI from historical data.

(4.1.4.1)

In Eq. (4.1.4.1), EBCIi is the estimated BCI for year i. For each year, the deviation between

actual and estimated BCIs was calculated and their combined effect was tested using the

three measures described below. The three measures used to test the data have been widely

used in relevant literature for similar studies (Xu & Moon 2013; Ashuri & Lu 2010; Lowe et

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al., 2006; Wilmot & Mei, 2005); these are Mean Absolute Percentage Error (MAPE), Mean

Squares Error (MSE), and Mean Absolute Error (MAE), and they can be calculated using

Eqs. (4.1.4.2) to (4.1.4.4), respectively.

(4.1.4.2)

(4.1.4.3)

(4.1.4.4)

The BCIs were estimated using both normal distribution and Loglogistic distribution (which

was the best fit to the data) for each year between 1980 and 2010. This process was

simulated for 1,000 times (because the percent change per year was modeled as a random

variable). Mean and standard deviation of 1,000 iterations for the three test statistics are

reported in Table 4.1.4.1. The means and standard deviations represent BCI index point

deviations between estimated and actual index values. As an example, using a normal

distribution to generate percent cost change and assuming independence among generated

random numbers, one can see that there is a difference of 255 points on average (Mean

Absolute Error) between the estimated and actual index values. The actual index values for

the period 1980-2010 varied between 1941 and 4883 (Table 4.1.3.1). The MAPE is about

7.6%. This same value is about 9.0% using the correlated approach.

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Table 4.2.4.1 - Measurement Values for Three Series

Independent Martingale Correlated

Normal Mean Standard Deviation

Mean Standard Deviation


MAPE 0.0756 0.0352 1.3013 3.7367 0.0899 0.0450

MSE 115157 133905 891590255 18480419147 174710 207780

MAE 255 130 5346 16389 309 167

Log Logistic Mean Standard Deviation



MAPE 0.0924 0.0678 255866 8088915 0.1086 0.0821

MSE 240759 965541 1.99x1022 6.30x1023 356301 1162637

MAE 317 252 1229492139 38869291114 377 306

By studying the results of the validation, one can see that normal distribution outperformed

Loglogistic distribution in all three tests because the mean and standard deviation of each

test statistic is smaller for the normal distribution.

As for the Independent, Martingale, and Correlated approaches, it was found that using the

Martingale approach results in large deviations from the actual BCIs. In fact, based on the

findings of this analysis, the use of Martingale series is not recommended. After comparing

the three approaches, it was found that the independent series provide better results based

on the MAPE, MSE, and MAE values. While this might be somewhat surprising, it is

welcome news because working with independent random variables simplifies the modeling

and validation of the results of the analysis.

4.2.5 Analysis of Results

After running 1,000 iterations for the BCI calculations, the percentile values were plotted.

Figures (4.1.5.1) to (4.1.5.3) are for Independent series, Martingale series and Correlated

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series, respectively. For each case, actual BCI values were plotted against the 25, 50, and 75

percentile values of the 1,000 simulated indices.

As Figure (4.1.5.1) indicates, the 50 percentile values are smaller than BCI historical data in

the first few years, and then the values are close to historical data until 1999 when the 50

percentile values becomes larger than the historical data. The 50 percentile values are very

close to historical data after 2004. The 25 and 75 percentile lines are also shown in the figure.

The BCI historical data are generally within the range except for the first few years where

BCI historical data is still higher than 75 percentile values. One reason might be the

recession in the early 1980s causing large inflations.

Figure 4.2.5.1 - Independent Series vs. Historical Data

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Using the simulated data, one can easily obtain a range instead of a single value for the BCI

values for a specific year. For example, in 2010, the 25 and 75 percentile values are 4,501 and

5,244, respectively. The range depends on the requirement and can be smaller if preferred. If

one is looking for one value for estimate, the 50 percentile value can also easily be read from

the generated data, which in this case is 4,919. An alternative way to use these data is to

calculate the percent change for various percentiles. For instance, in 2010, the percent

change is 2.6665% for the 25 percentile, 2.7768% for the 75 percentile, and 2.9790% for the

50 percentile.

Figure 4.1.5.2 shows the results using the Martingale series. The 50 percentile values are

smaller than BCI historical data before 2000 and then stay above historical data till the end,

which might not be clearly shown in the figure due to the scale; however, since the variances

are very high for these distributions, the range between the 25 and 75 percentile is huge

when compared to the Independent series.

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Figure 4.2.5.2 - Martingale Series vs. Historical Data

Figure (4.1.5.3) exhibits results similar to Independent series. The 50 percentile values start

off lower than BCI historical data then surpass historical data around 1998 and eventually

get close to BCI. The 25 and 75 percentile range also contains most of the BCI historical

data except for the first few years, but ranges a little wider than the Independent series.

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Figure 4.2.5.3 - Correlated Series vs. Historical Data

By looking at the data, one can see that both the Independent and the Correlated approaches

can provide reasonable estimates of cost escalation, if the assumption is that future price

movements will be similar to those in the past. Furthermore, using the approach suggested

in this research allows analysts to explicitly consider the randomness and inherent variability

of the escalation factor and to quantify the variance resulting from escalation in the context

of total variance in project cost.

4.2.6 Summary

Escalation has long been of interest to cost estimators and owners of major infrastructure

projects, especially projects with long development duration. This research has proposed an

approach for using a normal distribution to model the percent change for BCI published by

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10

Correlated Series vs. BCI Historical Data

BCI Correlated 50% Correlated 25% Correlated 75%

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the ENR. Three models were Independent Series, Martingale Series and Correlated Series. In

the Independent case, the value of percent change in costs was assumed to be independent

from similar values in various years. Three statistical methods were used to test and validate

the performance of the proposed methods: MAPE, MSE, and MAE. It was found that

assuming independence among escalation factors yields the best results in estimating the

magnitude of the BCI index values. The mean absolute percent error was 7.6% of the index

value. Assuming Pearson autocorrelation among percent change values from year to year

also resulted in acceptable results in predicting the index values. The Martingale series model

did not fare well compared to the other approaches. The proposed method is easy to

understand and to use, especially in cost estimates using the MC simulation approach.

4.3 Modeling and Forecasting Integrated Transit Index

4.3.1 Background

In the United States, construction cost indices published by the ENR and RS Means have

been widely used by industry professionals for preparing project budgets. These indices have

also been examined by scholars and researchers in academia, with the aim of improving the

accuracy of cost estimates and project budgets. According to ENR, both the CCI and BCI

are based on 20-city national averages for the material prices of structural steel, cement and

lumber; the only difference lies in the labor cost component – CCI uses common labor,

whereas BCI reflects skilled labor (Grogan, 1992). RS Means cost data, published since 1975,

has also been commonly used in the construction field. It provides estimators with location

and historical cost indices.

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Despite the prevalent use of these indices, it should be noted that they capture general price

movements. Difference in the nature of the project under consideration can cause a huge

variation in project cost. For example, preparing a cost estimate for a residential building can

be very different from a highway project. Especially for a transit project, the escalation cost –

due to the long development phase, multi-year construction period, and large capital

investments – can play a vital role in the cost estimate and thus the successful completion of

a project. For these long-duration projects, the impact of an accurate escalation estimate

cannot be overemphasized. The Transit Capital Cost Index Study (Federal Transit

Administration, 1995) noticed the difference between transit cost and general measures of

inflation, proposing the use of a Composite Input method to improve the estimation of

future capital costs for light rail and heavy rail fixed guideway projects. Their method

identified the percentage of three types of inputs – labor, material and equipment – and

combined with Producer Price Index (PPI) to obtain the indices for projects at three levels.

However, the price paid for the service markets does not equal the expenditure of the

project, and using PPI as the source for the three inputs also has its limitations.

Consequently, this research describes a cost index to be used exclusively for transit projects

in the United States – the Integrated Transit Index (ITI). For the purpose of forecasting ITI

values for future years, two methods are suggested: time series analysis and neural network.

4.3.2 Standard Cost Categories (SCC) for Capital Projects

According to the FTA (2011), all transit projects requesting federal support will have to

submit a cost estimate for their project according to the format called ‘Standard Cost

Categories’ (SCC). Started in 2005, SCC is “a consistent format for reporting, estimating and

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managing of capital costs for New Starts projects.” It is believed that the information

collected in this format from across the country could be beneficial to the FTA in future

cost estimates because it allows cost comparisons among transit projects and allows cost

anomalies to be identified more easily.

Based on FTA’s SCC for capital projects, a transit project’s cost is broken down into 10

categories (Table 4.2.2.1).

Table 4.3.2.1 - Standard Cost Categories for Capital Projects (FTA)

10 Guideway & Track Elements (Route Miles)

20 Stations, Stops, Terminals, Intermodal (Number)

30 Support Facilities: Yards, Shops, Administrative Buildings

40 Sitework & Special Conditions

50 Systems

60 Row, Land, Existing Improvements

70 Vehicles (Number)

80 Professional Services (Applies to Cats. 10-50)

90 Unallocated Contingency

100 Finance Charges

As explained by the FTA (2012), categories 10 through 50 cover the construction of fixed

infrastructure. Professional services associated with categories 10 to 50 should be included in

category 80, but professional services related to categories 60 and 70 should be estimated

under categories 60 and 70, respectively.

4.3.3 Integrated Transit Index

Based on the FTA’s SCC, the ITI has been proposed in this research. It was decided to

group these 10 categories into 5 main categories. Presented in Table 4.2.3.1, the following

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five categories have been considered: Construction (SCC10-40), Systems (SCC50), Real

Estate (SCC60), Vehicles (SCC70) and Soft Cost (SCC80). SCC90 and SCC100 only account

for a relatively small portion of the total project costs; so, these two categories are excluded

from our analysis. To estimate the weight of each cost category, we then used the Light Rail

Transit Capital Cost Study Update (2003) and Heavy Rail Transit Capital Cost Study Update

(2004) reports produced for the FTA by Booz Allen. These two reports collected actual cost

data from 51 transit projects in the United States and reported them according to the SCC.

Table 4.3.3.1 - Cost Categories and Percentages

01 Construction SCC10-40 57%

02 Systems SCC50 9%

03 Real Estate SCC60 4%

04 Vehicles SCC70 5%

05 Soft Cost SCC80 25%

The percentage values presented in Table 4.2.3.1 are based on an analysis of actual transit

cost data published by the FTA. Using capital cost data from 51 transit projects built in the

United States, we calculated the percentage of the total cost for each standard cost category

(Fig. 4.2.3.1).

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Figure 4.3.3.1 - Percentage of Each SCC to the Total Cost (Booz Allen & Hamilton, 2003 & 2004)

In order to improve the accuracy of the ITI, five sources have been selected to develop the

values for the five main categories. ENR’s BCI was used for category 01 Construction; the

Bureau of Labor Statistics’ electric power distribution price index was selected for 02 Systems;

the House Price Index from the Office of Federal Housing Enterprise Oversight was chosen

for 03 Real Estate; Public Transportation statistics published by American Public

Transportation Association (APTA) was selected for 04 Vehicle; and Employment Cost

Index for Private-Sector and Professional subgroup was chosen for 05 Soft Cost. For each of

these categories, historical data have been collected; however, due to the limited availability

of data, this research only utilizes data from 2004 onward. In order to obtain a weighted

composite cost index, the data has been adjusted to index values with a 2004 benchmark

value of 100. After applying the weight percentage values shown in Table 4.2.3.1, the ITI

and the percent changes for the ITI were computed and presented in Table 4.2.3.2.

Series1, SCC 10, 25.55%

Series1, SCC 20, 2.88%


Series1, SCC 40, 18.57% Series1, SCC 50,

9.06%



Series1, SCC 80, 25.28%

Percentage of Each SCC to the Total Cost (Average of 51 Transit Projects in the U.S.)

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Table 4.3.3.2 - Integrated Transit Index and Percent Changes

Categories 01 02 03 04 05 Index Percent Change

Percentage 57.00% 9.00% 4.00% 5.00% 25.00% 100.00%

Year Index Adjusted Index Adjusted Index Adjusted Index Adjusted Index Adjusted

2004 3,984.0 100.0 102.5 100.0 229.0 100.0 387,307.0 100.0 95.3 100.0 100.0

2005 4,205.0 105.5 107.1 104.5 260.8 113.9 339,756.7 87.7 99.1 104.0 104.5 4.4974%

2006 4,369.0 109.7 115.1 112.3 273.0 119.2 358,291.0 92.5 102.5 107.5 108.9 4.1967%

2007 4,485.0 112.6 118.9 116.0 275.2 120.2 421,811.0 108.9 106.2 111.4 112.7 3.5175%

2008 4,691.0 117.7 124.8 121.8 261.1 114.0 389,561.6 100.6 109.4 114.7 116.3 3.2248%

2009 4,769.0 119.7 127.7 124.6 250.0 109.1 432,624.4 111.7 111.2 116.7 118.6 1.9123%

2010 4,883.0 122.6 130.6 127.4 248.0 108.3 505,187.6 130.4 112.9 118.5 121.8 2.7223%

Mean 3.3452%

St. Dev. 0.9527%

As shown in Table 4.2.3.2, the average annual percent change for the ITI during 2004-2010

was 3.3452% with a standard deviation of 0.9527%, which is more or less consistent with

currently used indices such as BCI and CCI. Smaller changes in recent years, especially in

2009, are due to the economic slowdown in that time period. The ITI is superior to other

general indices because it considers all major elements of a transit project according to their

proper weight in order to model the change in price.

4.3.4 Forecast with Time Series Analysis and Neural Network

Since the research mainly focuses on transit projects, the long development phase can easily

cause the project’s duration to last more than 10 years. Using current indices to model the

escalation costs for the subsequent 10 years does not seem convincing. Several forecasting

approaches were reviewed for the purpose of selecting a method for estimating the

escalation factor in the future. Two approaches were used for this purpose: (1) time series

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analysis and (2) neural networks. It should be noted that due to the uncertainties, forecasting

the escalation for 20 years is very challenging if not impossible. The two methods proposed

here are aimed to improve the accuracy but not provide the perfect predictions. According

to Stergiou and Siganos (1996), the artificial neural network method, inspired by the

biological nervous system, aims to produce a human-brain-like paradigm to process

information. Using existing input and output data, the artificial neural network will be

trained to perform forecasting. Neural networks have become increasingly popular for

prediction purposes. Karunanithi et al. (1992) applied neural networks in reliability

prediction. Maier and Dandy (2000) reviewed 43 papers dealing with the use of neural

networks to predict and forecast water resources variables. Adebiyi et al. (2012) proposed a

neural network approach for stock prediction.

Taylor and Bowen (1987) categorized the predictive modeling into two groups: the causal

method and the time series method. In a causal method, certain independent explanatory

variables are used to decide the predicted variables. The relationship between the

independent explanatory variables and the predicted variables can be modeled by regression

approaches, although regression models are not necessarily causal; however, the time series

method suggests that past data can determine future outcomes (Wong et al., 2005). Using

this method, Ashuri and Lu (2010) have examined ENR’s CCI. Hwang (2011) proposed a

time series analysis model for construction cost index prediction. Researchers and scholars

have also applied time series models in various industrial fields (Box & Jenkins, 1976; Chin

& Mital, 1998).

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4.3.4.1 Neural Network

The first approach for forecasting the cost index is the use of artificial neural network. Two

types of neural networks have been used for comparison: General Regression Neural

Networks (GRNN) and Multi-layer Feed-forward Neural Networks (MLF). GRNN is

considered to be a useful tool due to its ability to converge to the underlying function when

available data is limited (Specht, 1991). MLF is the first and simplest neural network where

the signals move only in one direction and there are no cycle loops (Visual Numerics Inc.,

2012). With multiple layers of nodes, it can distinguish data that is not linear-separable.

Taking the first category 01 Construction, for example, the ENR’s BCI has been chosen for

analysis. For both neural networks, the inputs were the year (numerical variable) and month

(categorical variable), and the output was the BCI monthly values, BCI monthly changes, or

BCI monthly percent changes. After applying these two neural networks to monthly BCI

data from 2006 to 2010, the trained neural networks were used to predict the BCI values in

2011. MAPE is calculated to compare the predicted results with actual values; however, since

we need the actual BCI values in order to calculate our index, the predicted changes and

predicted percent changes are used to calculate BCI values. The forecasted values for BCI

monthly changes and BCI monthly percent changes will be applied to the BCI at the most

recent available time period; then, all of the predicted BCI values from that time period

onward can be obtained. The predicted results for BCI in year 2011 are shown in Table

4.2.4.1 where the MAPE has been computed for the sake of comparison.

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Table 4.3.4.1 - MAPE for BCI Prediction Using Neural Network

Data for training NN MAPE for BCI Prediction

GRNN MLF

BCI 3.93% 2.78%

BCI monthly changes 0.73% 0.31%

BCI monthly percent changes 0.23% 0.60%

Table 4.2.4.1 suggests that the two neural networks provide similar results; however, while

MLF generates better predictions using BCI and BCI monthly changes, GRNN works better

with BCI monthly percent changes.

4.3.4.2 Time Series Analysis

A time series analysis was also performed for the sake of comparison with the results

obtained by neural networks. Holt’s (double exponential smoothing) and Winter’s (triple

exponential smoothing) methods were selected here based on preliminary testing with

available data. For the simple moving average, the prediction was the unweighted mean of

previous observations. The exponential smoothing, however, assigned exponentially

decreasing weights over time, instead of equal weights as in the simple moving average. For

double smoothing, a trend smoothing factor with values larger than 0 and smaller than 1 is

introduced, while for triple exponential smoothing, a seasonal changes smoothing factor

with values larger than 0 is further added for analysis. Since it was believed that Holt’s and

Winter’s methods would provide better predictions in this case, these two time series analysis

methods have been utilized in this research. Moreover, it should be noted that Winter’s

method assumes that the series are positive, and thus Winter’s method is not applicable to

BCI monthly changes or BCI monthly percent changes.

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Results of the BCI prediction for year 2011 using these two methods are presented in Table

4.2.4.2. Holt’s method generally provides better results than Winter’s. Results obtained by

using Holt’s method are also better than GRNN, except for BCI monthly percent changes;

however, MLF is the strongest in predicting the index when working with BCI monthly

changes. It was decided to keep both neural networks and time series analysis; however, only

the best results, based on statistical results, in these two methods will be used for forecasting

the ITI.

Table 4.3.4.2 - MAPE for BCI Prediction Using Time Series Analysis

Data for Time Series Analysis MAPE for BCI Prediction

Holt’s Winter’s

BCI 0.43% 0.71%

BCI monthly changes 0.42% -

BCI monthly percent changes 0.36% -

4.3.5 Forecasting Integrated Transit Index Results

By applying both methods to the four other main categories, we obtained the forecasted

values for each category. Using percentage values for each category shown in Table 4.2.3.1,

we could also compute the forecasted ITI.

Tables 4.2.5.1 and 4.2.5.2 present the predictions for ITI using neural networks and time

series analysis.

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Table 4.3.5.1 - ITI Prediction Using Neural Networks

Year 10-40 BCI 50

SYSTEMS

60 ROW, LAND, EXISTING

IMPROVEMENTS 70 VEHICLES

80 PROFESSIONAL

SERVICES Index

Percentage 57.00% 9.00% 4.00% 5.00% 25.00% 100.00% %

Change

2004 3984 100.0 103 100.0 229 100.0 387,307.00 100.0 95 100.0 100.0

2005 4205 105.5 107 104.5 261 113.9 339,756.74 87.7 99 104.0 104.5 4.50%

2006 4369 109.7 115 112.3 273 119.2 358,290.99 92.5 102 107.5 108.9 4.20%

2007 4485 112.6 119 116.0 275 120.2 421,810.99 108.9 106 111.4 112.7 3.52%

2008 4691 117.7 125 121.8 261 114.0 389,561.64 100.6 109 114.7 116.3 3.22%

2009 4769 119.7 128 124.6 250 109.1 432,624.35 111.7 111 116.7 118.6 1.91%

2010 4883 122.6 131 127.4 248 108.3 505,187.62 130.4 113 118.5 121.8 2.72%

2011 5017 125.9 134 130.7 239 104.5 543,045.16 140.2 115 120.8 124.9 2.58%

2012 5149 129.3 139 135.2 240 104.9 585,339.40 151.1 117 122.8 128.3 2.69%

2013 5280 132.5 143 139.8 242 105.5 631,629.15 163.1 119 125.0 131.8 2.69%

2014 5410 135.8 148 144.7 243 106.2 681,511.49 176.0 121 127.2 135.3 2.67%

2015 5541 139.1 153 149.7 245 106.8 734,601.52 189.7 123 129.4 138.9 2.65%

2016 5673 142.4 159 154.9 246 107.5 790,527.05 204.1 126 131.7 142.5 2.64%

2017 5806 145.7 164 160.3 248 108.2 848,932.13 219.2 128 134.0 146.3 2.63%

2018 5942 149.2 170 165.9 249 108.8 909,483.56 234.8 130 136.4 150.1 2.63%

2019 6081 152.6 176 171.6 251 109.5 971,876.71 250.9 132 138.8 154.1 2.62%

2020 6223 156.2 182 177.6 252 110.2 1,035,839.09 267.4 135 141.2 158.1 2.61%

2021 6368 159.8 188 183.7 254 110.9 1,101,131.41 284.3 137 143.7 162.2 2.61%

2022 6517 163.6 195 190.1 256 111.6 1,167,546.65 301.5 139 146.2 166.4 2.60%

Mean 5284 132.6 146 142.7 251 109.4 675,579.09 174.4 119 124.7 132.7 2.87%

St. Dev 758 19.0 28 27.0 11 4.9 268,809.57 69.4 13 13.6 20.1 0.62%

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Table 4.3.5.2 - ITI Prediction Using Time Series Analysis

Year 10-40 BCI 50

SYSTEMS

60 ROW, LAND, EXISTING

IMPROVEMENTS 70 VEHICLES

80 PROFESSIONAL

SERVICES Index

Percentage 57.00% 9.00% 4.00% 5.00% 25.00% 100.00% %

Change

2004 3984 100.0 103 100.0 229 100.0 387,307.00 100.0 95 100.0 100.0

2005 4205 105.5 107 104.5 261 113.9 339,756.74 87.7 99 104.0 104.5 4.50%

2006 4369 109.7 115 112.3 273 119.2 358,290.99 92.5 102 107.5 108.9 4.20%

2007 4485 112.6 119 116.0 275 120.2 421,810.99 108.9 106 111.4 112.7 3.52%

2008 4691 117.7 125 121.8 261 114.0 389,561.64 100.6 109 114.7 116.3 3.22%

2009 4769 119.7 128 124.6 250 109.1 432,624.35 111.7 111 116.7 118.6 1.91%

2010 4883 122.6 131 127.4 248 108.3 505,187.62 130.4 113 118.5 121.8 2.72%

2011 5046 126.6 134 130.7 238 103.8 510,851.49 131.9 115 120.8 124.9 2.55%

2012 5204 130.6 139 135.7 231 100.9 533,665.51 137.8 117 122.3 128.2 2.62%

2013 5368 134.7 144 140.7 224 97.9 557,499.67 143.9 118 123.6 131.5 2.58%

2014 5537 139.0 149 145.8 217 94.8 582,395.60 150.4 119 124.7 134.8 2.54%

2015 5711 143.3 155 151.2 210 91.7 608,406.92 157.1 120 125.4 138.2 2.50%

2016 5890 147.9 161 156.8 203 88.5 635,579.53 164.1 120 125.9 141.6 2.47%

2017 6076 152.5 167 162.5 195 85.2 663,962.65 171.4 120 126.1 145.1 2.44%

2018 6267 157.3 173 168.5 188 81.9 693,613.63 179.1 120 126.0 148.6 2.42%

2019 6464 162.2 179 174.7 180 78.6 724,591.29 187.1 120 125.7 152.1 2.40%

2020 6667 167.3 186 181.2 173 75.3 756,953.19 195.4 119 125.1 155.7 2.38%

2021 6877 172.6 193 187.9 165 72.0 790,760.73 204.2 118 124.2 159.4 2.36%

2022 7093 178.0 200 194.8 157 68.8 826,076.60 213.3 117 123.0 163.2 2.35%

Mean 5452 136.8 148 144.1 220 96.0 564,152.43 145.7 114 119.2 131.9 2.76%

Std. Dev. 942 23.6 29 28.6 37 16.0 152,082.69 39.3 8 8.1 19.1 0.67%

When comparing Tables (4.2.5.1) and (4.2.5.2), the average percent change predicted by time

series analysis is 2.76%, which is lower than the 2.87% predicted by neural networks. The

actual ITI for 2011, calculated using the latest available information, was computed as 124.2.

After comparing the actual index value with the forecast value of 124.9 obtained by both

neural network and time series analysis, it is clear that the results are quite convincing.

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4.3.6 Summary

A new composite cost index called the ‘Integrated Transit Index’ (ITI) is proposed in this

research to improve the accuracy of cost escalation estimates for transit projects. The project

cost has been broken down into 5 main categories based on the FTA’s SCC. For each of the

categories, one specific source has been selected to model the cost component. The

weighted values of each category can be used to calculate the composite ITI. Due to the

limited availability of data, only data from the past 6 years have been applied in this process.

The index can be improved as more data becomes available.

Another major issue with escalation estimates in transit projects is their long duration. Using

current data to forecast transit projects in the future is not convincing; however, it is

believed that with forecasted ITI, cost estimates for future transit projects could be achieved

with greater accuracy. By applying both neural networks and time series analysis, the ITI has

been forecasted for the next 10 years. These forecasted values can help engineers and

estimators with preparing cost estimates for transit projects.

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CHAPTER 5 : BAYESIAN UPDATING FOR PORTFOLIO PROJECTS

5.1 Introduction

In this chapter, a mathematical model is proposed that uses Bayesian updating to perform

project cost and schedule updates. Bayesian updating was selected for this decision support

system due to the fact that the original estimates are usually based on assumptions that may

not materialize. Bayesian updating can combine historical information when preparing

original estimates and new observations as projects progress to achieve more accurate

estimates. Both project cost and duration were modeled as normal distributions. Each time

a new report was provided, an underlying normal distribution was also modeled. These two

distributions were then used to compute a new normal distribution, which is considered as

the most up-to-date estimate for project cost or duration. Eight projects from the East Side

Access project in New York City were selected to demonstrate this method. Forecasted

progress curves were generated by the newly obtained distribution and plotted. It should be

noted that the updating process needs to be performed repeatedly throughout the portfolio

life cycle. By constantly revising the estimates, we can achieve greater accuracy. This method

is believed to be quite beneficial not only for single projects but also portfolios.

5.2 Background

When engineers are preparing an estimate for project cost, the price information for the

building materials that they use are either current or from the past. In order to provide a

125

reasonable estimate of the cost for a project that will take place in the future, certain

assumptions must be made; however, the material costs in reality might change rapidly for

reasons such as supply and demand in the market and inflation. In order to stay current with

project’s financial needs, one must update the original estimate with new information as it

becomes available. Bayesian updating can combine the information used for the original

estimate and the new information obtained during the project life cycle in order to achieve

better predictions.

According to Ang and Tang (2007), when using classical statistical methods, the estimate for

distribution parameters is based on the assumption that these parameters remain constant

but unknown. Point or interval estimates could be obtained, but inevitably these estimates

can be imperfect, which is demonstrated by using confidence intervals to present the degree

of error. In most practical cases, engineers are working with limited data when preparing

estimates. Thus, observational information can be quite valuable and play a vital role in

achieving more accurate estimates; however, classical statistical methods are inadequate

when it comes to combining observational information with information obtained by using

classical statistical methods in regard to estimating distribution parameters because classical

statistical methods assume parameters are constant but unknown. That is why Bayesian

updating was selected to solve this issue.

Over a project’s life cycle, engineers commonly update original estimates for project cost and

schedule by using observational information. During the lengthy design process, especially in

large infrastructure projects such as transit projects, the estimates are revised and updated

several times. Each time a new estimate is prepared, some new information about project

characteristics, stakeholders, and politics is considered. It is hoped that, at every stage, a new

126

estimate will be more accurate and realistic because it is based on more information about

the project. Bayesian updating could be particularly helpful in transit projects where the

project duration is usually lengthy and many of the assumptions are subjective.

5.3 Bayesian Updating Concept and Mathematical Formulations

5.3.1 Bayesian Updating Concept

When engineers are preparing an estimate for distribution parameters, even if only limited

data is available, engineers can usually still provide possible values, or at least ranges, for

those parameters. These original estimates provide a basis for the updating process, which is

to be supplemented with observational data.

The basics of the Bayes’ theorem can be presented as follows:

( ) ( )( | )

( )

P X PP X

P X

(5.3.1.1)

where ( )P is the probability density function for parameter , also known as the prior,

( | )P X is the probability of observations X given parameter , or the likelihood function,

and ( | )P X is the posterior. Since ( )P X is considered as a constant, the whole formula can

be written as:

(5.3.1.2)

where posterior probability is proportional to the product of prior probability and likelihood function.

5.3.1.1 Continuous Distribution

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In the previous section, an estimated parameter with discrete possible values has been

discussed; however, in reality, the parameter could have continuous possible values.

Consequently, the assumption of continuous random variable is also examined.

As suggested by Ang and Tang (2007), in continuous cases, let’s assume to be the random

variable for the parameter of a distribution, with a prior density function (pdf) )(f . As

shown in Figure (5.3.1.2), has a prior probability of ).( if to fall in between i and

i . If is the observed outcome of the experiment, Bayes’ theorem can help with

modifying the prior distribution )(f to get the posterior probability that will be within

the range of i and i as follows:

1

( ) ( )( ) 1,2,...,

( ) ( )

i i

i n

i i

i

P ff i n

P f

(5.3.1.1.1)

where ( ) ( )i i iP P .

Figure 5.3.1.1 - Continuous prior distribution of parameter (Ang & Tang, 2007)

When considering the limit, this equation changes to the following:

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( ) ( )( )

( ) ( )

P ff

P f d

(5.3.1.1.2)

Since )( P is the conditional probability of observing as the outcome of the experiment,

assuming that the parameter value is , it is named the likelihood function of and

represented by L( ). Also, the denominator is a normalized constant to make ( )f a

proper density function and totally independent of . As a result, by introducing a

normalizing constant k ( 1])().([

dfPk ), we can transform the formula into:

( ) ( ) ( )f kL f (5.3.1.1.3)

where ( )L is the likelihood of observing as the outcome of the experiment when

assuming a given .

As shown in the equations for both discrete and continuous cases, the observed data has

been systematically implemented into the formulas, with the terms ( )f and ( )L ,

respectively.

5.4 Bayesian Updating for a Single Transit Project in a Portfolio

5.4.1 Mathematical Concept

After the portfolio project’s network is established, it is understood that the original estimate

is based on limited data at the beginning of the project. The distributions for each project’s

duration and cost can be considered as prior probability for the parameters. It is reasonable to

believe that, as the project progresses, more observational information and data will become

available, which can be combined with prior probability to obtain posterior probability.

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In this research, three phases have been considered: Draft Environmental Impact Statement

(DEIS), Preliminary Engineering (PE), and Final Design (FD). As the common development

phases for transit projects in the United Sates, they are commonly interpreted as follows:

DEIS is almost the same as the conceptual design phase; PE is when about 30% of the

design has been completed; and FD represents the time where the project design phase has

ended and the project is going out for bids in traditional design-bid-build contracts (Touran

& Zhang, 2011). It is assumed that the prior probability here is equivalent to the estimates

prepared in the DEIS phase in regard to project cost and duration. At the PE and FD

phases, two newly obtained observations were provided, and these will be transformed into

likelihood functions. In order to archive updates for project cost and duration, the posterior

probability at the PE phase can be computed using the prior probability at the DEIS phase and

the likelihood function at the PE phase. For updates at the FD phase, the posterior probability

from the previous update at the PE phase will now be considered as prior. Applying the

likelihood function at FD, we can now obtain the posterior probability at the FD. If more data

is observed in the future, then the posterior probability at FD will be considered as prior for the

next update.

Normal distribution has been selected here to model project cost and duration. It should be

noted that Bayesian updating has closed form solutions for conjugated distributions, and

normal distributions used for both prior and posterior meet the requirements, as well as

being used extensively in prior research. In order to apply this approach, a coefficient of

variation must be defined because most of the time, only one estimator is available and a

fixed number will be provided for project cost and duration. Not only does Prior need to be

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defined as a normal distribution but so do the likelihood functions. If multiple estimators are

available, then the likelihood functions can be easily obtained. Based on 28 transit projects

published by Booz Allen (2004), the normality assumptions can be assumed. It should be

noted that normal distribution is actually not a perfect choice, as it ranges from negative

infinity to positive infinity; however, about 99.7% of observations will fall within three

standard deviations of the mean, so the normality assumption will not produce negative

results. For normal distributions with known , the posterior mean and variance of

parameter can be obtained using Eqs. (5.3.1.1) and (5.3.1.2):

2 2

22

( / )

( / )

n x

n

(5.4.1.1)

22

22

( / )

( / )

n

n

(5.4.1.2)

where and are prior mean and standard deviation of parameter, respectively, and x

and are observational outcome mean and standard deviation, respectively.

It should also be noted that the normality assumption can be changed, and other

distributions can be chosen to model project cost and duration if more information is

available, such as historical data. A coefficient of variation will be assumed for both project

duration and cost. In this research, historical data for 28 transit projects, published by Booz

Allen (2004), has been used to assist with estimating the coefficient of variation. According

to the historical data, the average cost overrun from the DEIS phase to final completion is

about 20.36% and the coefficient of variation is about 1.10. As a result, the standard

deviation at the DEIS phase may be calculated by using estimated mean value at DEIS phase

131

to multiply the average cost overrun (20.36%) and the coefficient of variation (1.10). This

standard deviation will be used to model the prior probability; however, it should be noted that

as projects progress, some observations can be obtained to update the project cost and

duration. For these observations, if multiple observations are available, the likelihood

function can be easily obtained. If only one observation is available, then a standard

deviation will be assigned to the observation and a likelihood function can be defined. Based

on the Booz Allen data, the average cost overrun and coefficients of variation have been

listed in Table (5.4.1.1).

Table 5.4.1.1 - Standard Deviation Assumptions

Project Phases Cost Overruns Schedule Delays

Mean Coef. of Var. Mean Coef. of Var.

DEIS 20.36% 1.10 23.33% 0.57

PE 13.59% 1.46 12.84% 1.11

FD 7.64% 2.15 4.36% 2.50

5.4.2 Application

In this research, 28 transit projects published by Booz Allen were used to provide estimates

of the standard deviations (Table 5.4.1.1). For the application, 8 projects located in the

Manhattan area, as a part of the East Side Access Project, were selected to demonstrate the

methodology. Although these project are considered as a portfolio in this analysis, the East

Side Access Project is in fact a much larger program, which will “connect the Long Island

Rail Road's (LIRR) Main and Port Washington lines in Queens to a new LIRR terminal

beneath Grand Central Terminal in Manhattan” (MTA, 2012). The cost data for these 8

projects are all based on estimates prepared in March 2006 (Table 5.4.2.1). Changes and

132

revisions to these projects’ scope or description might have occurred later on several

occasions; however, the data is used here just for demonstration purposes. The network has

also been input into the Excel decision support system, and the Gantt chart is provided in

Figure (5.4.2.1).

Table 5.4.2.1 – Information on the 8 Projects in Manhattan

Project Description Cost (in 2004 US $)

Duration (Years)

GCT Concourse Civil & Structural 368,672,927 3.4

Manhattan Tunnel Excavation 419,462,465 3.8

GCT Caverns, 63rd St. Tunnel Rehab & Bellmouth 362,222,311 3

55th Street Vent Plant 43,360,944 1.8



GCT Concourse and Cavern Finish 210,847,181 3.5

GCT Surface Entrances 61,197,434 3.3

Figure 5.4.2.1 - Gantt Chart for 8 Projects in Manhattan

Taking the first project, Project 1 (GCT Concourse Civil & Structural) in this portfolio, for

example, the project cost and duration were originally estimated at 3.4 years and $369M. Due

to the normality and coefficient of variation assumptions, the standard deviations for the

normal distributions can be obtained by multiplying the project costs and durations in Table

133

(5.3.2.1) with respective overrun mean and coefficient of variations in Table (5.3.1.1). To

model Project 1’s cost and duration, two normal distributions are created [Normal (3.40,

0.73) and Normal(368.67, 82.25)]. Like the likelihood functions, based on observations,

project cost and duration are also modeled as normal distributions with coefficients of

variation at the PE and FD phases according to Table (5.4.1.1), respectively.

After Project 1 starts, more observational data and information will become available, based

on which a new estimate for the parameters can be established. Assuming that the following

estimates for project cost and duration in Table (5.4.2.2) have been obtained at the PE and

FD phase, respectively, these new estimates will be used to update the prior probability to

obtain the posterior probability using Bayesian inference.

Table 5.4.2.2 - Prior and Observations at Different Phases for Project 1

Schedule (Years) Cost (Dollars)

Phase Mean Std. Dev. Mean Std. Dev.

Prior 3.4000 0.4543 368.67 82.25

PE 3.9002 0.5577 425.09 84.44

FE 4.3388 0.4726 465.65 76.53

Since the new estimates occurred at various times, it is believed that they can be used to

modify the prior probability one at a time. Taking DEIS, for example, the parameters for prior

and

are given as 3.4000 and 0.4543, respectively, for project schedule. Likelihood

function parameters x and for Project 1’s schedule are also provided as 3.9002 and

0.55770, respectively. Using Eqs. (5.4.1.1) and (5.4.1.2), the posterior probability can be

obtained at PE (Fig. 5.4.2.2). The mean and standard deviation for PE posterior are 3.5995

and 0.3522, respectively (Eqs. 5.4.2.1 and 5.4.2.2).

134

2 2

22

3.4000 (0.5577 ) 3.9002 0.45433.5995

(0.5577 ) 0.4543

(5.4.2.1)

2 2

2 2

0.4543 (0.5577 )0.3522

0.4543 (0.5577 )

(5.4.2.2)

Figure 5.4.2.2 - Prior, Likelihood and Posterior Distributions for Schedule

According to Touran et al. (2004), construction projects’ planned S-curve can be modeled

using a beta distribution with a shape factor of 1.7 and 1.85. As a result, with specified

boundaries for the Beta distribution, the yearly expenditure can be generated and an S-Curve

can then be calculated. The schedule information obtained in the previous step can be used

to define the boundaries of the Beta distribution, based on which, a progress curve can be

generated. The posterior (forecast values) is also plotted against the prior (plan) to compare the

differences in Figure (5.4.2.3). It should be noted the forecast curve in Figure (5.4.2.3)

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

-0.2

35

0.07

5

0.38

5

0.69

5

1.00

5

1.31

5

1.62

5

1.93

5

2.24

5

2.55

5

2.86

5

3.17

5

3.48

5

3.79

5

4.10

5

4.41

5

4.72

5

5.03

5

5.34

5

5.65

5

5.96

5

6.27

5

6.58

5

6.89

5

7.20

5

7.51

5

7.82

5

Prior, Likelihood, and Posterior Distributions

Prior Posterior Likelihood

135

consists of actual data for the completed part of the project and forecasted data for the

incomplete part.

Figure 5.4.2.3 - Schedule Progress Curves for Plan and Forecast Distribution

Even though the two curves are close to each other, it is found that the Forecast curve has a

cumulative probability of almost 1 at year 3.6, which is slightly longer than the Plan curve’s

3.4 years. The 10 and 90 percentile values are also plotted for the Plan and Forecast (Fig.

5.4.2.4). It is shown that the Forecast duration range has decreased. The new range from 10

to 90 percentile is between 3.15 and 4.05 years, compared to the planned range that was

between 2.82 years and 3.98 years.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Schedule Progress Curves

Planned Forecast

136

Figure 5.4.2.4 - Duration Range for Project 1

The same method has been applied to project cost, and the mean and standard deviation for

the posterior of project cost are calculated as $396M and $58.9M, respectively (Fig. 5.4.2.5).

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

3.0000

3.5000

4.0000

4.5000

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Total Duration Range

Planned 10% Planned 90% Forecast 10% Forecast 90%

137

Figure 5.4.2.5 - Prior, Likelihood and Posterior Distributions for Cost

Since we have a Beta distribution, the project cost can be distributed among these years.

Consequently, the Cost S-Curve for Project 1 is obtained (Fig. 5.4.2.6).

0.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

-43

13

69

125

181

237

293

349

405

461

517

573

629

685

741

797

853

909

965

1,0

21

1,0

77

1,1

33

1,1

89

1,2

45

1,3

01

1,3

57

1,4

13

Prior, Likelihood, and Posterior Curves


138

Figure 5.4.2.6 - Cost S-Curves for Plan and Forecast Distribution

The S-curves in Fig. (5.4.2.6) indicate that Project 1 is likely to encounter a cost overrun. The

project cost range is also prepared, and presented in Fig. (5.4.2.7).

Figure 5.4.2.7 - Cost Range for Project 1

0

50

100

150

200

250

300

350

400

450

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 6.4 6.8

Cost S-Curves

Planned Forecast

-

100

200

300

400

500

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Total Cost Range


139

It is shown in Figure (5.4.2.7) that the cost range decreased and the 90 percentile value

decreased, but the 10 percentile value increased. The new cost range for Project 1 is from

$321M to $472M, as compared to the plan cost range of $263M to $474M.

The same steps can be applied to FD observational data. As the posterior probability obtained

from PE will now be considered as the prior, the data observed at FD will be considered as

observations following the likelihood function. Using Eqs. (5.4.1.1) and (5.4.1.2), parameters

of a new posterior can be calculated at FD. The posterior parameters (i.e., mean and standard

deviation) will then be considered as prior if more observations become available in the

future. It was found that the schedule posterior at FD is a normal distribution with a mean and

standard deviation of 3.864 and 0.282 years, respectively. The cost posterior was a normal

distribution with a mean and standard deviation of $422M and $46.7M, respectively.

5.5 Bayesian Updating for a Portfolio of Transit Projects

5.5.1 Mathematical Concept

Let us now consider a portfolio of transit projects. Because these projects are components

of a larger transit program, a precedence network can be generated for the program schedule.

To simplify the Bayesian updating process, it is assumed that the projects are largely

independent, and projects attributes such as resources, costs, labor, and equipment are

considered to have no interference with each other, except for the scheduled start where a

relationship between two projects can be defined as Finish to Start, Start to Start, Finish to

140

Finish, or Start to Finish. This is a limitation of the current updating model. However,

agencies like the FTA have projects all over the country. Such portfolios can be assumed to

be relatively independent. So the proposed system can be applied to most of the FTA annual

roster of projects in the United States. It is acknowledged that same labor pools and

equipment may be used by more than one project; however, it is assumed that these issues

have been taken into consideration when new cost and duration estimates were prepared.

The new estimates are applied to the original estimates to obtain revised estimates for

project cost and duration. Thus, for the portfolio, the total project cost can be obtained by

summing the costs of all projects; however, for the total duration, only projects on the

critical path(s) will be considered.

Portfolio’s total cost C can be calculated using Equations (5.5.1.1) and (5.5.1.2) for prior C

and posterior C , respectively.

1

( ) 1,2,...,m

i

i

C f c i m

(5.5.1.1)

1 1

( ) ( ) ( ) 1,2,...,m m

i i i

i i

C f c kL c f c i m

(5.5.1.2)

where m is the number of projects in a portfolio and ( )if c represents the probability

density function (pdf) of project cost.

Also, portfolio total schedule S can be calculated using Equations (5.5.1.3) and (5.5.1.4) for

prior S and posterior S , respectively.

1

( ) 1,2,...,p

i

i

S f s i p

(5.5.1.3)

141

1 1

( ) ( ) ( ) 1,2,...,p p

i i i

i i

S f s kL s f s i p

(5.5.1.4)

where p is the number of projects on the critical path(s) in a portfolio and ( )if s represents

the pdf of a project duration. It should be noted that critical path can change, and all

potential critical paths need to be examined.

5.5.2 Applications with PMDSS

Eight projects in Manhattan were selected for demonstration. The schedule and cost data is

shown in Table (5.4.2.1) and the network is presented in Figure (5.4.2.1). Two major aspects

of this study’s PPM analysis are project duration and cost. For both of these aspects, the

contingency levels have been established throughout the project life cycle. Also, a Bayesian

updating process has been used to update the original estimates in order to obtain the latest

estimates for both duration and cost. All of these analyses can be implemented in an Excel

toolkit developed for PPM in this research. This system, named the Portfolio Management

Decision Support System (PMDSS), provides not only basic project information about

project cost and schedule for each project in a portfolio but also contingency analysis,

Bayesian updating, escalation analysis and rankings of the projects in a portfolio.

Figure (5.5.2.1) shows the main steps of the contingency analysis and updating procedure

using the PMDSS. Basically, the original estimates will be used to generate a plan for both

project schedule and cost. The contingency can also be estimated according to the plan, after

which the singularity function will be used to produce a contingency drawdown curve for

each project in the portfolio. By summing up all of the contingency drawdown curves, the

142

total contingency can be obtained; however, as the projects progress, more information

becomes available; based on observational data, the original estimates can then be updated.

Bayesian updating is then applied to all of the projects to obtain updated cost and schedule

estimates. Then, these estimates are used to generate new contingency levels for the

portfolio throughout the project’s life cycle.

Figure 5.5.2.1 - Flow chart for Contingency Estimate Using PMDSS

In the developed system, the main file “PMDSS - General” will provide basic information,

such as start time, duration, and cost for all of the projects in this portfolio. These pieces of

information can be retrieved by other files in this decision support system. These estimates

Contingency

estimated for

each project in

a portfolio

Apply

singularity

function to

get

contingency

drawdown

curve for

one project

Sum up all

singularity

functions to

get total

contingency

Apply

escalation

factors to

get yearly

expenditure

Using

Bayesian

updating to

obtain

updated

project cost

and

schedule

Updating

the

contingenc

y using

new project

cost and

schedule

New total

Contingenc

y obtained

143

are considered to be prior, obtained with limited data. Also, after the updating process, new

estimates (i.e., posterior information) will be available in this spreadsheet to provide the most

up-to-date estimates for each project and the most up-do-date start time.

The “PMDSS - Contingency” file contains two main parts. First, it includes the cost

contingency in order to cover potential cost overruns. By using a singularity function to

model the shape of the contingency drawdown curve, it establishes the contingency level for

each project. Second, by combining the contingency levels of all projects, it obtains the total

cost contingency for the portfolio. After applying escalation factors, the final cost

contingency (Fig. 5.5.2.2) and yearly expenditure (Fig, 5.5.2.3) can be generated.

Figure 5.5.2.2 - Cost Contingency Drawdown for All Projects

0

100,000,000

200,000,000

300,000,000

400,000,000

500,000,000

600,000,000

0 2 4 6 8

To

tal

Co

nti

ng

en

cy

(d

oll

ars)

Duration (years)

Cost Contingency Drawdown For All Projects

Contingency Mean

144

Figure 5.5.2.3 - Year Expenditure for the Portfolio

A similar approach can also be applied to schedule; however, one major difference here is

that in calculating schedule contingency, the project critical path must be considered. First,

all possible critical paths will be identified. A Monte Carlo simulation will be conducted on

the schedule. For each iteration of the MC simulation, the longest path can be identified and

used to perform the schedule analysis; however, the critical path may be different for various

simulation runs. Since the goal is to identify the duration for the whole portfolio, only the

longest path is of interest in this analysis. As a result, all possible critical paths should be

included in this analysis. Figure (5.5.2.4) shows the schedule contingency drawdown for the

portfolio. It should be noted that the drawdown curve in Figure (5.5.2.4) only shows the

mean values of portfolio schedule contingency due to the variability provided by MC analysis.

As shown in Figure (5.5.2.4), the critical path requires about 1.2 years contingency at the

beginning according to estimates at the DEIS phase. As the portfolio starts, the contingency

will either be consumed or shifted to the base estimate. At approximately year 8, the

0

100,000,000

200,000,000

300,000,000

400,000,000

500,000,000

600,000,000

1 2 3 4 5 6 7 8 9

Ex

pe

nd

itu

re (

do

llar

s)

Duartion (years)

Expenditure For the Portfolio

Cummulative Expenditure Yearly Expenditure

145

contingency becomes 0 as the projects have been completed. It should also be noted that

schedule and cost contingency for each individual project is calculated in the spreadsheet.

Figure 5.5.2.4 Schedule Contingency Drawdown for All Projects

At various updating periods, the most up-to-date posterior can be obtained. When only one

estimate is available, based on observational data, the posterior parameters can be easily

calculated using Equations (5.4.1.1) and (5.4.1.2). It is assumed that the estimate will follow a

normal distribution; however, sometimes in practice, a fixed number may be provided.

Unless the project is complete and the final cost and duration is fixed, the proposed

approach will transform the “fixed” estimate into a normal distribution. When multiple

estimators are available, they can input their new estimates for project cost and duration into

the spreadsheet. With the mean and standard deviation of the estimates being calculated,

Equations (5.4.1.1) and (5.4.1.2) could again be applied to obtain the posterior. Estimators

may have different estimates regarding the project cost and schedule based on the data they

obtain and the experience they have. These variations in estimating will not be considered as

errors but rather as opinion-based estimates. With multiple inputs from estimators, the

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 2 4 6 8

To

tal

Co

nti

ng

en

cy

(y

ear

s)

Duration (months)

Schedule Contingency Drawdown for All Projects (in Years)

Contingency Mean

146

accuracy is expected to be improved. The combination of subjective input and objective

measures of project progress could be beneficial for projects. It should also be noted that a

new posterior will be obtained in each update. That is to say, whenever an update is prepared,

a posterior can be obtained for the rest of the project; however, this posterior is considered as

effective until the next update, whereupon this “old posterior” will be treated as prior and

used to calculate the new posterior for the incomplete remainder of the projects, excluding

those projects that are complete or have not been started yet. In order to obtain the forecast

S-Curve, the user must identify the time when the update is prepared. After the update time

is identified, the S-curve from that point on should differ from the older S-Curve. By doing

this, one can compare the forecast S-curve (with projection) against the planned S-curve.

Figures (5.5.2.4) and (5.5.2.5) show the Bayesian updating outcomes for schedule at PE and

FD. The duration increased from about 7 to 7.4 years after the update at PE, and further

increased to about 8.2 years after the update at FD. Thus, the portfolio of projects is

expecting delays.

147

Figure 5.5.2.4 - Planned vs. Forecast Schedule Curve for the Portfolio at PE

Figure 5.5.2.5 - Planned vs. Forecast Schedule Curve for the Portfolio at FD

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Schedule Curves

Planned Forecast

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Schedule Curves

Planned Forecast

148

With more information becoming available, the variance of outcome is expected to diminish;

consequently, the range of the estimate will become smaller than the original estimate (Figs.

5.5.2.6 and 5.5.2.7). As shown in Figure (5.5.2.6), the x- and y-axes represent time and

duration in years, respectively. As time goes by and updates are made, the range for the

duration estimates changes. The 10 and 90 percentile values for the original estimates are in

blue and red, respectively, which are based on the original plan and remain constant, while

the percentiles for forecast estimates are in green and purple, respectively. The ranges

become even smaller after the second update at FD.

Figure 5.5.2.6 – Portfolio Duration Range at PE

0

2

4

6

8

10

12

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0



149

Figure 5.5.2.7 – Portfolio Duration Range at FD

The updating process at PE for the portfolio can also be observed in Figures (5.5.2.8) and

(5.5.2.9), where the x-axis values are the possible values for project duration and the y-axis

represents the probability of observing these values and cumulative probability, respectively.

Figure 5.5.2.8 - Prior, Likelihood, and Posterior Curves at PE

0

2

4

6

8

10

12

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0



0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

3.84

8

4.17

8

4.50

8

4.83

8

5.16

8

5.49

8

5.82

8

6.15

8

6.48

8

6.81

8

7.14

8

7.47

8

7.80

8

8.13

8

8.46

8

8.79

8

9.12

8

9.45

8

9.78

8

10.1

18

10.4

48

10.7

78

11.1

08

11.4

38

11.7

68

12.0

98

12.4

28

12.7

58



150

Figure 5.5.2.9 - Prior, Likelihood, and Posterior Cumulative S-Curves at PE

After the PE update, another at FD will be applied at FD. Figures (5.5.2.10) and (5.5.2.11)

indicate the probability of observing these values and cumulative probability, respectively.

Figure 5.5.2.10 - Prior, Likelihood, and Posterior Curves at FD

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

3.84

8

4.18

8

4.52

8

4.86

8

5.20

8

5.54

8

5.88

8

6.22

8

6.56

8

6.90

8

7.24

8

7.58

8

7.92

8

8.26

8

8.60

8

8.94

8

9.28

8

9.62

8

9.96

8

10.3

08

10.6

48

10.9

88

11.3

28

11.6

68

12.0

08

12.3

48

12.6

88



0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

3.84

8

4.18

8

4.52

8

4.86

8

5.20

8

5.54

8

5.88

8

6.22

8

6.56

8

6.90

8

7.24

8

7.58

8

7.92

8

8.26

8

8.60

8

8.94

8

9.28

8

9.62

8

9.96

8

10.3

08

10.6

48

10.9

88

11.3

28

11.6

68

12.0

08

12.3

48

12.6

88



151

Figure 5.5.2.11 - Prior, Likelihood, and Posterior Curves at FD

Again, for the updating process, the project total cost and total duration are the major

concerns. On the first sheet in this spreadsheet, the information has been provided to give

an overview of what the total cost and duration might look like (Fig. 5.5.2.12).

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

3.84

8

4.18

8

4.52

8

4.86

8

5.20

8

5.54

8

5.88

8

6.22

8

6.56

8

6.90

8

7.24

8

7.58

8

7.92

8

8.26

8

8.60

8

8.94

8

9.28

8

9.62

8

9.96

8

10.3

08

10.6

48

10.9

88

11.3

28

11.6

68

12.0

08

12.3

48

12.6

88



153

Figure 5.5.2.12 – Key Components on the First Worksheet of the Spreadsheet

As discussed earlier in the chapter, the total cost can be easily obtained by using the sum of

all project costs in the portfolio; however, the schedule should only consider projects on the

critical path. There is always a possibility that one path which is unlikely to be critical in the

planning phase may somehow end up being critical later due to various factors such as

interruptions, regulations or project delays. To cover these scenarios, all possible paths will

be considered. When the MC simulation is applied, the duration for the longest path in each

iteration, also considered as the duration for the portfolio, will be obtained and used to

obtain the percentile values for total project duration.

Figure 5.5.2.13 - Project Schedule for the remainder of the Project (Percentile Values)

5.8000 6.0000 6.2000 6.4000 6.6000 6.8000 7.0000 7.2000 7.4000

5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 98%

Years

Pe

rce

nti

le

Project Schedule for Imcomplete Part (Percentile)

Percentile

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Another piece of information provided by the system (Fig. 5.5.2.13) is the duration for the

incomplete portion of the portfolio. This can be easily calculated by subtracting the most up-

to-date posterior for project duration from the date when the update is performed. For

example, the posterior is estimated with a mean of 8 years, and the update is prepared at the

end of year 2 after the portfolio starts. The duration for the incomplete part would probably

be a distribution with a mean of 6.4 years. These percentile values will provide project

managers with a better understanding in regard to the incomplete part of the project’s

schedule; however, it should be noted that not all projects are updated at the same time. For

example, at the end of 1.2 years after the portfolio starts, some of the projects have not even

started. Thus, the updating process should only be applied to those projects that have

actually started. The updating time here is not the same for all of the projects but rather for

the portfolio.

The Bayesian updating file will provide the latest information, which means that previous

updates will not be stored; however, one can save a copy for future reference each time an

update is executed.

Lastly, after an update has been completed, the next step is to return to “PMDSS - General”

and “PMDSS - Contingency” spreadsheets to obtain the latest estimates on project cost and

schedule. A new Gantt chart will be provided according to the latest information from the

update. Also, “PMDSS - Contingency” will have the latest estimates on project cost and

schedule contingency.

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5.6 Summary

The use of Bayesian updating in PPM was discussed in this chapter. The reason why

Bayesian updating was selected for the decision support system is because the original

estimate was prepared based on assumptions, which are uncertain by nature. Bayesian

updating was applied to both project cost and schedule to obtain the most up-to-date cost

and schedule estimates throughout the project’s life cycle. It is believed that better

predictions can be achieved by combining the information used for original estimate and the

new information obtained during the Bayesian updating of the project life cycle.

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CHAPTER 6 : THE PORTFOLIO MANAGEMENT DECISION SUPPORT SYSTEM

6.1 Introduction

By implementing the data into Excel, we developed the Portfolio Management Decision

Support System (PMDSS), which consists of four modules: (1) Portfolio Management Decision

Support System – General (PMDSS-G), (2) Portfolio Management Decision Support System – Bayesian

Updating (PMDSS-B), (3) Portfolio Management Decision Support System – Contingency (PMDSS-C)

and (4) Portfolio Management Decision Support System – Escalation (PMDSS-E). These four files

are closely interconnected with each other because much of the analysis requires the

utilization of all four files. The following sections discuss the modules included in this

system and explain their use.

6.1.1 The Four Modules of the PMDSS

The PMDSS-G contains general information for all projects in the portfolio, as well as

ranking orders for all projects, using the PROMETHEE-GAIA method. It contains both

Prior and Posterior information regarding each project’s duration, cost, and ranking. The

PMDSS-B is used to update project duration and cost. Users can input the most recent

estimate into this file, and a Bayesian updating algorithm provides new estimates for project

duration and cost by combining historical data and newly observed information. The new

estimates generated by this file are then applied to other files to generate desired analysis

results. In the PMDSS-C, cost and schedule contingency analyses are performed. Both Prior

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and Posterior contingency levels for project schedule and cost can be obtained in this module.

The PMDSS-E is for escalation analysis. The source data used for computing ITI are

provided, and forecast results can also be calculated using neural networks and time series

analysis. Figure (6.1.1.1) is a flowchart for the PMDSS system.

Figure 6.1.1.1 - Flowchart for PMDSS

PMDSS-C:

Define

contingency

levels at 3

phases

PMDSS-C:

Cost and

schedule

contingency

reports

PMDSS-B:

Update cost and duration

for each

project in portfolio

PMDSS-B:

Define possible

critical paths

PMDSS-B:

Updated cost

and schedule

reports

PMDSS-G:

Define cost

and duration for each

project in

portfolio

PMDSS-G: Define design

cost and

construction

cost

PMDSS-G: Define design

duration and

construction

duration

PMDSS-G:

Define escalation

rates

PMDSS-E:

Computations of

escalation rates

PMDSS-G: Yearly

expenditures

reports

PMDSS-G: Ranking

reports

PMDSS-G:

Ranking criteria

inputs

PMDSS-E:

Collecting

data for ITI

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6.2 Portfolio Management Decision Support System - General (PMDSS-G)

6.2.1 General Information

In the PMDSS-G module, the general information for all projects in the portfolio is

presented. This includes project duration, cost, yearly expenditure, and ranks. In the table

shown in Figure (6.2.1.1), users can enter project name, duration and cost as well as define

predecessors for each project and the relationship between the projects (e.g., finish to start,

start to start). The table calculates the start and end point for each project, and calculates the

total duration for the portfolio based on the information inputted.

Figure 6.2.1.1 - Project Information Table

A Gantt chart is then automatically generated (Fig. 6.2.1.2), with lighter blue bars

representing the design phase and darker blue bars representing the construction phase. In

this case, it is assumed that all of these projects belong to a program and they all start as

soon as the program starts. Figure (6.2.1.2) shows all of the projects’ design phases starting

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at the same time; however, the system is also applicable to projects that start at different

times despite belonging to the same portfolio. This situation was covered in Chapter 5. The

escalation rates are shown below the Gantt chart, where one can either use fixed rates for all

years of the portfolio or use results generated PMDSS-E. By applying the escalation rates, we

can use the PMDSS to compute project costs and total portfolio cost.

Figure 6.2.1.2 - Gantt Chart and Escalation Rates

Project cost is then divided into two parts: design cost and construction cost. Here, a

percentage is used to present the design cost as a part of the total project cost. For example,

15% of the project cost is design cost, so 85% is for construction. For the design phase, the

cost is assumed to be uniformly distributed. For the construction phase, a Beta distribution

has been selected to model the construction expenditure as explained in previous chapters.

Again, the Beta distribution is not mandatory and other distributions can be used to model

planned expenditures for construction cost. For each project in the portfolio, the yearly

expenditures will be automatically computed. After adding all expenditures of all projects in

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the portfolio, the total yearly expenditure for the portfolio is obtained. The yearly

expenditure and cumulative expenditure values are generated and plotted by the system (Fig.

6.2.1.3).

Figure 6.2.1.3 - Yearly and Cumulative Expenditures

The same calculations are applied to all projects based on revised or updated estimates from

the Bayesian updating process. As updated project durations and costs are automatically

obtained from PMDSS-B, there is no need to manually enter the revised information.

6.2.2 Ranking System

The ranking system is also included in this PMDSS-G. The main idea is to facilitate the use

of PROMETHEE-GAIA software so that users who have little experience with the original

software can see the results of the ranking in Excel. The users need to input the values of

0

200,000,000

400,000,000

600,000,000

800,000,000

1,000,000,000

1,200,000,000

1,400,000,000

1,600,000,000

1,800,000,000

2,000,000,000

0

100,000,000

200,000,000

300,000,000

400,000,000

500,000,000

600,000,000

Cu

mu

lati

ve

Co

sts

YO

E

Years

YOE Cumulative

161

those criteria for which no information was previously provided, such as criticality and

stakeholders (Fig. 6.2.2.1). In this table, information for project name, cost, duration and start time is

retrieved from the general information section of this module, while users’ inputs for

criticality and stakeholders are required. Taking Project CM009 shown in Figure (6.2.2.1) for

example, the project has cost and duration estimates with mean values of $428M and 8 years,

respectively. Its criticality is ranked as the highest in the portfolio because, according to

quarterly reports, this project is on the critical path and expecting delays. For stakeholders,

the information is not available from quarterly reports; thus, all projects, including CM009,

are given the same average rating. For each criterion, a preference function is also selected,

based on which, the values for PROMETHEE ranking can be calculated. A detailed

calculation report is not presented here but provided in the module, elaborating the steps

required in order to obtain the ranking results.

Figure 6.2.2.1 - Prior Project Ranking Criteria

The ranking results will be presented in the following table (Fig. 6.2.2.2). Phi+ and Phi-

values are for PROMETHEE I Partial Ranking, while Phi is for PROMETHEE II

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Complete Ranking. The ranks shown in the figure are based on complete ranking. It should

be noted that even if the rank here is based on complete ranking (which eliminates the

possibilities of incomparability), in order to fully understand the actual situation, users can

look up the partial ranking result as it preserves the information that is lost in the process of

taking the subtraction of Phi. In this case, CM019 ranked as the most preferred or significant

project in the portfolio with the highest Phi value of 0.2327.

Figure 6.2.2.2 - PROMETHEE I & II Rankings

Many graphics are prepared to visually display the results, as was shown in Chapter 3. It

should be noted that the Posterior ranking will use the Bayesian updating results. Also, more

criteria may become necessary, requiring users to input corresponding values. The rank

orders might also be changed as a result of the updates.

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6.3 Portfolio Management Decision Support System – Bayesian Updating

(PMDSS-B)


The first screen of this file shows the information for all projects both before and after

updates. The new project duration and costs are presented, and the total project cost and

duration are also recalculated based on the new information. Portfolio costs are calculated as

the summation of all project costs in the portfolio; however, to calculate duration, all

possible critical paths need to be defined, as there might be more than one possible critical

path and the durations of several paths may be relatively close. Figure (6.3.1.1) shows a table

that enables the user to define possible critical paths by entering the project ID. The

duration of the project will be the largest value for all possible critical paths. In this case,

since each project is considered to be independent from others in the portfolio, there is only

one project on each path. The path with the longest duration will be chosen as ‘critical’ and

shown under the furthest right column. When the MC simulation is performed, the critical

path might change for various simulation runs, and this table will automatically pick the

longest path and identify it as the critical path.

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Figure 6.3.1.1 - Defining Possible Critical Paths

A cumulative percentile curve for portfolio cost and duration is also plotted. Users can

clearly see what the portfolio is likely to cost if the owner wants an 85% confidence level or

80% confidence level, for example. The same type of information is generated for portfolio

duration (Figs. 6.3.1.2, 6.3.1.3).

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Figure 6.3.1.2 - Portfolio Total Cost (Probability of Not Exceeding)

Figure 6.3.1.3 - Portfolio Total Duration (Probability of Not Exceeding)

0 200 400 600 800 1,000 1,200 1,400 1,600

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

95%

98%

Portfolio Total Cost (Million US$)

Pro

ba

bit

y o

f N

ot

Esc

ee

din

g

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

95%

98%

Portfolio Total Duration (Years)

Pro

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ot

Ex

cee

din

g

166

By subtracting the time when the updating is prepared from the total duration, the duration

of the remaining part can also be easily estimated.

6.3.2 Updating Projects

Bayesian updating is applied to each project in the portfolio, each of which has its own

worksheet in the spreadsheet file. This process can be easily completed by going to each

project’s sheet in the PMDSS-B module. As shown in Figure (6.3.2.1), the original project

duration is obtained from PMDSS-G. Users need to define the time when the updates were

prepared, under the Phase column. The percentage is the duration of the completed part of

the project divided by the total duration of the project. Also, the users are required to enter

new estimates into the table on the right (Fig. 6.3.2.1). The underlying distribution or the

likelihood function can be calculated based on the inputs. By combining the likelihood

function and the original estimate (prior), we can calculate the posterior probability and save

it in the table on the right bottom. The most recent posterior will be selected and considered

as the updated duration for this project. The same steps are applied to project cost, and the

most recent posterior is considered as the updated cost for this project. Based on the results

from this table, several graphics are prepared to show the update effects, which have been

presented in Chapter 5 and thus are not repeated here.

167

Figure 6.3.2.1 - Bayesian Updating Table

For this project, 9 updates were performed. The original duration estimate for this project,

shown at the top of this table, was a normal distribution with a mean of 8 years. For MC

simulation, in each iteration the duration for this project will be a sampled value from the

normal distribution. This sampled duration value is also considered to be the range of Beta

distribution, used for distributing project expenditures. Users of this module then need to

input the updated estimates for this project. On the right side, under the Multiple Estimators

section, users can enter the updated duration estimates. Taking the first update, for example,

three users have inputted the new duration estimates of 9.67, 9.82 and 9.5 years for this

project. Then, under the Updates section, the likelihood function will be automatically

computed based on the new inputs, as the normal distribution with a mean of 9.66 years.

168

Based on the time of performing the update, the percent complete is also shown under the

Phase column, while the Duration column shows how long ago this project started. This table

shows that 7.17 years had elapsed between the project start and the time of the first update,

and this duration represents 74% of the revised duration of 9.66 years. The sample section

shows the statistics of all updates performed. After the original estimate and updated inputs

have been completed, the posteriors can be calculated. In the bottom right section, in the

Posteriors section, one can see all posteriors from each update. The most recent posterior will

be presented in the bottom left, in the Posterior section, where it indicates that after 9 updates,

the project is now expected to be completed in 9.88 years.

6.4 Portfolio Management Decision Support System – Contingency (PMDSS-

C)


The contingency analysis module requires users’ inputs as well. It contains two input sheets

where users input the information needed to generate cost and schedule contingency reports.

First, users need to define the design duration and the construction duration. For this, two

options are available: whether the design duration is a percentage of the total project

duration, or the design duration and construction duration can be defined independently (Fig.

6.4.1.1). This information will later be utilized in contingency calculations.

169

Figure 6.4.1.1 - Bayesian Updating Table

Figure (6.4.1.1) shows the design durations and construction durations. For example, Project

5 has a design duration of 6.67 years and construction duration of 2.08 years.

The second step is to enter cost contingency at three time periods: 10% Design, Pre-Bid, and

Post-Bid. Again, two options are available: defining contingency as a percentage of project

total cost or entering a figure for cost contingency (Fig. 6.4.1.2). When the percentage

number has been selected, the table will automatically calculate contingency for all projects

in the portfolio. For this case, a percentage of 35% has been selected, and the contingency

values at 10% design were automatically calculated such that Project 5, for example, has a

contingency of $15M at this phase.

170

Figure 6.4.1.2 - Defining Contingency at 10% Design

However, besides the two options listed above, during the Pre-Bid phase, users can also

define a contingency change between Pre-Bid and Post-Bid. This is suitable when historical

data is available in regard to the possible contingency changes at the bidding time for similar

types of past projects (Fig. 6.4.1.3). Using the changes, users can also generate a Pre-Bid

contingency for each project in the portfolio. It should be noted that this approach is used

only when a limited amount of data is available regarding Pre-Bid contingency. In these cases,

one can use historical data to generate contingency changes, so Pre-Bid contingency can be

calculated using the “contingency changes” values. Users can enter the mean and standard

deviation in order to model the distribution based on historical data on the left side (Fig.

6.4.1.3). After the distribution is defined, under the Random column, the changes will be

sampled from the distribution and the Pre-Bid contingency will be calculated based on the

changes. Otherwise, the Pre-Bid contingency will be obtained from other options listed

above. In this case, the historical data is not applied and the Pre-Bid contingency is

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calculated based on other options introduced in the previous section. As shown in the figure,

Project 3 has the largest Pre-Bid contingency, which is about $72.6M.

Figure 6.4.1.3 - Defining Contingency at Pre-Bid Using Historical Data

6.4.2 Cost and Schedule Contingency

After defining the durations for design and construction phases and defining the

contingencies at various phases, users can obtain the cost and schedule contingency reports

containing contingency drawdown curve values. As the calculations are automatically

completed by the module, users still need to become familiar with the singularity functions

to understand the underlying mathematics in this module. For each project, the remaining

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contingency at the end of each year can be obtained. By summing up all the contingencies

for the portfolio and then applying escalation rates, the cost contingency drawdown curve is

produced (Fig. 6.4.2.1). As Figure (6.4.2.1) indicates for this portfolio of projects, the total

contingency has a mean value of $500M at the beginning, drops down to $200M after 5

years into the project, and is completely consumed after about 14 years.

Figure 6.4.2.1 - Cost Contingency Drawdown for the Portfolio

For schedule contingency, only those critical paths that are possible will be considered.

Again, the users need to define possible critical paths. The path with the longest duration

will be selected and the schedule contingency for projects falling on this path will be added

up to obtain the total schedule contingency for the portfolio. Figure (6.4.2.2) shows the

critical path of a portfolio of projects with 3.9 years of schedule contingency at the beginning,

dropping to 0.5 year in about 3 years and becoming 0 at around 14 years. It should be noted

that the critical path might change when running MC simulations, and the values shown in

Figure (6.4.2.2) are the mean values of schedule contingency.

0

100,000,000

200,000,000

300,000,000

400,000,000

500,000,000

600,000,000

0 5 10 15 20

To

tal

Co

nti

ng

en

cy

(d

oll

ars)

Duration (years)

Contingency Mean

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Figure 6.4.2.2 - Schedule Contingency Drawdown for the Portfolio

The same procedure is applied to posterior contingency analysis as users are required to

input necessary information to generate contingency reports. It should be noted that after

the updates, users can change the design duration, construction duration, and contingency

levels at various phases. Users need to enter the updated information to observe changes for

project contingency, as explained in Chapter 5.

6.5 Portfolio Management Decision Support System – Escalation (PMDSS-E)

6.5.1 Integrated Transit Index

The ITI was developed as part of this research to model the escalation costs in transit

projects, as described in Chapter 4. The ITI is presented in this module. The five major

categories and the weights of the categories were pre-defined according to the analysis in

Chapter 4. These five major categories and the weights are shown at the top of the table in

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 5 10 15 20

To

tal

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en

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Duration (months)

Contingency Mean

174

Figure (6.5.1.1). The calculation of ITI has been implemented from 2004 to 2011. The ITI

value in 2004 was set to the benchmark value of 100, and the rest were calculated

accordingly. Whenever new data becomes available, this table can be used to calculate new

index values. The ITI is presented in bold print, and the annual percent changes for the ITI

are also calculated (Fig. 6.5.1.1). An ITI average of 113.37 has been obtained as well.

Figure 6.5.1.1 - Integrated Transit Index

6.5.2 Integrated Transit Index Forecast

As mentioned previously, after the ITI was established, two methods were utilized to

forecast ITI: neural networks and time series. These two methods are first applied to each of

the five major categories, and then combined together based on the weights of each category

to obtain the forecasted ITI for the next 10 years. As examined and elaborated upon in

Chapter 4, results generated by both methods are kept and presented in a table format

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similar to Figure (6.5.2.1). The forecasted values for the categories are shown in light green,

and the forecasted ITI from 2011 to 2022 are presented in bold with 2022’s ITI forecasted

to be 163.2. In order to perform the neural networks and time series forecast in Excel,

@Risk software is required. These two methods have been implemented into the latest

version of the software (@Risk 6.0.0), making it convenient for users to run these analyses

without using additional software outside Excel.

Figure 6.5.2.1 - Forecasted Integrated Transit Index Using Time-Series Analysis

The escalation rates used in other modules of the PMDSS are the rates according to

forecasted ITI. The average percentage changes can also be used as the escalation rates for

all years. As shown in Figure (6.5.2.1), the average percentage changes are shown in bold

print as 2.76% with a standard deviation of 0.67%. Besides using the actual forecasted values

176

for ITI, users can model the escalation using a fixed escalation rate of 2.76%, or using a

distribution with a mean of 2.76% and standard deviation of 0.67%. This module requires no

information from other modules but provides the escalation rates for project expenditure

and cost contingency that will be used in other modules.

6.6 Summary

This chapter presented the Portfolio Management Decision Support System and its

implementation in Excel. The PMDSS is a powerful tool for portfolio project management

consisting of four modules: Portfolio Management Decision Support System – General

(PMDSS-G), Portfolio Management Decision Support System – Bayesian Updating

(PMDSS-B), Portfolio Management Decision Support System – Contingency (PMDSS-C)

and Portfolio Management Decision Support System – Escalation (PMDSS-E). With the

user’s input, these four modules provide detailed analysis of project expenditures, ranking,

contingency, projects cost and duration updating, and escalation.

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CHAPTER 7 : APPLICATION OF PORTFOLIO MANAGEMENT DECISION SUPPORT SYSTEM

7.1 Introduction

The developed PMDSS was tested and applied to real project data. In this chapter, real

project data collected from 10 large transit projects were used to demonstrate the operation

of the decision support system. It is proved that the system can be utilized as a planning tool

to establish planned expenditures for the portfolio. The system can also be used as a

management tool, providing better estimates for both individual and portfolio expenditures

with regular updates. As projects progress, the forecast results provided by the system

continually improve. It is believed that the results would become even better than the results

included in this chapter if more updates were performed. Another note is that the system

copes very well with huge changes in project budgets.

7.1.1 The Projects

In order to demonstrate and test the PMDSS, a group of 10 large transit projects was

selected. These projects constitute a major portion of the East Side Access Project in New

York City. The East Side Access Project will connect the Long Island Rail Road (LIRR)

Main and Port Washington lines in Queens to a new terminal beneath the Grand Central

Terminal in Manhattan to provide better and faster access to the Manhattan’s east side for

Long Island and Queens commuters. The planned improvement is shown in Figure (7.1.1.1),

with new tunnels “bored from the existing bellmouth structure at Second Avenue and 63rd

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Street, west and then south, under Park Avenue and Metro-North Railroad's four-track right

of way in Manhattan” (MTA, 2013). In this research, we consider these 10 projects as

belonging to a portfolio or program and apply the developed system to the portfolio data.

One reason for selecting these projects was that progress reports for the program were

available online. Quarterly reports have been collected from the project’s website. The data

used in this analysis start in 2009, Quarter 3. Related information, such as project notice to

proceed date, originally estimated duration, forecasted duration, original contract amount,

and current approved budget have been collected from project progress reports for system

validation. While the East Side Access Program consists of many more projects even just in

the Manhattan area, information on these 10 projects is available in sufficient detail from the

3rd Quarter of 2009 onward. The main idea here is to compare our planned expenditure at

the end of each year to their planned expenditure, and our revised expenditure at the end of

each year to their actual expenditure. Mean Absolute Percentage Difference (MAPD) has

been calculated to compare the results statistically. If the MAPD is not large, then we can

conclude that the developed decision support system has been effective in analyzing the

project performance and predicting future outcomes. With the provision of updates at

various times, the system is expected to provide better results as presented in the quarterly

reports for these projects.

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Figure 7.1.1.1 - Planned Improvements of East Side Access (MTA, 2013)

Another reason why the ESA Project was selected is the fact the project is facing huge delays

and cost overruns, as reported by various sources (New York Post, 2011; New York Times,

2012; ENR, 2013; The Wall Street Journal, 2012; Bloomberg, 2013). The New York Post

(2011) reported a delay of 16 months with officials admitting that they were “so far behind”

on the project and it would be difficult to meet the deadline of September 2016. Revising

their schedule, they stated that they were hoping to finish the project by April 2018. The

New York Times (May 2012) reported however, that the project was facing delays and cost

overruns, and according to MTA officials, the new estimates indicated that the new

completion date was August 2019 and the budget had risen from $6.3B to $8.24B. The

officials also stated that the project had been expected to finish by the end of 2013 but

several delays had occurred. ENR (2013) called the ESA the “largest public transportation

project nationwide” and reported that the project was facing heavy criticism for “missing its

180

budget by $4.4 billion and its completion date by 10 years”. The project was originally

expected to cost about $4.3 billion and begin service in 2009, while with the new estimates,

the project is now supposed to be completed in 2019 with a total cost of $8.76 billion. The

construction under Grand Central Terminal accounts for one quarter of the cost overruns,

jumping from $709 million to $1.9 billion. East Side Access was delayed due to various

reasons, including “upgrading century-old infrastructure during night and over weekends;

work cancelled due to Amtrak, which controls access to the tracks, celebrating the National

Train Day (The Wall Street Journal, 2012)”. For all these reasons, and due to the fact that

quarterly progress data were available, we decided to use ESA as the case study for the

implementation of the developed DSS. A history of ESA budget and completion year

changes, based on news media and MTA reports, is provided in Figure (7.1.1.2).

Figure 7.1.1.2 - A History of ESA Budget and Completion Year Estimates from Media and MTA Reports

2009, $4.30 ENR (2013)

2013, $6.30 NYT (2012)

2015, $7.24 MTA (2008)

2016, $7.33 MTA (2009)

2018, $8 NYP (2011)

2019, $8.10 WSJ (2012)

2019, $8.24 NYT (2012)

2019, $8.76 ENR (2013)

$0.00

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2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

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The location of those projects that were active during 2009 Quarter 3 is presented in Figure

(7.1.1.3). Some of the projects that started later are not shown in this figure but are available

in other reports.

Figure 7.1.1.3 - Manhattan Contracts Active during 2009 Quarter 3

Brief project descriptions are also provided in the MTA reports and quoted below:

1. Manhattan Tunnels Excavation (CM009) – The Manhattan tunnels excavation contract includes procurement of two 22-foot-diameter rock-tunnel-boring machines (TBM), installation of temporary utilities, excavation of chambers and wyes, TBM (4 drives) excavation of approximately 25,000 linear feet (lf) of tunnels and final concrete lining of 11,600 lf of the running tunnels;

182

2. Manhattan Structures (CM019) – Excavation and lining of four tunnel drives, shafts, escalator well-ways, air plenums, cross passages, and caverns mainly under Grand Central Terminal (GCT);

3. Manhattan Structures Part 1 – MNR (FMM19) – MNR Railroad resources in support of the contracts CM019, CM008A, CM004 and General Conditions contracts in the vicinity of GCT. These resources include both direct and indirect labor, work train support, and track outages;

4. Madison Yard Site Clearance (CM008A) – Dismantle rail, ballast, concrete slab, crash walls, two platforms, and miscellaneous buildings; demolish elevators and remove accompanying mechanical/electrical equipment. Duct removal and installation and fan work, and all other mechanical/electrical systems. Construct new MNR Commissary;

5. GCT Expansion Joint Repairs and Structural Closures (CM002) – Rehabilitation of GCT expansion joints, fire stopping and structural closures at the suburban roof level;

6. 44th St. Demolition & Construct Fan Plant Structure & 245 Park Ave. Entrance (CM004) – 47 E. 44th Street: Demolish existing building, perform soil and rock excavation. Construct shell of new building. 245 Park Avenue Entrance: Conduct environmental abatement and demolition; construct new foundations, walls and supports, furnish and install escalator. Install architectural finishes, plumbing, fire protection, HVAC, lighting, power, fire alarm, and communication systems;

7. 50th St. Ventilation Facility (CM013) – Construction of new ventilation building structure and vertical utility shaft form building foundation at 50th St;

8. MNR Traction Power MODs & 13.2 kV Loop (FM216) – Furnish, deliver and install automated system for motor operated disconnect switches (MODs). Scope of work also includes reconfiguration of 13.2kV Traction Power feeder cables;

9. GCT Protection Works (CS790) – Make all necessary concrete repairs to roof slabs, columns and beams and install protective netting in GCT from 42nd through 51st Streets (Upper Level Tracks 32 thru 42, Lower Level Tracks 113 thru 115);

10. Vertical Circulation – Escalators & Elevators (VM014) – The base scope includes the fabrication and installation of 17 elevators and 45 escalators for the Concourse, Caverns, 44th and 50th St. Ventilation Facilities, and MNR facilities. Options exist for an additional five elevators and two escalators.

7.2 Data

According to the Risk Assessment Spot Report for the East Side Access Project (FTA, 2006),

the “Preliminary Engineering (PE) has reached 100% completion in July 2002 for all

portions of the project, with the exception of Harold Interlocking and Grand Central

Terminal (GCT), allowing engineering development to advance into the Final Design phase.”

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As a result, July 2002 is considered as the start of the portfolio, and is also assumed to be the

start of the design phase. Notice to Proceed (NTP) dates are also available, which are

considered as the start of the construction phase. The bidding time has been regarded as a

relatively short time period since year is selected in our system as the main time unit, and

thus the duration from July 2002 to NTP is considered as the design duration. The duration

from NTP till the end of the project is considered as the construction duration. Also, since

the original contract award is for construction, the project design costs have been assumed

to be 0 and the construction costs have been modeled using the Beta distribution as

described in previous chapters. It should be noted that the Beta distribution assumption is

selected here when data is not available for preparing expenditure estimates. When a well-

prepared progress plan is available, the expenditure can be obtained to improve the results.

As in a portfolio, for projects with limited data, users can still model the expenditure by

means of a Beta distribution, which is not mandatory. Moreover, planned percent complete

and actual percent complete have been provided in the reports, and the planned and actual

expenditure can then be calculated for the sake of comparison.

7.2.1 Expenditures from Quarterly Reports

As the PMDSS uses year as the time unit, three year-end expenditures can be used for

comparisons. Tables (7.2.1.1) to (7.2.1.3) show the planned and actual expenditures at the

end of 2009, 2010 and 2011, respectively. CM002, CM013 and VM014 started at a later time

as they are shown to be 0% complete in the 2009 Q4 report. FM216 and CS790 were both

completed in 2010, whereas CM008A was completed in 2011. For projects CM002, CM004

and CM013, huge differences exist between the planned percent complete and actual percent

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complete, and large differences exist between planned and actual expenditure. These projects

are expecting delays, and mitigation plans have been implemented to expedite them.

Table 7.2.1.1 - Planned Expenditure and Actual Expenditure from 2009 Q4 Report

Project Name Planned Percent

Complete Planned Expenditure

Actual Percent

Complete Actual Expenditure

CM009 – Manhattan Tunnels Excavations 66.40% $ 284,125,600.00 62.70% $ 278,459,000.00

CM019 – Manhattan Structures 1 24.30% $ 178,362,000.00 20.20% $ 149,442,000.00

FMM19 – Manhattan Force Account Support – MNR 50.00% $ 6,800,000.00 0.00% $ -

CM008A – Madison Yard Site Clearance 71.60% $ 27,924,000.00 62.40% $ 24,332,000.00

CM002 – GCT Expansion Joint Repairs and Structural Closures

0.00% $ - 0.00% $ -

CM004 – 44th St. Demolition & Construct Fan Plan Structure & 245 Park Ave. Entrance

1.40% $ 571,200.00 1.50% $ 628,000.00

CM013 – 50th St. Vent Facility 0.00% $ - 0.00% $ -

FM216 – MNR Traction Power MODs & 13.2 kV Loop

84.95% $ 11,723,100.00 50.20% $ 8,986,000.00

CS790 – GCT Protection Works 77.00% $ 7,931,000.00 64.00% $ 7,260,000.00

VM014 – Vertical Circulation (Escalators & Elevators) 0.00% $ - 0.00% $ -

Total

$ 517,436,900.00

$ 469,107,000.00




Actual Percent




FMM19 – Manhattan Force Account Support – MNR 61.00% $ 8,296,000.00 61.00% $ 14,483,000.00



0.00% $ - 0.00% $ -


31.10% $ 12,688,800.00 23.80% $ 9,704,000.00

CM013 – 50th St. Vent Facility 26.50% $ 25,016,000.00 21.60% $ 20,688,000.00


100.00% $ 13,800,000.00 100.00% $ 17,000,000.00


VM014 – Vertical Circulation (Escalators & Elevators) 0.00% $ - 0.00% $ 127,000.00

Total

$ 797,440,100.00

$ 822,001,000.00

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Actual Percent




FMM19 – Manhattan Force Account Support – MNR 62.00% $ 8,432,000.00 62.00% $ 16,998,000.00



44.80% $ 2,016,000.00 23.30% $ 1,117,000.00


99.50% $ 40,596,000.00 60.80% $ 26,988,000.00

CM013 – 50th St. Vent Facility 65.60% $ 61,926,400.00 45.30% $ 43,269,000.00


100.00% $ 13,800,000.00 100.00% $ 17,000,000.00


VM014 – Vertical Circulation (Escalators & Elevators) 0.00% $ - 2.00% $ 2,889,000.00

Total

$ 1,205,813,500.00

$ 1,078,733,000.00

As shown in Table (7.2.1.1), several projects are suffering from delays as the actual percent

completes are lower than the planned completion at the end of 2009. According to the

report, the schedule was not revised for CM009 and CS790 due to delays; however, for other

projects, although the completion date was not changed, the delays were observed and

contractors were trying to mitigate delays and catch up with the schedule. Table (7.2.1.2)

shows that at the end of 2010, the percent completes of CM009 and CM008A were higher

than the planned completes, while CM019, CM004 and CM013 were still behind plan. The

report indicated that, except for CM004 and CM013, most projects had a revised schedule

with delays ranging from 3 months to 2 years. For CM004 and CM013, even though the

schedule was not changed, delays arose due to reasons such as unforeseen conditions, and

contractors were trying to recover schedule by using extra shifts. Table (7.2.1.3) suggests that

most projects were expecting delays again at the end of 2011. Other than CM004 and

CM013, most projects were suffering from delays ranging from 3 months to 3 years,

according to the report.

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7.2.2 PMDSS Calculated Expenditure vs. Planned Expenditure from Reports

As discussed in previous chapters, the PMDSS can be utilized as a planning tool to establish

expenditures for all projects in the portfolio. In this particular case, the design costs have

been assumed to be 0, while the construction costs follow a beta distribution. Based on these

assumptions, the expenditure for all 10 projects can be obtained at the end of year 2009,

2010 and 2011. Tables (7.2.2.1) to (7.2.2.3) present the results of the forecasted expenditures

prepared by PMDSS and the absolute percent differences of the expenditures compared

with the planned expenditures obtained from quarterly reports for each project as well as for

the portfolio. The absolute percent differences for portfolio total expenditure dropped from

61% to 26% from 2009 to 2011 as more projects’ construction phases started and some

projects were completed. The intent here is to show that PMDSS provides a viable

alternative for estimating planned expenditures in an efficient and convenient way. It is

understood that a more accurate estimate of planned expenditures can be obtained by

carefully examining the schedule of values for each project in the portfolio.

187

Table 7.2.2.1 - PMDSS Calculated Expenditure vs. Planned Expenditure from 2009 Q4 Report

Project Name PMDSS-calculated

Expenditure

Difference from Planned Expenditure from 2009 Q4

Report

CM009 – Manhattan Tunnels Excavations $ 399,856,395.97 40.73%

CM019 – Manhattan Structures 1 $ 299,784,397.17 68.08%

FMM19 – Manhattan Force Account Support – MNR $ 5,554,588.29 18.31%

CM008A – Madison Yard Site Clearance $ 25,347,449.20 9.23%


$ - -


$ 2,519,887.66 341.16%

CM013 – 50th St. Vent Facility $ - -


$ 12,651,393.19 7.92%

CS790 – GCT Protection Works $ 10,300,000.00 29.87%

VM014 – Vertical Circulation (Escalators & Elevators) $ - -

$ 756,014,111.49 61%



Expenditure


Report






$ - -


$ 29,255,284.48 130.56%

CM013 – 50th St. Vent Facility $ 32,610,761.86 30.36%


$ 13,800,000.00 0.00%


VM014 – Vertical Circulation (Escalators & Elevators) $ 338,692.10 -

Total $ 1,117,554,796.75 36%

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Expenditure


Report






$ 2,330,563.00 15.60%


$ 40,800,000.00 0.50%

CM013 – 50th St. Vent Facility $ 83,084,950.27 34.17%


$ 13,800,000.00 0.00%


VM014 – Vertical Circulation (Escalators & Elevators) $ 4,997,812.87 -

Total $ 1,358,952,632.56 26%

MAPD is used to present the differences between the PMDSS-calculated expenditures and

the planned expenditures from the reports. The equation is shown below:

(7.2.2.1)

where Pi is the planned expenditure from reports and Qi is the expenditure forecasted by

PMDSS.

MAPD values are reported in Table (7.2.2.4). From 2009 to 2011, it drops from 89% to 44%.

Compared to the results reported before that, the absolute percent differences for portfolio

total expenditure dropped from 61% to 26% from 2009 to 2011, which suggests that the

system performs better on the portfolio level than on the project level.

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Table 7.2.2.4 – PMDSS Calculated Expenditure vs. Planned Expenditure Based on Report MAPD

Year MAPD

2009 89%

2010 64%

2011 44%

It should be noted that all of the expenditures simulated by the modules are random

variables, which means that the numbers presented in the tables above are actually the mean

values of distributions.

7.2.3 2009 Q3 Update vs. Actual (Bayesian Updating)

The Bayesian updating method has been applied to update the original estimates of project

costs prepared in 2006 with data collected from the 2009 Quarter 3 report. The updated

project costs are utilized to forecast expenditures at the end of 2009, 2010 and 2011. Tables

(7.2.3.1) to (7.2.3.3) are the results of updated forecasted expenditures prepared at 2009

Quarter 3 and absolute percent differences of the expenditures compared with actual

expenditures obtained from quarterly reports for both individual projects and the portfolio.

The absolute percent differences for portfolio total expenditure dropped from 56% to 27%

from 2009 to 2011 as more projects started construction and some projects reached

completion. The results are relatively close to those in Section 7.2.2. It should be noted that

the actual expenditures are different from the plan, and some projects have huge differences

between these two figures due to scope changes and delays. With only one update, the

PMDSS can produce results close to Section 7.2.2 even though the huge variations between

planned and actual expenditures exist.

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Table 7.2.3.1 - PMDSS 2009 Q3 Updated Expenditure vs. Actual Expenditure Based on Report (at 2009 Q4)

Project Name Updated Expenditure Vs. Actual

CM009 – Manhattan Tunnels Excavations $ 371,494,362.63 33%

CM019 – Manhattan Structures 1 $ 301,444,568.65 102%

FMM19 – Manhattan Force Account Support – MNR $ 5,554,588.29 -

CM008A – Madison Yard Site Clearance $ 25,347,449.20 4%


$ - -


$ 2,542,055.72 305%

CM013 – 50th St. Vent Facility $ - -


$ 12,827,206.89 43%

CS790 – GCT Protection Works $ 11,231,084.41 55%

VM014 – Vertical Circulation (Escalators & Elevators) $ - -

Total $ 730,441,315.78 56%





FMM19 – Manhattan Force Account Support – MNR $ 10,266,400.20 29%



$ - -


$ 29,433,131.13 203%

CM013 – 50th St. Vent Facility $ 32,610,761.86 58%


$ 13,991,775.63 18%


VM014 – Vertical Circulation (Escalators & Elevators) $ 338,692.10 167%

Total $ 1,128,310,904.53 37%

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$ 2,330,563.00 109%


$ 40,800,000.00 51%



$ 13,991,775.63 18%


VM014 – Vertical Circulation (Escalators & Elevators) $ 4,997,812.87 73%

Total $ 1,370,574,358.32 27%

MAPD (Table 7.2.3.4) is also close to Section 7.2.2. MAPD drops from 90% to 44% from

2009 to 2011.

Table 7.2.3.4 - PMDSS 2009 Q3 Updated Expenditure vs. Actual Expenditure Based on Report MAPD

Year MAPD

2009 90%

2010 63%

2011 44%

7.2.4 2010 Q3 Update vs. Actual

The Bayesian updating method has been applied to the 10 projects four more times (i.e., at

the end of 2009 Q4, 2010 Q1, 2010 Q2 and 2010 Q3), as reports from 2009 Quarter 4 to

2010 Quarter 3 were utilized to update project costs step by step. The updated expenditure

at the end of 2010 and 2011 can be forecast using these reports and compared with actual

expenditures at the end of 2010 and 2011. Tables (7.2.4.1) and (7.2.4.2) are the results of

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planned expenditures prepared at 2010 Quarter 3 after five updates (i.e., at the end of 2009

Q3, 2009 Q4, 2010 Q1, 2010 Q2 and 2010 Q3) from original plan, and absolute percent

differences for both individual project and the portfolio have been calculated again. The

absolute percent differences for portfolio total expenditure dropped from 19% to 12% from

2010 to 2011. The results have also been significantly improved from Section 7.2.2 and 7.2.3.

With more observations and more updates, the results become much better than previous

planned expenditures.








$ - -


$ 28,747,936.82 196%



$ 17,000,000.00 0%


VM014 – Vertical Circulation (Escalators & Elevators) $ - 100%

Total $ 978,012,545.10 19%

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$ 2,330,563.00 109%


$ 40,800,000.00 51%



$ 17,000,000.00 0%



Total $ 1,204,158,315.89 12%

MAPD (Table 7.2.4.3) has also improved from Sections 7.2.2 and 7.2.3. It drops from 47%

to 30% from 2010 to 2011 as more projects are completed.

Table 7.2.4.3 - PMDSS 2010 Q3 Updated Expenditure vs. Actual Expenditure Based on Report MAPD

Year MAPD

2010 47%

2011 30%

7.2.5 2011 Q3 Update vs. Actual

The Bayesian updating method was again applied to the 10 projects with additional

information from 2010 Quarter 4 to 2011 Quarter 3 reports. The updates are performed step

by step based on the information obtained from the reports. The updated expenditure

forecast at the end of 2011 was obtained and compared with actual expenditures at the end

of 2011. Table (7.2.5.1) shows the results of planned expenditures prepared at 2011 Quarter

3 after nine updates to the original plan as well as absolute percent differences for individual

194

projects and the portfolio as a whole. The absolute percent error for the portfolio’s total

expenditure was about 15% for 2011. This result is close to Section 7.2.4, while much better

than Sections 7.2.2 and 7.2.3. The reason why the error is slightly higher than in Section 7.2.4

is because project CM019’s budget dropped from $734M to $528M in 2010 only to rise to

$751M in 2011. Even with the huge changes in the budget (the project has an option

affecting its budget), the PMDSS can still provide relatively good results compared to

sections 7.2.3 and 7.2.4.








$ 2,330,563.00 109%


$ 41,085,541.91 52%



$ 17,000,000.00 0%



Total $ 1,241,589,226.96 15%

However, even though the error for portfolio total expenditure has increased from Section

7.2.4, the MAPD for all the projects in the portfolio (Table 7.2.5.2) was smaller than in

Section 7.2.4. With 29% MAPD, the result obtained after 9 updates is significantly improved

from 44% when only one update was performed.

195

Table 7.2.5.2 - PMDSS 2011 Q3 Updated Expenditure vs. Actual Expenditure MAPD

Year MAPD

2011 29%

It should also be noted that the three projects with high errors are those expecting delays of

as much as more than one year; however, these delays are indicated in the reports without

any revisions being made to project durations, probably in the hopes that mitigation plans

can reduce the extent of the delay. These projects have huge differences between their

planned percent complete and actual percent complete. If these three projects were excluded

from this analysis, the MAPD would be as low as 5% for the remaining seven projects in the

portfolio.

7.2.6 Bayesian Updating Summary

The Bayesian updating process for project costs mean values is presented in Figure (7.2.6.1).

The original estimates are listed under the Original column, and will be considered as prior for

the next update. After defining the likelihood function and applying Bayesian updating, the

posterior can be obtained. This posterior is then treated as prior for the next update. Taking

CM009, for example, the project has an original estimate with a mean of $428M. At 2009 Q3,

when updating the project, a likelihood function was computed with a mean of $438M. This

is based on the users’ input as if there are multiple estimators available; this mean value of

the likelihood function could be the average of their inputs, or if there is only one estimate

available, it is usually assumed that the input is the mean of the likelihood function, and a

standard deviation is assigned in order to apply Bayesian updating. In this case, there is only

one input of $438M available, and it is considered to be the mean of the likelihood function.

Another note here is that the likelihood function presented in Figure (7.2.6.1) is the

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likelihood function at 2009 Q3, 2010 Q3 and 2011 Q3. As explained in previous sections, in

order to obtain the posterior at 2010 Q3, there are actually 5 updates at 2009 Q3, 2009 Q4,

2010 Q1, 2010 Q2 and 2010 Q3. As a result, there are 5 likelihood functions and 5 posteriors for

these 5 updates. This figure just provides the likelihood functions and posteriors at last update for

2009 Q3, 2010 Q3 and 2011 Q3, which is intended to show the main idea of the Bayesian

updating process instead of listing all of the likelihood functions and posteriors. By applying

Bayesian updating, the posterior at 2009 Q3 can be calculated with a mean of $434M. This

posterior is considered to be prior when performing the next update at 2010 Q3. With a mean

of $448M for the likelihood function, the posterior at 2010 Q3 is computed with a mean of

$441M, which is again considered as prior for the next update at 2011 Q3. The likelihood

function is defined with a mean of $448M, and as a result, the posterior at 2011 Q3 is obtained

with a mean of $444M. As another example, CM002 started late as the first update happened

in 2011, whereas CM008A was completed in 2011. Both FM216 and CS790 were finished in

2010, too. Again, these are the mean values of cost distributions at various updating times.

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Figure 7.2.6.1 - Bayesian Updating Flowchart for Project Costs Means

The MAPD results are also presented in Table (7.2.6.1). It is shown that based on the

quarterly reports, the MAPD between planned expenditure and actual expenditure has

changed from 14% to 40%. Unlike the increasing trend in MAPD for the quarterly reports,

PMDSS’s forecasted expenditure has a decreasing MAPD from 89% to 44%; however, the

PMDSS system automatically corrects itself as the MAPD becomes smaller with more

updates becoming available. The updated PMDSS expenditure forecasts at 2010 Q3

provided a much better MAPD value of 30%, compared to the MAPD of quarterly reports

198

of 40% in 2011 Q4. By continually updating with PMDSS until the end of 2011 Q3, the

MAPD of forecasted expenditures for 2011 Q4 has been further reduced to 29%. This result

is considerably more accurate than the quarterly reports, not to mention that some of the

projects had plans prepared at a much earlier time, as compared to the planned expenditures

in the quarterly reports, which are only available from 2009 onward.

Table 7.2.6.1 - MAPD Comparisons

MAPD 2009 Q4 2010 Q4 2011 Q4

Quarterly Reported Plan vs. Actual 14% 29% 40%

Updated PMDSS Plan at 2009 Q3 vs. Actual 90% 63% 44%

Updated PMDSS Plan at 2010 Q3 vs. Actual

47% 30%

Updated PMDSS Plan at 2011 Q3 vs. Actual 29%

7.3 Ranking of the Projects in the Portfolio

The portfolio project ranking procedure has been explained in Chapter 3. Although the

reports prepared by the MTA have not explicitly pointed out any ranking for the projects,

we decided to generate the ranking reports to test for any possible connections between the

results and the information in the reports. Four ranking results could be obtained: original

ranking in 2006, updated ranking at 2009 Q3, updated ranking at 2010 Q3, and updated

ranking at 2011 Q3. The ranking orders can change when data for criteria such as projects’

cost and schedule changes. Changes in ranking provide users with a warning as to the

current state of the portfolio and which projects require more attention. The final ranking is

based on Complete Ranking, which removes the possibility of incomparability; however,

199

since Complete Ranking omits certain information in the calculation process, the results of

Partial Ranking are also provided.

Since several projects were not started until late 2011, six projects that started before 2009

Quarter 3 were selected to demonstrate the methodology and show possible ranking changes

during the updating period. These six projects were CM009, CM019, CM008A, CM004,

FM216 and CS790. The rankings are based on the information that is available at the time of

the project updates being prepared. This means that as soon as the updates are completed,

the updated ranking orders can also be obtained. In theory, the ranking orders in this case

could change as many as nine times as we have 9 quarterly reports for the portfolio; however,

since previous analysis based on the updated results at the end of 2009 Quarter 3, 2010

Quarter 3 and 2011 Quarter 3, the rankings have only been checked at these three points in

time, in order to be consistent with previous analyses.

7.3.1 Ranking Based on Original Estimates

First, the ranking can be obtained based on original estimates. Figure (7.3.1.1) presents the

information needed for calculating the Phi values and obtaining the ranking results. For

example, CM009 has an original cost estimate of $428M and a duration estimate of 8 years.

Its criticality is rated as 5, and the start time is 0.58 years, while the criterion stakeholders is

rated as 3. These criteria have been explained in Chapter 3.

200

Figure 7.3.1.1 - Ranking Input Based on Original Estimates

Based on the original estimates, the ranking order for the projects is as follows: CM019,

CM009, CM004, CM008A, FM216 and CS790 (Fig. 7.3.1.2). For example, CM009 has a

Phi+ value of 0.2622 and a Phi- value of 0.0556. The Phi value is 0.2067 for CM009, which

is ranked the second highest among the six projects.

Figure 7.3.1.2 - Ranking Orders Based on Original Estimates

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The original ranking results in this case are mainly based on projects’ cost and duration as

the other criteria, such as starting time, stakeholders and criticality, are mostly the same for

each project. The projects with larger budget and longer duration, like CM019 and CM009,

appeared at the top of the list whereas projects with smaller cost and shorter duration, like

FM216 and CS790, ranked lowest. It was noticed that even though CM019 is ranked lower

than CM009 for the criterion criticality, the much larger cost and longer duration still put

CM019 above CM009. Projects CM019 and CM009 both have much higher Phi values than

the rest, and FM216 and CS790 have very close results. For projects with close results, a

probability analysis has been performed to assess the likelihood of the ranks changing.

Figure 7.3.1.3 - Ranking Orders Probability Analysis: CM009 vs. CM019

A probability analysis shows that the difference of the Phi values between CM009 and

CM019 will be negative 83.2% of the time. It found that CM019 was ranked as more

significant than CM009 with a probability of 83.2% (Fig. 7.3.1.3).

202

Figure 7.3.1.4 - Ranking Orders Probability Analysis: FM216 vs. CS790

The difference of Phi values between FM216 and CS790 is positive with a probability of

59.8% (Fig. 7.1.14). This result indicates that even though Project FM216 is considered

slightly more important, the preference is not as dominant as the case presented in Figure

(7.1.1.3).

7.3.2 Updated Ranking at 2009 Quarter 3

The projects have been updated at 2009 Quarter 3. Figure (7.3.2.1) shows the updated

ranking for the six selected projects in the following order: CM019, CM009, CS790, CM004,

CM008A and FM216. With only one update, CS790 jumped from sixth to third on the list,

while CS790, CM004, CM008A and FM216 all have relatively close results. Also, even

though CM019 and CM009 remained at the top of the list, the gap between the Phi values

becomes smaller. As indicated in the report, both CM009 and CM019 were expecting 4.5-

month delays with efforts being made to recover the schedule, while trending within budget.

203

For CS790, however, the schedule was adjusted to support blasting operations and the

completion date was also modified. As CS790 was the only project reported with delays

among CM008A, CM004, FM216 and CS790, it jumped from the bottom of the list to

number three, only behind CM009 and CM019.

Figure 7.3.2.1 - Updated Ranking Orders at 2009 Q3

The probability analysis was then applied to two pairs: CS790 and CM004 as well as FM216

and CM008A, as they are very closely ranked. Figure (7.3.2.2) indicates that CS790 ranked

higher than CM004 but only for 54.8% of the time. CM004’s preliminary schedule was under

review, whereas CS790 had its schedule modified and is expecting delays.

204

Figure 7.3.2.2 - Ranking Orders Probability Analysis: CM004 vs. CS790

Figure 7.3.2.3 - Ranking Orders Probability Analysis: CM008A vs. FM216

Figure (7.3.2.3) shows the probability analysis of the difference between the Phi value of

CM008A and FM216, suggesting that there is a 58% chance that project CM008A will be

ranked higher than FM216. According to the reports, CM008A, which had no cost overruns,

205

had two safety incidents but was believed have suffered no impact in terms of substantial

completion date. FM216 was behind schedule due to difficulty getting track outage, but no

impact was anticipated for follow-on contracts and it was still within budget. Both pairs

show that there were no dominant preferences between projects in these pairs.


The projects have been updated five times based on quarterly reports from 2009 Q3 to 2010

Q3. The updated ranking at this date (2010 Q3) is as follows: CM019, CM009, CM004,

CS790, CM008A and FM216 (Fig. 7.3.3.1). As project FM216 was completed, it has a Phi

value of -0.0828, and ranked lowest on the list.


From the reports, it appears that CM019 and CM009 were both facing about 3 months of

delay while trending within budget. In order to mitigate the delays caused by various changes

and claims, the Contractor was trying to develop a recovery schedule to cope with these

206

modifications. CS790 was facing cost overruns and a slight delay for substantial completion.

CM008A was supposed to meet all contractual milestones but encountered potential delays

due to additional tiling and drainage in Commissary Zone 1, and its budget was also

increased due to scope transfer and modifications for unforeseen conditions in Madison

Yard and Commissary. Compared to the original ranking, CS790 now ranked higher than

CM008A, which is consistent with the previous update. This suggests that factors such as

cost overruns and delay caused CS790 to be ranked higher than CM008A, which was still

supposed to meet all milestones even with the expectation of potential delays and a budget

increase for the time being. For CM004, unforeseen foundation conditions at the 47 E. 44th

St. building were analyzed, and the start of perimeter drilling was delayed. Contractor

Yonkers Contracting Company, Inc. (YCC) was trying to recover schedule by using extra

shifts. This made the rank of CM004 higher than CS790, as compared to previous updated

ranking in 2009 Q3.


After nine updates based on reports from 2009 Q3 to 2011 Q3, the new ranking for the 6

projects is as follows: CM019, CM009, CM004, CM008A, CS790 and FM216 (Fig. 7.3.4.1).

CM019 still ranked on top with a Phi value of 0.1261.

207


The Phi values for projects CM008A, CS790 and FM216 are extremely close. As these three

projects have already been completed, they ranked at the bottom of the list. CM009 and

CM019 have much higher Phi values than CM004, and these two projects are considered to

be much more significant than CM004; however, the Phi value was increased for CM004, as

it was reported to be facing delays and cost overruns due to various design changes at 245

Park Ave & 44th St. As for CM009 and CM019; both projects were trending within budget,

but both projects were facing huge delays. MTA and contractor Dragados/Judlau (DJ) were

working together trying to optimize work plan and catch up to the schedule.

7.3.5 Ranking Changes

The ranking did change for the updates described in previous sections. As introduced in

Chapter 3, users can define the inputs for criteria, and the changes of the inputs will cause

changes in ranking. Each time a user is preparing the ranking, the values for the criteria can

be defined according to the most recent information. The ranking changes for the six

208

selected projects were recorded and presented in Figure (7.3.5.1). It is shown that CM019

and CM009 kept being ranked as the top two among the six projects. CM004 was ranked

number three in 2002 but dropped to fourth place in 2009 and returned to number three in

2010. CM008A started as number four, dropped to number five in 2009 and 2010 but

climbed back to number four in 2011. FM216 went from number five in 2002 to number six

and remained there since. CS790 was at the bottom of the list but climbed to number three

in 2009; however, it dropped one spot in 2010 and then another in 2011, finally becoming

number five. The reasons for the ranking changes have been examined previously and thus

will not be repeated here.

Figure 7.3.5.1 - Ranking Order Changes for Six Selected Projects

It should be noted that the ranking results presented in Fig. 7.3.5.1 were based on Bayesian

updating, and the consequences of diverse attentions were not considered. For example,

when project CS790 was ranked higher than CM004, it did not mean the current work on

CM004 would be abandoned. It was suggesting the states of the two projects rather than

completely stopping working on one project and focusing on the other.

1

2

3

4

5

6

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

CM009 CM019 CM008A CM004 FM216 CS790

209

The ranking capability of the PMDSS is an important contribution to PPM because it

provides timely feedback to the management team, enabling them to focus their attention on

the hotspots and to proactively deal with various issues that may threaten portfolio goals.

7.4 Summary

The New York City’s East Side Access (ESA) Program was selected to demonstrate the

application of the PMDSS developed in this research and validate its performance. Ten large

projects were selected from the ESA Program for this purpose because their progress data

were readily available. Data for these 10 projects were collected from quarterly reports

published on the project website. Four comparisons were performed:

(1) PMDSS-forecasted expenditure vs. planned expenditure from the project’s progress

reports;

(2) PMDSS-forecasted expenditure at 2009 Q3 vs. actual expenditures from reports in

2009, 2010 and 2011;


2010 and 2011; and


2011.

These four comparisons indicate that the system can be used as a planning tool to establish

planned expenditures for the portfolio. Forecasts continually improve as projects start and

report progress. To update estimates, the system combines progress from the most recent

period and project progress history. The system can also be utilized as a management tool,

providing stronger estimates in regard to both individual projects and portfolio expenditures

with regular updates. The results are expected to improve significantly as more updates are

210

implemented, and it copes very well with huge changes in project budgets; however, this

analysis is tied to project duration and cost estimates. If the projects are expecting delays or

cost overruns, but neither reports nor revisions are provided for duration and cost estimates,

the system cannot reflect the effect that those delays and cost overruns will have on the

expenditure plan.

The PMDSS also provides a ranking for each project within the portfolio. This is important

in portfolio management because it focuses management’s energy and attention on problem

areas. It can also cause timely diversion of project resources to cope with impending

problems or resolve current issues. The rankings provided by the original estimates were

compared with updated rankings at 2009 Q3, 2010 Q3 and 2011 Q3, which showed that the

ranking orders changed after updates. By checking with reports, we examined possible

relationships between the ranking changes and status of the projects. A probability analysis

was applied to project rankings that obtained close results. The analysis showed the

likelihood that specific project rank would change.

211

CHAPTER 8 : CONCLUSION

8.1Summary of Completed Work

Transit projects commonly encounter the problems of cost overruns and schedule delays. In

this research, three aspects of transit projects – namely, schedule, cost and escalation – were

examined both at the individual project and portfolio levels. With schedule and cost being

obvious choices, in light of all the delays and overruns reported for various transit projects,

escalation is introduced here due to the long duration and large capital investments involved

in transit projects.

A new probabilistic analysis system called the ‘Portfolio Management Decision Support

System’ (PMDSS) has been developed. The four modules of this system – (1) Portfolio

Management Decision Support System – General (PMDSS-G), (2) Portfolio Management Decision

Support System – Bayesian Updating (PMDSS-B), (3) Portfolio Management Decision Support System –

Contingency (PMDSS-C) and (4) Portfolio Management Decision Support System – Escalation

(PMDSS-E) – are mainly Excel-based and are easily accessible by users. With the help of

these four modules, the management team can perform expenditure planning, contingency

planning, escalation analysis, portfolio ranking and Bayesian updating.

The main purpose of this research is to develop a decision support system that can be used

throughout project life cycle as a planning tool from the early planning phase, and a project

controls tool throughout the project’s execution. The system developed can perform this

planning and control function at both the individual and portfolio levels.

212

Highlights of original contributions in this research include the introduction of singularity

functions in the context of contingency planning, the establishment of a new index for

transit projects called the ‘Integrated Transit Index’, forecasting ITI by using neural network

and time series analysis, applying PROMETHEE-GAIA for ranking of the projects in the

portfolio, probability ranking, and the use of Bayesian updating for both schedule and cost

in portfolio updating analysis (for expenditure, contingency and ranking) throughout a

project’s life cycle.

One important feature of the proposed system is that the cost and duration of every project

within the portfolio is modeled as a probability distribution, thereby allowing the uncertainty

with these components to be explicitly considered. The modeling of the uncertainties is

made possible with a Monte Carlo simulation approach, a probabilistic approach that allows

users to obtain much more detailed information than deterministic analysis and thus better

enables them to cope with future uncertainties and plan appropriate mitigation efforts.

With transit projects experiencing huge cost overruns and delays, and due to the ever-

increasing scarcity of public funds, there is a strong demand for more accurate estimates of

project cost and schedule. For contingency analysis, a rigorous mathematical model is

introduced in this research that can be used for estimating project contingency for both cost

and schedule at the individual and portfolio levels. For cost escalation purposes, a new cost

index is developed and named Integrated Transit Index (ITI) which is believed to be

superior to the commonly used escalation indices, such as BCI or CCI published by ENR or

RS Means, as it is specifically designed for transit projects. Bayesian updating allows users to

update project cost and schedule throughout a project’s life cycle based on previous

estimated values and the new information that becomes available as the project progresses.

213

Together with the ranking system, this updating process provides timely information to

decision-makers so that mitigation plans can be promptly made to avoid potential cost

overruns and delays. The application of the system is demonstrated by applying it to a subset

of the New York’s East Side Access Projects. Comparisons were made between the actual

reported expenditures and the results produced by the system. It is demonstrated that the

system is capable of improving estimates as the portfolio of projects progresses.

8.2 Limitations of the Proposed System

It should be noted that the main purpose of this research is to provide a logical framework

for PPM while considering uncertainties. Analysis of the three suggested aspects – namely,

cost, schedule, and escalation – have been studied and modeled with this intention in mind.

The intent was not to develop a ready-to-use commercial product; however, it is believed

that, with necessary modifications, the system can be transformed into a useful product and

adopted in the industry.

Also, certain analyses are based on somewhat limited data. For example, for some categories

of the ITI, only data from the past 6 years are available online; however, the proposed

methodologies can incorporate future data and become more robust in their predictive

capability..

A mathematical limitation of the Bayesian approach for portfolio analysis is the assumption

of independence among projects. If the portfolio is composed of projects that are

geographically diverse (such as the portfolio of transit projects sponsored by the Federal

Transit Administration in a given fiscal year in the United States), then the assumption of

214

independence is reasonable. If on the other hand the model is applied to a large program

consisting of several subprojects, then the assumption of independence will create an

underestimation of variances. Another noteworthy observation is that the equal weights

assigned to all criteria introduced in the ranking system can be improved. The criteria

selected are both objective and subjective. Objective criteria such as project cost and

duration are tied to all other aspects of a project and can be affected by many factors.

Including these objective criteria in the research distinguishes the DSS from other methods

like AHP, which only consider subjective criteria. As no previous research has used these

criteria, and due to the general dearth of relevant data, it would be very difficult to obtain

information about weighting sets. It is also acknowledged that the weighting methods alone

require deep investigations and enormous efforts.

Moreover, the developed Portfolio Management Decision Support System (PMDSS)

described in this research can potentially contain over 10,000 distributions. Accordingly,

running the MC simulation might be a somewhat lengthy process. One solution is to

implement the whole system using a more efficient software system.

8.3 Recommended Work for Future

The system performance and reliability will improve as more data becomes available. For

example, normal distribution assumptions have been used in this research; however, with

more historical data, the distribution can be better defined. Also, for the time being, the

Integrated Escalation Index is based on data from the past 6 years. The inclusion of more

data will improve the results and achieve better escalation forecasts. Moreover, although the

fact that the system is mainly Excel-based makes it easily accessible to all users, it also

215

presents some limitations. In order to be applied for practical use, the system should be

transformed into a more efficient software product, although the typical end-user might be

more familiar and comfortable with Excel. Furthermore, equal weights were assigned to

selected criteria in the developed rank system. It is suggested to collect more data to

investigate the weights of all the criteria, so better ranking results can be achieved.

216

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