A Methodology for Estimating the Level of Aggressiveness inCompetitive Bidding Markets

Janet D. Sparks

Thesis submitted to the Faculty of theVirginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Sciencein

Civil and Environmental Engineering

Michael C. Vorster, chairJulio C. MartinezW. Eric Showalter

December 9, 1999Blacksburg, Virginia

Keywords: competitive bidding, bidding model, market analysis

Copyright 1999, Janet D. Sparks

A Methodology for Estimating the Level of Aggressiveness in Competitive BiddingMarkets

Janet D. Sparks

(ABSTRACT)

Competitive bidding, where the project is awarded to the lowest bidder, is a basic part ofthe construction industry. This method of project delivery is designed to promote healthycompetition in an attempt ensure the lowest price for the project. A contractor knows thatlowering a bid price increases his probability of being awarded the project. However,without a clear understanding of the market in which he is competing, he can not knowhow low he should bid in order to win. One of the most important competitive forces in acompetitive bidding market is the how low the contractors are willing bid, i.e., howaggressively they are pursuing the project. Contractors need a simple way to examine thelevel of aggressiveness in their market.

The purpose of this research is to develop a methodology to enable contractors to betterunderstand this level of aggressiveness. The level of aggressiveness is quantified by theratio of the low bid to the pack price, where the pack price is defined as the lower of thetwo bids that are closest together. The examination of two competitive bidding markets--the Virginia Department of Transportation market between 1996 and 1998 and theTennessee Department of Transportation market from 1996 to 1998--tests the validity ofthe methodology. The methodology for estimating the level of aggressiveness in acompetitive bidding market produces a set of success curves and charts, which can beused by contractors to optimize their competitive bid amounts for future projects.

iii

For my ParentsThank you....

iv

Author's Acknowledgements

First, I would like to thank my Thesis committee, Dr. Julio Martinez, Dr. W. Eric

Showalter, and especially, the committee chair, Dr. Mike Vorster. Without their

guidance and support, this research would not have been possible. The assistance of the

Virginia Department of Transportation and the Tennessee Roadbuilder's Association,

both of whom provided bidding result data free of charge, was invaluable. The Statistical

Consulting Center provided much-needed assistance with statistical analysis of the

research results. Finally, I would like to thank the Via Endowment Program for my Via

Master's Fellowship, which enabled me to attend graduate school at Virginia Tech.

vTable of Contents

Chapter 1: Introduction ....................................................................................................... 1

1.1 Competitive Bidding ................................................................................................. 1

1.2 Statement of the Problem .......................................................................................... 2

1.3 Purpose of the Research ............................................................................................ 2

1.4 Basic Premises of the Research................................................................................. 3

1.4.1 The Competitive Bidding Pack .......................................................................... 3

1.4.2 The Pack Price.................................................................................................... 3

1.5 Scope of the Research ............................................................................................... 4

1.6 Benefits of the Research............................................................................................ 4

1.7 Summary ................................................................................................................... 4

Chapter 2: Review of Literature.......................................................................................... 6

2.1 Market Analysis ........................................................................................................ 6

2.2 Competitive Strategy................................................................................................. 6

2.3 Analysis of Competition............................................................................................ 7

2.4 Aggressiveness in Competitive Market Analysis...................................................... 8

2.5 Analysis of Competitive Bidding Markets................................................................ 9

2.6 Friedman's Competitive Bidding Strategy .............................................................. 10

2.6.1 Bidding Strategy Objective .............................................................................. 10

2.6.2 Bias of Estimated Cost ..................................................................................... 10

2.6.3 Expected Profit................................................................................................. 10

2.6.4 Probability of Winning..................................................................................... 11

2.6.5 Optimum Bid Determination............................................................................ 12

2.7 Gates' Bidding Model.............................................................................................. 13

2.7.1 Bidding Strategy Objective .............................................................................. 13

2.7.2 Lone-Bidder ..................................................................................................... 13

2.7.3 Two-Bidder Strategy ........................................................................................ 13

2.7.4 Many-Bidders Strategy .................................................................................... 14

2.7.5 All-Bidders-Known Strategy............................................................................ 14

2.7.6 Least-Spread Strategy....................................................................................... 15

2.8 Friedman vs. Gates.................................................................................................. 15

vi

2.9 OPBID..................................................................................................................... 17

2.10 Combining the Models with Instinct ..................................................................... 19

2.11 LOMARK.............................................................................................................. 19

2.12 Carr's Bidding Model ............................................................................................ 20

2.12.1 Using Multiple Regression............................................................................. 20

2.12.2 General Bidding Model.................................................................................. 20

2.12.3 Impact of the Number of Bidders................................................................... 21

2.12.4 Competitive Bidding and Opportunity Costs ................................................. 22

2.13 Optimum Bid Approximation Model.................................................................... 22

2.14 Symmetry and State of Information ...................................................................... 23

2.15 Bids Considering Multiple Criteria ....................................................................... 23

2.16 Winning over Key Competitors ............................................................................ 24

2.17 DBID ..................................................................................................................... 24

2.18 Sequential Competitive Bidding ........................................................................... 25

2.19 Self-explanatory Artificial Neural Networks ........................................................ 26

2.20 Average-Bid Method Bidding Model ................................................................... 27

2.21 Use of Bidding Models ......................................................................................... 27

2.21.1 Actual Use of Competitive Bidding Models .................................................. 27

2.21.2 Effective Use of Competitive Bidding Models .............................................. 28

2.22 Bidding Patterns in Virginia.................................................................................. 29

2.23 Summary ............................................................................................................... 29

Chapter 3: Methodology for Estimating the Level of Aggressiveness ............................. 31

3.1 Research Concept.................................................................................................... 31

3.1.1 The Level of Aggressiveness ........................................................................... 32

3.1.2 The Pack Price.................................................................................................. 32

3.1.3 The Level of Agreement .................................................................................. 33

3.1.4 The Ratio of the Low Bid to Pack Price........................................................... 33

3.1.5 Limitations ....................................................................................................... 36

3.1.6 Usefulness ........................................................................................................ 36

3.2 Research Methodology............................................................................................ 37

3.2.1 Gathering the Data ........................................................................................... 37

vii

3.2.2 Determining the Pack Price.............................................................................. 39

3.2.3 Validating the Pack Price ................................................................................. 39

3.2.4 Calculating the Ratio of the Low Bid to the Pack Price................................... 40

3.2.5 Plotting the Data Curve .................................................................................... 40

3.2.6 Determining the Probability of Success ........................................................... 41

3.2.7 Plotting the Success Curve............................................................................... 42

3.2.8 Grouping the Data Set To Investigate Potential Influencing Factors............... 42

3.2.9 Constructing the Success Charts ...................................................................... 45

3.3 Summary ................................................................................................................. 49

Chapter 4: Results and Analysis........................................................................................ 51

4.1 The Pack Price as a Predictor of the Low Bid......................................................... 51

4.2 Analyzing the Level of Aggressiveness in the Market ........................................... 52

4.2.1 The Process of Analysis ................................................................................... 52

4.2.2 Analyzing the Level of Aggressiveness in the Virginia Market ...................... 54

4.2.3 Analyzing the Level of Aggressiveness in the Tennessee Market................... 59

4.3 Determining Which Factors Have a Real Effect on the Level of Aggressiveness.. 63

4.3.1 The Virginia Market......................................................................................... 63

4.3.2 The Tennessee Market ..................................................................................... 63

4.4 Comparison between the Virginia and the Tennessee Market................................ 64

4.5 Summary ................................................................................................................. 65

Chapter 5: Field Implementation....................................................................................... 66

5.1 The Steps ................................................................................................................. 66

5.2 Gather the Data........................................................................................................ 66

5.3 Determine the Pack Price ........................................................................................ 69

5.4 Validate the Pack Price ........................................................................................... 69

5.5 Calculate the Ratio .................................................................................................. 70

5.6 Plot the Data Curve ................................................................................................. 70

5.7 Determine the Probability of Success .................................................................... 71

5.8 Plot the Success Curve ............................................................................................ 71

5.9 Group the Data to Investigate Potential Influencing Factors .................................. 72

5.10 Construct the Success Charts ................................................................................ 73

viii

5.11 Analyze the Level of Aggressiveness in the Market............................................. 74

5.12 Consider Factors That Influence the Pack Price ................................................... 75

5.13 Using the Pack Price Method for Future Projects ................................................. 75

5.14 Importance of Updating the Pack Price Method ................................................... 77

5.15 Summary ............................................................................................................... 77

Chapter 6: Conclusion....................................................................................................... 78

6.1 Summary of Research ............................................................................................. 78

6.2 Conclusions ............................................................................................................. 78

6.3 Future Research....................................................................................................... 79

6.4 Final Thought .......................................................................................................... 80

Appendix A: References ................................................................................................. 81

Appendix B: Research Graphs........................................................................................ 86

Appendix C: Success Charts......................................................................................... 100

Appendix D: Virginia and Tennessee Data Sets........................................................... 108

ix

List of Equations

Equation 2-1: Estimate Cost Corrected for Bias ... 10

Equation 2-2: Expected Profit ... 10

Equation 2-3: Fit of the Average Bidder's Distribution ... 12

Equation 2-4: Probability of Winning With k Bidders 12

Equation 2-5: Probability of Having k Bidders .. 12

Equation 2-6: Expected Profit With a Bid of x 12

Equation 2-7: Expected Value of a Project. 13

Equation 2-8: Probability of Winning Over n Known Competitors.. 14

Equation 2-9: Average Spread.. 15

Equation 2-10: Relationship Between Increasing a Bid and Probability of Winning.. 15

Equation 2-11: Friedman's Probability of Winning Over n Competitors 16

Equation 2-12: Gates' Probability of Winning Over n Competitors 16

Equation 2-13: LOMARK'S Probability of Losing... 20

Equation 2-14: Probability of Having a Lower LBC than Opponent 21

Equation 2-15: Adjustment for the Number of Bidders 21

Equation 2-16: Probability of Winning with Sequential Bidding 22

Equation 2-17: Optimum Bid Approximation Model 22

Equation 2-18: Expected Value for a Series of Projects 26

xList of Figures

Figure 2-1: Components of Competitor Analysis ............................................................... 8

Figure 2-2: Friedman's Method of Determining the Probablity of Winning..................... 11

Figure 2-3: Summary Flow Chart for OPBID................................................................... 18

Figure 2-4: Queuing Model Representation of Flow of Limited Resources..................... 25

Figure 2-5: Hierarchical Structure of the Artificial Neural Network................................ 27

Figure 3-1: The Pack Price Concept ................................................................................. 33

Figure 3-2: Different Levels of Aggressiveness ............................................................... 34

Figure 3-3: Example of Ratio of Low Bid to Pack Price ................................................. 35

Figure 3-4: Example Historical Bidding Results .............................................................. 38

Figure 3-5: Projects Considered for the Two Markets...................................................... 40

Figure 3-6: Partial Ratio Range Success Chart ................................................................. 47

Figure 3-7: Partial Probability of Success Range Success Chart ...................................... 49

Figure 4-1: Correlation Between the Low Bid and Its Predictors..................................... 52

Figure 4-2: VDOT Districts .............................................................................................. 56

Figure 4-3: TDOT Regions ............................................................................................... 61

Figure 5-1: Example Bidding Results ............................................................................... 68

Figure 5-2: Example Ratios and Cumulative Percentage for Ratios................................. 70

Figure 5-3: Chart of the Probability of Success for the Different Levels of the Ratio ..... 73

Figure 5-4: Chart of the Ratio for the Different Levels of the Probability of Success ..... 74

Figure C - 1: Virginia Ratio Range Success Chart.......................................................... 101

Figure C - 2: Tennesse Ratio RangeSuccess Chart ......................................................... 103

Figure C - 3: Virginia Probability Range Success Chart ................................................ 104

Figure C - 4: Tennessee Probability Range Success Chart ............................................. 107

xi

List of Graphs

Graph 3-1: Example Data Curve....................................................................................... 41

Graph 3-2: Ranges for the Ratio of the Low Bid to the Pack Price .................................. 46

Graph 3-3: Ranges for the Probability of Future Success................................................. 48

Graph 4-1: Probability at the Ratio = 1.00 and the Slope of the Graph ............................ 53

Graph 5-1: Example Data Curve....................................................................................... 71

Graph 5-2: Example Success Curve.................................................................................. 72

Graph B - 1: 1996-1998 Virginia Projects (1478 Projects)............................................... 86

Graph B - 2: 1996-1998 Tennessee Projects (744 Projects) ............................................. 87

Graph B - 3: Low Bid vs. Pack Price for 137 Virginia Projects ....................................... 87

Graph B - 4: Low Bid vs. Engineer's Estimate for 137 Virginia Projects ........................ 88

Graph B - 5: Low Bid vs. Pack Price (119 Virginia Projects, $5 Million) ........ 90

Graph B - 9 : Virginia Projects Grouped By Year ............................................................ 90

Graph B - 10: Virginia Projects Grouped By Time of Year ............................................. 91

Graph B - 11: Virginia Projects Grouped by Location ..................................................... 91

Graph B - 12: Virginia Projects Grouped By Project Size................................................ 92

Graph B - 13: Virginia Projects Grouped by Previous Month's Volume of Work ........... 92

Graph B - 14: Virginia Projects Grouped by Current Month's Volume of Work ............. 93

Graph B - 15: Virginia Projects Grouped by Following Month's Volume of Work......... 93

Graph B - 16: Virginia Projects Grouped by Number of Bidders..................................... 94

Graph B - 17: Virginia Projects Grouped by Type of Project........................................... 94

Graph B - 18: Tennessee Projects Grouped by Year ........................................................ 95

Graph B - 19: Tennessee Projects Grouped by Time of Year........................................... 95

Graph B - 20: Tennessee Projects Grouped by Location .................................................. 96

Graph B - 21: Tennessee Projects Grouped by Size of Project......................................... 96

Graph B - 22: Tennessee Projects Grouped by Previous Month's Volume of Work........ 97

Graph B - 23: Tennessee Projects Grouped by Current Month's Volume of Work.......... 97

Graph B - 24: Tennessee Projects Grouped by Following Month's Volume of Work ..... 98

xii

Graph B - 25: Tennessee Projects Grouped by Number of Bidders ................................. 98

Graph B - 26: Virginia Market and Tennessee Market..................................................... 99

Graph B - 27: Tennessee Projects Grouped into Two Groups by Number of Bidders ..... 99

1Chapter 1: Introduction

The purpose of this chapter is to introduce the research contained in this paper. The

concept of competitive bidding is briefly discussed. The statement of the problem and

the purpose of this research are outlined. Along with the benefits of successfully

completing the research, the basic premises of the research and its scope are explained.

1.1 Competitive Bidding

Competitive bidding, where the project is awarded to the lowest bidder, is a basic part of

the construction industry. This method of project delivery is designed to promote healthy

competition in an attempt to ensure the lowest price for the project. While private owners

may chose to award contracts in any way, many public agencies are required by law to

award the project to the lowest bidder. Most all types of governments in the United

States--local, state, and federal--favor competitive bidding over negotiated contracts for

public projects (Morris 1988). Public projects are those defined as construction work that

is financed by public funds, such as taxes or sale of bonds (Bartholomew 1998).

Recently there has been a trend toward project delivery methods other than competitive

bidding. For example, the industry is showing increased interest in design-build

contracts. Another method of awarding projects, which is growing in popularity is the

average-bid method. Florida's Department of Transportation has begun using a modified

average-bid method to award part of their projects ("Low" 1998). The fact that a public

agency is beginning to study alternative methods of awarding contracts might lead one to

think that the use of competitive bidding, where the project is awarded to the lowest

bidder, is ebbing. However, the tradition is still strong, and competitive bidding will

remain as long as the public is concerned over how tax money is spent.

Public contracts are usually advertised and let according to bidding statutes. Contractors

who are interested in obtaining the project submit bids to the owner at a set time. The

project is then awarded to the lowest responsive and responsible bidder. A responsive

2bidder is one that meets all the requirements for the project and has filled the forms out

correctly, while a responsible bidder is one that has enough experience and money to do

the work (Bartholomew 1998).

1.2 Statement of the Problem

Estimating and bidding is a costly and time-consuming process. All of this effort is

wasted each time the contractor's bid is not the lowest. The contractor needs to optimize

his position, bidding low enough to get the work but only slightly lower than the second

lowest bidder. When he underbids the next highest competitor by a large amount, the

contractor loses additional money, which he could have added to the bid and still won.

A contractor knows that lowering a bid price increases his probability of being awarded

the project. However, without a clear understanding of the market in which he is

competing, he can not know how low will be too low. How much he should raise or

lower his bid depends on many market factors. In competitive bidding, one of the most

important competitive forces at work is how low the other contractors are willing to bid,

i.e., how aggressively they are pursuing the project. Contractors need a simple way to

examine the level of aggressiveness in a market.

1.3 Purpose of the Research

This research is designed to provide contractors, who are seeking work through

competitive bidding, a method to improve their understanding of the level of

aggressiveness in their bidding markets. The level of aggressiveness in a market is a

measure of how interested contractors are in obtaining work and is a result of the

economic conditions of the market. This research is not a competitive bidding model; it

is a market aggressiveness model.

31.4 Basic Premises of the Research

1.4.1 The Competitive Bidding Pack

Imagine a pack of wolves hunting for prey. The pack may run very close together or

spread out over a significant distance. As they hunt, the leader of the pack changes

frequently. Sometimes, being the leader has it advantages. If the pack encounters a small

rabbit, the leader will be able to catch the rabbit for itself, regardless of the distribution of

the pack. However, if they encounter a bear while spread out, the leader is probably going

to die before help arrives. Obviously, the optimum position for any one wolf is to be the

first in line for lunch without running so far ahead of the rest of the pack that it is lunch.

The leaders of the pack will be the aggressive wolves, who are hungry and willing to take

the risk of leading. Other wolves may tend to be apathetic about hunting and

disinterested in leading the pack.

A group of contractors, who bid competitively for work, can be similar to the pack of

wolves (Vorster 1978). They are hunting for work in a hostile environment. Like the

lead wolf, the lead contractor needs to optimize his position, bidding low enough to get

work but not bidding much lower than his closest competitor. To find the optimum

position, the contractor must take into account how hungry/aggressive, or how

satiated/disinterested, the other contractors are.

1.4.2 The Pack Price

The backbone of this research is the concept of the pack price. The pack price is defined

as the lower of the two bids that are closest together (Vorster 1978). The pack price is the

price upon which two, independent, equally informed, competitive contractors came

closest to agreeing. The hypothesis of this research is that the pack price marks the

division point between the aggressive contractors, who will bid lower than the pack price,

and the disinterested contractors, who will tend to bid more than the pack price. The

pack price can also be defined as the break point between the aggressive bidders and the

disinterested bidders. Thus, the pack price should reveal what the price of the project

4would be if there were no aggressive bidders desperately trying to beat everyone else and

if there were not disinterested bidders purposely bidding high.

1.5 Scope of the Research

The data sets studied for this research project include the final bidding results from two

different sources. The results of lettings by the Virginia Department of Transportation

(VDOT) and the Tennessee Department of Transportation (TDOT) during the years

1996-1998 were studied. The pack price for each project in the data sets is determined;

then the ratio of the low bid to the pack will be calculated. For both data sets, the

probability of winning a project with a certain ratio will be determined. The relationship

between the ratio of the low bid to the pack price and the probability of success will be

studied.

1.6 Benefits of the Research

The main benefit of the successful completion of this research project is to enable

contractors to better understand the level of aggressiveness in his competitive bidding

market with only a relatively small amount of data. As a result, he may be able to

estimate the probability of success for a project based on how aggressively contractors

are seeking working in his market. This would give him one more piece of information

to use to improve his bidding strategies. He may find that his probability of winning with

that price is unsatisfactory, so he can either lower his margin or work to lower his costs.

Lowering his bid to the point that he has a reasonable probability of winning may not be

feasible for him. If so, the contractor can withdraw from bidding. Then, the company is

saved the additional expense of bidding on a project that it has a low probability of being

awarded.

1.7 Summary

This chapter outlined the basics of the research contained in this document. The

statement of the problem that this research proposes to solve followed a general

5discussion of competitive bidding. The purpose of the research, its basic premises, and

scope were discussed. The benefits of this research were also examined.

6Chapter 2: Review of Literature

The purpose of this chapter is to present the past research into the analysis of competitive

markets. For some industries, competitive market analysis is accomplished through

general market reports, the development of competitive strategies, or a study of

aggressiveness in the market. For the construction industry, this research generally took

the form of the development of competitive bidding models. Several different bidding

models will be explained, with special attention devoted to the bidding models of

Friedman, Gates, and Carr. The use of bidding models in actual situations will be

examined. Finally, an earlier study of the bidding patterns in Virginia will be discussed.

2.1 Market Analysis

Market analysis is an extremely broad topic encompassing many disciplines. The

detailed analysis of a single competitive market can include an almost unlimited number

of considerations. For example, an analysis of the worlds coffee market (Akiyama and

Ducan 1982) contains a detailed description of the leading producers, a complete

discussion of the export rate and areas of demand, and a price study. Weather patterns,

along with any new legislation or government decisions and their effect on the market are

studied. The coffee market analysis also discussed a model developed to evaluate the

long-term market outlook. It is apparent from the examination of this one market

analysis that many different skills and an extensive amount of information is needed to

produce a market analysis with this level of detail.

2.2 Competitive Strategy

Performing an in-depth market analysis, similar to the one described in the previous

section, is probably not within the resources of most firms. An individual firm can

analyze a competitive market while developing a competitive strategy. The goal of a

competitive strategy is to find the place in the industry where the company can best

7defend itself against the competitive forces. This defense can only occur if the firm

explores the nature of its market and of the competitive forces listed below (Porter 1980).

1) Bargaining power of suppliers

2) Bargaining power of buyers

3) Threat of new entrants into the industry

4) Threat of substitute products

5) Rivalry among existing firms

By understanding how these forces affect the market, firms can analyze the competition

in that market.

2.3 Analysis of Competition

In order to understand the rivalry among existing firms, an analysis of each competitor

should be done. The objectives of analyzing competitors includes (Porter 1980):

1) To develop a profile of the nature and success of the likely strategy changes each

competitor might make,

2) To determine each competitors probable response to the range of feasible

strategic moves other firms could initiate,

3) To examine each competitors probable reaction to the array of industrial changes

that might occur.

A lack of quality, detailed information can make competitor analysis difficult. A firm

will have a better understanding of its competitive environment if it answers the

questions shown in Figure 2-1 (Porter 1980 p. 49) and develops a response profile for

each competitor. The questions can be answered by gathering information about the

competition's future goals, current strategy, assumptions, and capabilities.

8Figure 2-1: Components of Competitor Analysis

2.4 Aggressiveness in Competitive Market Analysis

Recent research into competitive market analysis has used the level of aggressiveness as

one factor in the analysis (Jogaratnam et al. 1999). Aggressiveness was defined as the

aggressive allocation of resources to improve market position and pursue market share at

What Drives theCompetitor

What the Competitor IsDoing and Can Do

CURRENT STRATEGY

How the business is currentlycompeting

ASSUMPTIONS

Held about itself andthe industry

CAPABILITIES

Both strengths andweaknesses

FUTURE GOALS

At all levels of managementand in multiple dimensions

COMPETITOR'S RESPONSE PROFILE

Is the competitor satisfied with its currentposition?

What likely moves or strategy shifts will thecompetitor make?

Where is the competitor vulnerable?

What will provoke the greatest and most effectiveretaliation by the competitor?

9a faster rate than competitors (Jogaratnam et al. 1999 p. 91). The concept of

aggressiveness was applied to the analysis of the independent restaurant market in United

States. The research found that aggressiveness commonly took the form of lowering

prices and seeking market share at the expense of profits. As a result, restaurants with

lower levels of aggressiveness were generally more successful. The level of

aggressiveness of one firm appears to have a negative effect on the successfulness of the

firm. Understanding the level of aggressiveness for an entire market would be an

important factor in a complete competitive market analysis.

2.5 Analysis of Competitive Bidding Markets

For most industries, the analysis of the level of competition, focuses on markets where

the price for individual goods or services are controlled by the interaction of supply and

demand. In that situation, many suppliers are selling basically identical items and the

consumers have a choice of choosing to buy or not to buy at a certain price. As a result

of the consumer's choices, the price for the item is set.

While it is true that the amount of work available in an area may affect the price of a

project, the situation described above is not the exact situation for much of the

construction industry. The construction industry often set the price for an individual

project through competitive bidding, where the low bidder is awarded the project. In

competitive bidding, the suppliers are not selling exactly the same thing. In fact,

contractors may be selling extremely different methods of completing a project, and the

owner must accept the lowest price. For this reason, research into and analysis of the

competitive environment of the construction industry has focused primarily on the

development of competitive bidding models, rather than on more conventional methods

of market analysis.

10

2.6 Friedman's Competitive Bidding Strategy

2.6.1 Bidding Strategy Objective

Friedman's competitive bidding strategy (Friedman 1956) is the pioneering work in the

study of competitive bidding. He asserted that a company has several objectives when

bidding on a project. A few of the possible objectives are to maximize the total expected

profit, minimize the total expected losses, or to obtain the project even at a loss. While

all of these objectives are valid, the one that Friedman chose as the basis of his bidding

strategy is to maximize the total expected profits. He chose this objective because it is

common one for any company and because it is "one of the easiest to handle in a bidding

situation of this type" (Friedman 1956).

2.6.2 Bias of Estimated Cost

Friedman recognized that a company's estimated cost, C, and the actual cost of the

completed project could be quite different. To account for this in the model, he

developed a method of determining the bias of an estimated cost from a comparison of

the estimated cost and actual cost of the company's previous projects. The estimated cost

corrected for bias, C', is calculated by Equation 2-1 (Friedman 1956 p. 106), where S is

the ratio of past estimated costs to past actual costs and h(S) dS is the probability that the

ratio of the true cost to the estimated cost is between S and S+dS. If the company is

using the model to help refine their bidding practices, this bias will eventually be zero.

dSSShCC =0

)(' ------------------------------------ (2-1)

2.6.3 Expected Profit

After determining the bias of the estimated cost, a company can calculate the expected

profit of a future project. If x is the amount bid for the contract, then the expected profit

for the project, E(x), is given by Equation 2-2 (Friedman 1956 p. 106), where P(x) is

probability of winning if the bid is x.

)')(()( CxxPxE = -------------------------------- (2-2)

11

2.6.4 Probability of Winning

The equation for determining the expected profit is deceptively simple. C' and x are

known, but determining the probability of winning can be quite difficult. Friedman

concluded that one way to determine the probability of winning is to examine the bidding

patterns of the competition in relation to the contractor's own bidding pattern. Any

competitor's bidding pattern can be understood by examining the ratio of the

competition's bid to the contractor's cost for past projects. With this information, a

probability distribution of that ratio can be constructed. If a contractor knows that the

estimated cost is C and has constructed the distribution, then he can determine the

probability of winning with a bid of x. The probability of winning is equal to the area

under the distribution curve greater than the ratio of x for the current project to C for the

current project. See Figure 2-2 for an example. For more than one competitor, the

probability of winning with a bid x is the product of the probability of defeating each of

the competitors.

Figure 2-2: Friedman's Method of Determining the Probablity of Winning

If all the competitors are not known, then the probability of winning can be determined

by using Friedman's concept of an average bidder. The average bidder is a composite of

all bidders that the contractor has faced in the past. The probability distribution of the

Ratio of Competition's Bid to Contractor's Cost

Pro

babi

lity

of

rati

o oc

curr

ing

in th

e fu

ture

Probability of winning with a bid of xand a cost of C = Area shown here

x/C for the new project

12

ratio of the average competitor's bid to the contractor's costs is called f(r) and is

determined by fitting a curve to the set of ratios of the opposition's bid to the contractor's

costs for past projects. A gamma distribution is frequently a good fit for this data

(Friedman 1956), so Equation 2-3 (Friedman 1956 p. 108) can be used for )(rf , where a

and b are constants from fitting the data to the curve.

arbb erbarf += )!()( 1 ------------------------------- (2-3)

If the probability of having k bidders for the project is represented by g(k), then the

probability of winning with a bid of x, P(x), is shown in Equation 2-4 (Friedman 1956 p.

108).

k

C

xok

drrfkgxP

=

=

)()()( ---------------------- (2-4)

Assuming that the number of bidders follows a Poisson distribution, then g(k) is given by

Equation 2-5 (Friedman 1956 p. 108 )

!)( kekg k = ------------------------------- (2-5)

2.6.5 Optimum Bid Determination

Remember that the goal of Friedman's model is to optimize the expected profit.

Combining Equations 2-3, 2-4, and 2-5, Friedman developed Equation 2-6 (1956 p. 109),

which gives the expected profit when submitting a bid of x. The expected profit can be

calculated for different values of x until the optimum value is determined. Knowing the

optimum value of the bid and the estimated costs, the contractor can calculate the

optimum markup.

== =

b

i

Cax

i

eC

axCxxPCxPE

0 !1

11exp)'()()'(.. -- (2-6)

13

2.7 Gates' Bidding Model

2.7.1 Bidding Strategy Objective

The other pioneer in the study of competitive bidding is Marvin Gates. Like Friedman's,

Gates' bidding model is based on the goal of maximizing the profits for a job (Gates

1967). Gates presents six different strategies for use by contractors in different

situations. All the strategies utilize Equation 2-7 (Gates 1967 p. 75), which calculates the

expected value of the project, EV, for different bid amounts, P. P is known, so the

complication lies in determining the probability of winning, (p).

EVPp =*)( --------------------------------------- (2-7)

2.7.2 Lone-Bidder

In the unique situation that the contractor finds that he is the only bidder, Gates suggests

that the contractor just estimate the probability of winning. The contractor's probability

of winning will be based on the contractor's estimate of the highest bid that the owner

will accept. By carefully considering this and other factors, the contractor can determine

the value of (p) for different bids. By using Equation 2-7, the expected value for each bid

amount can be determined. The bid with the greatest expected value should be

submitted, thereby maximizing the profits for bidding situation.

2.7.3 Two-Bidder Strategy

If the contractor is one of two bidders for a project, Gates proposes that the contractor

should carefully estimate the probability of winning with certain bid amounts. After

discovering that there are only two bidders, a contractor might raise his bid because there

is less competition. Different situations, which should be considered, revolve around

whether neither, both, or either of the two competitors raise their bids. Then, using the

game-theory approach, the contractor can determine what bid amount to submit to

maximize the profit for the job (Gates 1967). Neither the lone-bidder nor the two-bidder

situations are customary in the real world.

14

2.7.4 Many-Bidders Strategy

The most common situation, which a contractor encounters, is bidding against many

others for a project. In this situation, Gates proposes the use of an average bidder to

represent all the other competitors. Using historical information, the contractor studies

his bid in relation to the low bidder by subtracting the ratio of the low bid to the

contractor's bid from one. This percentage tells the contractor how much he would have

needed to reduce his bid in order to be the low bidder. If the contractor was the low

bidder, then the ratio between the second lowest bid and the low bid (the contractor's bid)

is subtracted from one. In this situation, the percentage is negative and expresses how

much the contractor could have raised his bid and still been the low bidder. The

contractor can create a cumulative probability distribution to determine the probability

that certain ratios of his bids to the low bids will occur in the future. From that

distribution, he can develop a relationship between the probability of winning and the

amount of the bid. Then, using Equation 2-7, the contractor can get the expected value

for different bid amounts and pick the bid amount that maximizes that expected value.

2.7.5 All-Bidders-Known Strategy

The all-bidders-known strategy would be used when the contractor is familiar with and

has historical bidding information for all the other bidders for a project. This strategy is

very similar to the many-bidders strategy. The difference is that the historical bidding

data is sorted by which competitor was the low bidder. Then, a separate analysis, like the

one done for the many-bidders strategy, is done for each opponent. When the probability

of beating each opponent is known, the probability of wining over all the competitors is

calculated using Equation 2-8 (Gates 1967 p. 85), where Pn is the probability of beating

contractor n.. When the contractor knows the probability of winning, he can use

Equation 2-7 to calculate the maximum expect value.

( ) ( ) ( ) ( )nn

C

C

B

B

A

A

p

p

p

p

p

p

p

pp

)](1[...

)](1[)](1[)](1[1

1)(

++

+

+

+= ----------- (2-8)

15

2.7.6 Least-Spread Strategy

In competitive bidding, contractors are almost as concerned about being the low bidder

by a large amount as they are about entirely losing the project. The amount of money

"left on the table" is equal to the amount of money that could have been added to the bid,

while maintaining the contractor's position as the low bidder. This amount, which is the

difference between the low bid and second lowest bid, can also be called the spread

(Gates 1967). By studying 400 construction contracts, Gates determined that the average

spread, Bavg, could be determined with Equation 2-9 (Gates 1967 p. 90), where C is the

low bid amount.

734.008.1 CBavg = ------------------------------ (2-9)

Gates' least-spread strategy is designed to allow the contractor to determine how adding a

certain amount of money to a bid affects the probability of winning. The probability of

winning relates to an increase in the bid as shown in Equation 2-10 (Gates 1967 p. 90),

where (p) is the probability of wining and P' is the amount added to the bid. Once the

contractor knows the probability of wining after increasing the bid, he can determine the

new expected value of the project with Equation 2-7. After examining the set of potential

increases effect on the expected value, the contractor can find the maximum expected

profit and the optimum bid amount.

( )pB

P

avg

=

167

---------------------------------- (2-10)

2.8 Friedman vs. Gates

There has been much controversy over the validity of Friedman's bidding model and

Gates' bidding model. The debate centered on the equation used to determine the

probability of wining against known competitors. Friedman said that the probability of

winning over n known competitors was the product of winning over each known

competitor, as shown in Equation 2-11 (Friedman 1956). To make the comparison

simpler, Gates' method of determining the probability of winning over n known

competitors is restated in Equation 2-12 (Gates 1967 p. 85). For both Friedman's and

16

Gates' equations, (p) is the probability of winning and (pX) is the probability of winning

over competitor x.

))...()()(()( nCBA Ppppp = ---------------------------- (2-11)

( ) ( ) ( ) ( )nn

C

C

B

B

A

A

p

p

p

p

p

p

p

pp

)](1[...

)](1[)](1[)](1[1

1)(

++

+

+

+= ------- (2-12)

This controversy began with a published discussion between R.M. Stark and Gates

concerning Gates' bidding model (Benjamin and Meador 1979). Many different people

entered the fray at one time or another (Rosenshine 1972, Dixie 1974, Fuerst 1976, and

Gates 1976), each presenting a different derivation of the equations or a different

interpretation of the correct applications of the models.

However, it was not until 1979, that someone published an actual comparison of the

results of using the two different models (Benjamin and Meador 1979). The premise of

the study was that if one of the models was more correct, then the more correct model

would yield better results over time. Since both models have the goal of maximizing the

expected profits, the researchers decided that the better model would provide the

contractor with higher long-term profits. During the study, it was determined that

Friedman's model results in the contractor adding a smaller markup to a project than

Gates' model. As a result of a smaller markup, Friedman's model will help the contractor

win more projects than Gates' model.

Thus, at first glance, it would appear that Friedman's model is better, but Friedman's

model does not necessarily provide the contractor with higher long-term profits. In fact,

to obtain the same profit as the profit that results from using Gates' model, the contractor,

using Friedman's model, would need to obtain approximately twice the volume of work

(Benjamin and Meador 1979). So, it is not clear which model is better. The researchers

indicate that the better model depends on a particular contractor's situation.

17

2.9 OPBID

As early as 1969, researchers were developing bidding models for the computer. The

OPBID (Optimum BID) program is basically a computerized version of Friedman's

bidding model (Morin and Clough 1968). The OPBID program uses the same goal as

Friedman does--to maximize the total expected profits. OPBID improves on Friedman's

model by taking in to account that competitors bid differently for different class of work

and by giving more recent data more weight in the calculations. By weighting more

recent information, OPBID is recognizing that bidding strategies and the market

environment can change over time. The contractor enters data for past biddings, such as

his estimated cost, the bids of each of the competitors, and the class of work. For each

new project, the contractor enters his estimated cost and which competitors he thinks will

be bidding. OPBID processes the information and tells the contractor the optimum

markup for that particular project. Figure 2-3 (Morin and Clough 1968 p. 95) shows the

process that OPBID uses to determine the optimum markup.

18

Figure 2-3: Summary Flow Chart for OPBID

Start

Read data on job to be bid

Read past bidding data on all biddings that were the same class of work as jobto be bid

Compute ratio of other bids to contractor's costs and data weights for past biddngs

Estimate the number of competitors

Differentiate betweenkey and average

competitors

Calculate distribution function for averagecompetitor

Calculate distribution function for keycompetitor

Stop

Calculate probability of winning and expected profit forfixed values of the markup

Write probability of wining and expected profit for each valueof the markup

Write optimum markup

Find maximum expected profit and corresponding optimum markup

19

2.10 Combining the Models with Instinct

Choosing the correct bidding model to use can be very confusing for a contractor.

Recognizing this, researchers developed a method for selecting the best model (Shaffer

and Micheau 1971). The method also allows the contractor to incorporate his instinct

into the bidding strategy by defining a range of potential bids, from which the contractor

can choose. The range of possible bids is developed through the use of several different

bidding models. By applying the different bidding models to past bidding situations, the

contractor can determine which model would have yielded the largest number of low

bids. This model is then used in future bidding situations to determine the lower bound

of the bidding range. The bidding model that most often produced the second lowest bid

and the largest profit margin in past biddings is used to set the upper bound of the bidding

range for new projects. After the range of possible bids is set, the contractor chooses a

bid for the new project based on his instinct and the needed profits for the job. Thus, the

contractor can choose which models best fits his bidding style and still use his experience

to chose the best bid. The method should be evaluated regularly because the models used

to set the range may change.

2.11 LOMARK

The LOMARK bidding model is designed to be used by small to medium sized

contractors to analyze their local market (Wade and Harris 1976). This model focuses on

the local market because bidders in a local market typically have similar constraints for a

project. Also, competitors in one particular area usually know each other personally.

LOMARK's creators think that this personal knowledge allows a contract to better predict

his opponents' behavior. The LOMARK method is basically the same as Friedman's

model for all known competitors. Because all competitors are known, there is no use of

the average bidder concept in the LOMARK method. If the contractor does not have

information about another bidder, then he can only guess as to what that bidder will do.

The only difference between the LOMARK method and Friedman's model for all known

competitors is the way in which probability of winning is calculated. LOMARK

20

calculates the probability of winning as one minus the probability of losing. The

probability of contractor Y losing to contractors X, Q, and W is given by Equation 2-13

(Wade and Harris 1976 p. 204). The probability of Y losing is estimated subtracting the

probability of winning as determined by Friedman's method The probability that another

contractor will bid is fairly easy to estimate by seeing who has expressed interest in the

job by obtaining plans or by contacting subcontractors about the project.

Prob(Y loses) = Prob(Y loses to X, Q, W) Prob(X, Q, W will bid)----- (2-13)

2.12 Carr's Bidding Model

2.12.1 Using Multiple Regression

Multiple regression involves the use of a group of independent variable to predict one

dependent variable. Researchers applied this prediction method to competitive bidding

by saying that the ratio of a project's low bid to the contractor's estimated cost (LBC) was

dependent on many of the projects characteristics (Carr and Sandahl 1978). A contractor

could use multiple regression by developing a list of project characteristics which he

thinks influence the LBC. After gathering data, which includes the LBC and the project

characteristics, from past projects, the contractor can develop a personal and specific

equation for the LBC. Then, it is a simple matter to predict the LBC for future projects.

The equation would need to be updated approximately every six months.

The LBC equation can also be used to find specific areas for improvement. If the

contractor notices that one of the project characteristics has a large impact on the LBC,

then he can work to improve his reaction to that characteristic. This will improve his

competitive position in his market.

2.12.2 General Bidding Model

The first model designed specifically for the construction industry was Carr's general

bidding model (Carr 1982). Like other models, this competitive bidding model is based

21

on the idea that a contractor can compare his bidding strategy to his competitors' bidding

strategies by looking at the ratio of opponents' bids to his estimated cost.

"If these three assumptions are valid: (1) bidders have the same variance

in their cost estimates, (2) variances in cost estimates are substantially

greater than the variances in markups, and (3) the magnitude of markups

are not large" (Carr 1982 p. 643),

then Equation 2-14 (Carr 1982 p. 643) can be used to determine the probability that the

lowest of the opponents on project k will exceed the contractor's bid to cost ratio, b. The

symbol represents the standard deviation of the cost estimates, and MBC is the mean

bid to cost ratio for all projects.

( ) ( )[ ] ( )[ ][ ] dxdyMBCyfxfbLBCP knik => 221)( --- (2-14)The goal of the model is to maximize the expected profit, which is equal to the bid

amount multiplied by the probability of winning. The contractor can see how his

probability of winning, [1 - P(LBCik>b)], varies as he uses different bid to cost ratios.

2.12.3 Impact of the Number of Bidders

Recognizing that an increase in the number of competitors can greatly decrease a

contractor's chance of winning a bid and that opponents tend to adjust their own bids to

try to win, Carr incorporated the number of bidders into his general bidding model (Carr

1983). The number of bidders is included by adjusting the MBC, the mean bid to cost

ratio for all projects. Equation 2-15 (Carr 1983 p. 63) shows how the MBC is adjusted.

The mean bid to cost ratio if contractor faced n competitors, MBCn, is substituted into

Equation 2-14 in place of MBC. MBC1 is the mean bid to cost ratio if the contractor had

faced only one competitor, the symbol represents the standard deviation of the cost

estimates, and n is the estimated adjustment that each opponent makes when bidding

against more than one opponent.

nn MBCMBC = 1 -------------------------- (2-15)

22

2.12.4 Competitive Bidding and Opportunity Costs

Gates general bidding model had the goal of maximizing expected profits for a project,

but maximizing profits on a project by project basis does not guarantee that the overall

profitability of the company will be maximized (Carr 1987). In order to increase

profitability over a set of projects, the contractor must understand that certain resources

limit him, so winning one project reduces his ability to win other projects. If a contractor

accepts one project, he may give up the chance to make a profit on a different project.

These lost profits are called opportunity costs (Carr 1987). So, a contractor needs to be

able to calculate the expected profit of a series of jobs when he is limited by a certain

resource. The expected value for a set of projects is simply the total amount of the bids

submitted for the projects multiplied by the probability of winning.

Equation 2-16 (Carr 1987 p. 158) shows how the probability of winning x projects, P(x |

i,j), if i projects are available and the contractor can only accept j projects because of

resource constraint. P(W) is the probability of winning and can be read from a table that

Carr provides (Carr 1987 p. 156). The probability of winning based on the mean of the

ratios of the lowest bid to the contractor's estimated costs for past projects. P(L) is the

probability of losing and is 1-P(W).

P(x | i,j) = P(W)*P(x-1 | i-1, j-1) + P(L)*P(x | i-1, j)-------------- (2-16)

2.13 Optimum Bid Approximation Model

In an effort to simplify the use of competitive bidding models, the optimum bid

approximation model was developed (Sugrue 1980). This model requires minimal

computational effort because it has reduced Carr's multiple regression model into a single

equation. Applying simple calculus to the multiple regression models and to Friedman's

model, Sugrue developed Equation 2-17 (1980 p. 503). Y1 is the approximate optimum

bid to cost ratio, while M and S are the estimated mean and standard deviation of the

distribution of the bid to cost ratio, Y.

Y1 = 0.5M + 0.627S +0.5-------------------------------- (2-17)

23

All the contractor needs to do to use this model is determine the ratios between the lowest

competitor's bid and his estimated costs for past projects. Then, the distribution of the

ratios is determined. Knowing the distribution, S and M are easily estimated. Then, it is

a simple matter to determine the optimum bid to cost ratio. The contractor knows his

estimated costs, so the optimum bid is simply the estimated costs multiplied by the

optimum bid to cost ratio. The model should be continually updated with new bid

results.

2.14 Symmetry and State of Information

One important factors in bidding decisions centers on the amount of information

available. Ioannou explored this factor by determining a contractor's probability of

winning when n contractors bid, in relation to the amount of information available

(1988). He determined that the level of information and amount of control over the

situation, which the person using a bidding model has, directly affects the validity and

usefulness of the model. Two levels of information and control were considered--that of

a contractor bidding on a project and that of an outsider predicting the outcome of the

bidding. A contractor is part of the situation, has a higher level of information, and can

affect the outcome. Ioannou states that bidding models that do not model the competitive

bidding situation from the point of view of a competitor are flawed (Ioannou 1988 p.

231).

2.15 Bids Considering Multiple Criteria

In real bidding decisions, there are many important factors, including profit, to be

considered. For example, a contractor might need a bid that optimizes the amount of risk,

work force continuity, and the amount of profit (Seydel and Olson 1990). In an attempt

to address these many factors, researchers proposed the use of the analytical hierarchy

process (AHP). AHP was developed by Saaty in 1977 to optimize multiple criteria when

there is a limited set of options (Seydel and Olsen 1990). In simple terms, using AHP for

bidding decisions involves the contractor choosing certain criteria to be optimized and

assigning each of the potential options a score for each criterion. The option with the

24

best score is the optimum solution. If one criterion is to maximize profit, then other

bidding models can be used to calculate the expected profit for the different options, then

weights are assigned based on the expected profit. The main advantage of using AHP for

bidding decisions is that it bolsters the common sense and professional experience of the

contractor.

2.16 Winning over Key Competitors

The key competitor model is similar to Gates' all-bidders-known model, except that there

is only one known bidder, the main or key competitor (Griffis 1992). Also, this model

recognizes the importance of the competition's limitations, in regards to taking on more

work, by incorporating the amount of work currently being done by the key competitior

into the model. To use this model, the contractor must accumulate an extensive database

of bidding information on the key competitor in order to develop a three dimensional

probability distribution function for winning over the key competitor. The distribution is

three-dimensional because the probability is a function of the key competitor's past bids

divided by the contractor's estimated costs and of the volume of work on hand expressed

in dollars. This three-dimensional probability is then incorporated in Gates' bidding

model to determine the optimum bid amount. The model can be expanded to include

more that one key competitor, but the contractor must have the same large amount of

bidding data for each key competitor included.

2.17 DBID

During the 1980's, researchers were quite interested in the potential of computer neural

network to solve construction problems. In 1990, Moselhi, Hegazy, and Fazio developed

software called DBID, which uses neural networks to mesh many of the factors in

bidding (Moselhi, et al. 1993). Computer neural networks are based on artificial

intelligence research and are trained by inputting many project situations and the

associated results. After training, the neural network can generate results for new

situations by comparing the new problem with the training situations. The neural network

for DBID was trained using past projects from Canada and the United States.

25

The contractor inputs data concerning her company, data concerning the bids currently

under consideration, and information about bidding done on past projects. The company

and past bidding information is stored in a database, so it needs to be entered only once.

The past bidding information is extremely important since it incorporates the contractor's

natural bidding tendencies into the model by adding specific training to the neural

network. DBID produces the optimum markup, not just for one project, but for the entire

set of bids under consideration. This new artificial intelligence bidding technologies

models the actual bidding decision by incorporating both the subjective and objective

bidding factors and by allowing the contractor to obtain information for all the bids under

consideration.

2.18 Sequential Competitive Bidding

The main idea behind sequential competitive bidding is the recognition of the fact that

contractors have limited resources, such as expensive equipment, labor, or managerial

time (Chen et al. 1994). In order to incorporate this fact into a bidding model, the

competitive bidding market is modeled as a queuing system, as shown in Figure 2-4

(Chen et al. 1994 p. 1549). If the capacity is not available to do a job, i.e., there is not a

sufficient amount of some resource, then the project is not bid.

Figure 2-4: Queuing Model Representation of Flow of Limited Resources

Is CapacityAvailable?

Participate inBidding

Project Lost

Lose

Yes

No

Win

Project1

Project2

Project3

Project4

ProjectCompletion

ProjectOpportunityArrivalStream

26

The sequential bidding model is limited; it can only model the situation of one

constraining resource. The goal of the model is to maximize the expected value over a

series of projects. Equation 2-18 (Chen et al. 1994 p.1551) shows how this expected

value, E(V) is calculated for this model, where P(i) is the probability that i units of the

limited resource are in use and k is the total number of units of the resource that is owned

by the contractor. The conditional expected profit, E(V|i), is calculated with an

extremely complicated equation that requires an analytical and numerical approach to

solve.

=

=

k

i

iPiVEVE0

)()|()( -------------------------------- (2-18)

2.19 Self-explanatory Artificial Neural Networks

Research into the use of artificial neural networks to aid in competitive bidding models

has continued to the present (Li et al. 1999). However, the neural network's inability to

explain why it made a certain decision has limited its use. Users do not want to trust a

system that just spits out an optimum markup unless they can understand the reasoning

behind the choice

Researchers used an optimum markup estimation neural network to try and add a self-

explanatory feature (Li et al. 1999). A certain method was used to extract rules, the basis

of the system's decisions, from the network through a layer by layer search. The system

is composed of three layers--the input layer, the hidden layer, and the output layer, as

shown in Figure 2-5 (Li et al. 1999 p. 185). The extracted rules from each layer can then

be used to develop a rough explanation of why a certain markup was chosen.

27

Figure 2-5: Hierarchical Structure of the Artificial Neural Network

2.20 Average-Bid Method Bidding Model

As briefly mentioned in Chapter 1, the average-bid method of awarding competitively bid

contractors has been growing in popularity. In 1993, Ioannou developed a bidding model

that could be used by contractors submitting bids for a project that was going to be

awarded with an average-bid method. This situation is "significantly more difficult to

model than the low-bid method" (Ioannou 1993 p. 133). This bidding situation was

explored with a mathematical model and through a Monte Carlo simulation.

2.21 Use of Bidding Models

2.21.1 Actual Use of Competitive Bidding Models

As can be seen from the above discussion, the construction industry has several bidding

Mark-up Percentage

Economic Company Project

Market Conditions

No. of Competitors

Working CashRequirement

Overhead Rate

Current Workload

Labor Availability

Type

Location

Complexity

Size

28

models to use to determine the optimum markup for the project. However, the question

remains if the models are merely the concern of academia of if contractors are making

use of these competitive bidding models.

In 1988, Ahmad and Minkarah conducted a survey of contractors, who had been named

in ENR's 1986 Top 400 contractors. The survey attempted to determine the bidding

habits of contractors. Approximately 80% of their study group did not use statistical

methods of determining their bid prices (Ahamd and Minkarah 1988). This result is

surprising when considering about thirty years had passed since the first competitive

bidding model was introduced.

Another important result of the survey concerned the factors that influence contractors'

bidding decisions. The statistical types of bidding models are mainly concerned with

expected profit, but the survey results indicate that several other factors were considered

more important. The top five factors that affect the percent markup decision, in order of

decreasing importance, were degree of hazard, degree of difficulty, type of job,

uncertainty in estimate, and historic profit. The condition of the economy was the

fifteenth most important factor, followed at sixteen by competition (Ahamd and

Minkarah 1988 p. 235). Either because they were not familiar with the models or

because the models did not address the issues most important to them, the contractors

were not using the available models.

2.21.2 Effective Use of Competitive Bidding Models

Perhaps, the models were not being used because the required a large amount of

information. As early as 1972, the fact that a contractor might not be able to gather the

data needed to effectively use bidding models against known competitors was expressed

(Benjamin 1972). In a bidding data study for a certain contractor, three years of bidding

29

data was examined. The contractor bid on 704 projects against 189 different competitors.

Of the 189 competitors, 97 (approximately 51%) where rivals only once. The contractor

faced 153 (about 81%) of the others five or fewer times.

While this study was of only one contractor, it effectively points out the concern that

some contractors may not have sufficient information to effectively utilize known-

competitor-bidding models. The contractor could still use models based on an average

competitor, but the most effective model of a real life situation would include modeling

real life competitors. As Gates said, "The value of the investigation is increased when

you know all your competitors" (1967 p. 84).

2.22 Bidding Patterns in Virginia

In 1989, a study, using VDOT data, was done of the bidding patterns in Virginia between

1982 and 1989 (Venkateswaran 1989). The study considered 178 projects with four or

more bidders. The ratio between the "pack price" and the lowest bid was used to

calculate a probability of being the successful bidder in the future. However, the pack

price was defined differently than as defined for the purpose of the research presented in

this document. The analysis of the data using the pack price was part of a larger study

and only the variation of the relationship due to the size of the project was considered. It

would be interesting to compare the results of the this study, done ten years ago, with

results of the Virginia case study presented here, but such a comparison would be invalid

since the definition of pack price is not consistent between the two research projects.

2.23 Summary

In this chapter, past research into the study of competitive markets were examined.

General research into market analysis, including general market analysis and competitive

strategies, was discussed. The level of aggressiveness as a factor of competitive market

analysis was considered. In construction research, the focus has been on the many

competitive bidding models. Friedman's, Gates', and Carr's models were carefully

examined because these three form the basis for many of the other models. Two major

30

problems with the use of bidding models in the construction industry were discussed--the

lack of use by contractors and the inability to accumulate the large amount of data needed

to effectively model real-life bidding situations. Also, an earlier study of Virginia's

bidding patterns was discussed.

31

Chapter 3: Methodology for Estimating the Level of Aggressiveness

The purpose of this chapter is to explain the methodology for estimating the level of

aggressiveness. The research concept will be discussed, including a discussion

concerning of the terminology. The methodology that guided this research will be

outlined in the second part of the chapter. The characteristics of the two markets that

were used for this research are also presented.

3.1 Research Concept

This research, which estimates the level of aggressiveness in a competitive bidding

market, though designed for use in the construction industry, is not a bidding model. The

methodology does not result in an optimum markup for a project nor give an exact bid

amount that should be used. The purpose of this research is to allow a contractor to better

understand how aggressive his bidding market is. The contractor can define his market

as narrowly or as widely as he wishes. It could be one state in which he bids, one type of

project on which he bids, or all the work on which he bids.

As seen in Chapter 2, determining the level of aggressiveness in a competitive bidding

environment can not be accomplished through conventional market analysis. This is

mainly due to conventional market analysis being designed for markets where the price is

determined through the interaction of supply and demand, not through competitive

bidding. Competitive bidding models do exist that enable the contractor to better

understand his competition. However, theses models can be quite complicated and

expensive to use. There is a need in the construction industry for a simple method for

contractors to better understand the level of aggressiveness in their markets.

32

3.1.1 The Level of Aggressiveness

The level of aggressiveness in a market is a measure of how interested contractors are in

obtaining work. The reasons that a contractor may want a project are obvious. This

interest is reflected in the aggressive manner in which the contractor bids as low as

possible. Some contractors may even bid so low that their estimated cost exceeds the

prices that they submit.. On the other hand, some contractors may be less interested, or

even disinterested, in obtaining the work. They illustrate this by submitting bids that are

much higher than their estimated costs. A few possible reasons for disinterest include a

bad location, a lack of resources, and an unacceptably high risk. The level of

aggressiveness, i.e., the level of interest vs. disinterest, among contractors bidding on a

project will be reflected in the difference between the each contractor's cost and price.

The level of aggressiveness is important because it speaks to the economic conditions of

the market. In his study of competitive bidding models, Benjamin underscores the

importance of understanding the economic conditions when he states that the economic

conditions of the bidding market do "have some influence on the lowest competitor's

bidding practices" (1972 p. 328). Understanding the level of aggressiveness through the

use of the pack price method can help a contractor position himself in a favorable place to

win the bids he wants.

3.1.2 The Pack Price

As discussed in Chapter 1, the pack price is the lower of the two bids that are closest

together for a project. The pack price is a valid price for a project because it is the price

upon which two, independent, equally informed, competitive contractors came closest to

agreeing. The pack price can also be defined as the break point between the aggressive

bidders and the disinterested bidders. It reveals what the price of the project would be if

there were no aggressive bidders desperately trying to beat everyone else and if there

were not disinterested bidders purposely bidding high.

Figure 3-1 displays a graphic of a set of bids for a project. The bids decrease in amount

from the left to the right, as is shown by the low bid marker on the far right. Notice that

33

the spread of bids is the difference between the highest and lowest bid. The pack price,

marked by the red triangle, is the lower of the two bids that are closest together. It

separates the set of aggressive bidders from the disinterested bidders.

Figure 3-1: The Pack Price Concept

3.1.3 The Level of Agreement

The pack price is a good representation of the project's non-aggressive price only if there

was an actual consensus between the two prices that define the pack price. By examining

the percent difference between these two bids, the level of agreement can be determined.

The level of agreement reflects the closeness of the two bids or the amount of

concurrence between the two contractors for a fair and reasonable bid for the project. If

the percent difference between the pack price and the next highest bid is small, then there

is a high level of agreement between the two bids, and the confidence level of the pack

price increases.

3.1.4 The Ratio of the Low Bid to Pack Price

The level of aggression is reflected in the "distance" between the low bidder and the pack

price, as is shown on Figure 3-2. This "distance" is determined by calculating the ratio of

the low bid to the pack price. This ratio is important because it quantifies the level of

aggression for each project. The ratio will always be less than or equal to one. If the

Disinterest Aggression

= pack price = low bid

Spread

X X X X X X X X

X = bid

ratio is equal to one, then the pack price and low bid are equal, showing the level of

aggressiveness to be low, such as case #1 of Figure 3-2. Case #3 of Figure 3-2

demonstrates a high level of aggression where the low bid is much lower than the pack

price and ratio is less than one.

Case

#Ratio of Low Bid to Pack Price

Level of

Aggressiveness

1Ratio =

1.00

Low Bidder is

not aggressive

with respect to

the other

bidders.

2Ratio = 3 bids, = 3 bids, >15% difference between pack price and next highest bid

56 3%

Tennessee

744 56%

20 2%

Virginia

Description

566 43%

1330 100%

41

ratio occurred in the data set. The two data sets were analyzed separately. For each data

set, the ratios were listed in order from highest to lowest. The cumulative percentage of

ratios greater than or equal to ratio x was determined by dividing the number of ratios

greater than or equal to x by the total number of ratios in the data set.

The list of ratios and cumulative percentages can be very hard to read and use, especially

if the market contains a large number of projects. By graphing the research results, it is

much simpler to understand the level of aggressiveness in the market. The data curves

show the ratio of the low bid to the pack price on the x-axis, in decreasing order, and the

cumulative percentage of the ratios that are greater than or equal the ratio on the y-axis,

in increasing order. See Graph 3-1 for an example. From this graph, it is simple to

determine that 30% of the ratios were equal to 1.0, while 95% of the ratios were greater

than or equal to 0.7.

Graph 3-1: Example Data Curve

3.2.6 Determining the Probability of Success

For this research, the probability of success for a ratio of x, is defined as the probability

that the contractor will be the low bidder for a project if the ratio of his bid to the pack

price matches the ratio of x. Consider the case when a contractor decides to submit a bid

that is 80% of the pack price. He will not win unless his bid is the lowest bid, meaning

1.0

Ratio of Low Bid to Pack Price

Cum

ulat

ive

% o

f R

atio

s

X

X 0.60.8 0.70.90

100

30

95

75

42

that he will not win unless the ratio of his bid to the pack price is lower than the ratio of

any other contractor's bid to the pack price. From Graph 3-1, it is observed that 75% of

the ratios were greater than or equal to 0.80. Thus, there is a 25% chance of the ratio of

the low bid to the pack price for this project being less than 0.80. So, the contractor has a

25% chance of not winning because there is a 25% chance that the ratio will be less than

0.80. If his chance of not winning is 25%, then his probability of success is 75%.

Determining the probability of success for the ratios in this manner does assume that the

future behavior of the competitive bidding market will remain similar to its past behavior.

While this may seem like a large assumption, the performance of the competitive bidding

market is only being predicted for a short time into the future. If the contractor

frequently updates the information used in the pack price method, then the results will

adapt to the changes in the market as they happen, and he will not be using outdated

information for his future predictions.

3.2.7 Plotting the Success Curve

From the example in the previous section, it is apparent that the probability of success for

a ratio of x is equal to the cumulative percentage of ratios that are greater than or equal to

x. By simply changing the label on the y-axis on the data curves, the success curves for

the data sets were plotted.

For example, consider Graph B - 1 and Graph B - 2 (found in Appendix B), which are the

success curves for the Virginia and Tennessee markets, respectively. Notice that as the

ratio decreases the probability of success increases, which is the expected result. If a

contractor bids less than the pack price, he is much more likely to be awarded the work.

In fact, the more aggressive that a contractor is the lower bid he will submit and the

higher his probability of success is.

3.2.8 Grouping the Data Set To Investigate Potential Influencing Factors

The level of aggressiveness reflects the economic environment of the competitive bidding

market. There are many factors that compose a certain economic environment, and each

43

factor can affect the level of aggressiveness differently. This research into the pack price

and probability of success relationship for the two data sets included examination of

different factors to determine if their influence on the level of aggressiveness. To

determine if each factor affected the level of aggressiveness of the market, the data was

sorted into groups based on one characteristic, such as the year the project was let. Then

a success curve was constructed for each group, and the differences were examined. The

success curve for the potential influencing factors for both data sets can be found in

Appendix B.

The year in which the project was let is one potential influencing factor. Investigation of

this factor might reveal if the level of aggressiv