A new approach to model cost and duration of projects

in stochastic environments

Niam Yaraghi

Mansour Hajbagheri

Royal Institute of Technology (KTH), Sweden

SRA 2009 Annual Meeting

December 7th-9th , 2009

Baltimore, MA, USA

Motivations

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Combining historical data with expert ideas

Avoiding subjectivity

Minimizing the variations in expert judgments

Introduction

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Projects are temporarily and unique endeavors, so it is more

difficult to have an accurate estimation of their associated

activities due to relatively few number of past executions.

The experts in the projects have a higher degree of disagreement

due to their field of expertise, knowledge and experience.

The proposed model as a decision support tool, is designed to

help decision maker with more promising cost/time estimates

by combining expert ideas with empirical data available from

past projects.

Why Simulation?

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The need to cope with few amount of available historical data

The need to reflect uncertainty and risks associated with time and

cost estimates

The need to provide decision makers with flexible and robust tools

Objective: To make a model which uses Monte Carlo simulation

for analyzing the expert judgment risks

For each activity, planned and actual value of its cost and duration are fitted to the proper probability distribution function by using Maximum Likelihood Method (MLE)

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Model Development

Model Development (Cont’d)

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• The detailed results of Monte-Carlo simulation is used as an input to calculate a more accurate linear correlation between planned and actual cost/time of the projects

Model Development (Cont’d)

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• As the second step, in order to create a PERT distribution for each activity, experts are asked to give their estimation about minimum, most likely and maximum value of each activity’s cost and time.

• These Judgments are combined into one probability function based on the credit and reliability of each expert.

• The final estimates is then inserted in the later correlation formula to have a better estimate about the actual time/cost of the activities.

• By this step, we have three different estimates upon

– (1) previous actual cost and time values as objective data,

– (2) expert estimates as subjective data and

– (3) an estimate based on combination of subjective and objective data.

Master's Thesis Presentation Mansour Hajbagheri

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Model Development (Cont’d)

EST 1: RiskPert(12,37,67)EST 2: RiskDiscrete(A2:C2,A4:C4)EST 3: 1.1577*E4-5.43

Model Development (Cont’d)

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• After running the model, results are handed over among the experts in order to revise their estimates and also indicate their perception about the simulation results in terms of five linguistic variables: very optimistic, optimistic, pragmatic and pessimistic and very pessimistic.

• By deploying Fuzzy Logic, these linguistic variables are quantified so that the accuracy of each simulation is weighted.

• As the final step, three previous estimates are again combined with respect to

their relative importance to reach the most possible accurate estimation

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