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
Top Related