COMPETITIVE BIDDING STRATEGY MODEL ANDSOFTWARE SYSTEM FOR BID PREPARATION
By Aminah Fayek1
ABSTRACT: This paper presents a competitive bidding strategy model for use in setting a margin (markup) forcivil engineering and building construction projects. The goal of this model is to help a company to achieve itsobjectives in bidding. The model provides more than 90 factors that may influence the choice of margin size,and it enables the decision-maker to assess the impact of those that are relevant to his or her bid situation. Theuse of fuzzy set theory allows assessments to be made in qualitative and approximate terms, which suit thesubjective nature of the margin-size decision. The model has been implemented in the form of a prototypesoftware system named PRESTIO, which is described. One conclusion of this paper is that fuzzy set theorycan be applied successfully to model the margin-size decision. A second conclusion is that use of this competitivebidding strategy model can improve the quality of the decision-making process used in setting a margin andcan help contractors to gain a competitive edge in bidding. The competitive bidding strategy model has beenvalidated with actual project bids collected from a survey of the Australian construction industry; validation willbe described in a companion paper.
INTRODUCTION
Estimating and bidding are two important functions performed by construction contractors. Many of the decisions required in arriving at the final bid price are based on experienceand intuition. Deciding on an appropriate margin, or markup,to add to the estimated cost of a project is one such decision.A margin is defined as the amount of money added to theestimated cost of the project (i.e., project direct costs and project overhead costs) to arrive at the contract (selling) price. Amargin may cover both corporate overhead costs (i.e., headoffice and branch office running costs) and profit. Some companies may treat corporate overheads as a separate project costitem, since they should be allocated to each project and recovered just like other project costs. For some projects, particularly small ones, the margin may include the project riskand opportunity allowance. The margin is usually expressedas a percentage of the total estimated cost, although in somecases it is expressed as a percentage of the contract price, oras a lump sum.
The margin-size decision involves a largely qualitative andsubjective assessment of the conditions surrounding the bidsituation. Traditionally, the margin-size decision has not beenbased on a standard or formal procedure but rather on principles learned through years of experience, which are appliedto each new bid situation (Fayek I996a). A need exists tostructure and formalize the decision-making process used insetting a margin, since the margin-size decision is critical to acompany's success in winning work and its subsequent profitability.
The purpose of this paper is to present a competitive biddingstrategy model that uses techniques of fuzzy set theory to helpa decision-maker choose an appropriate margin to add to theestimated cost of a project. This model provides a systematicand standard methodology for setting a margin on civil engineering and building project bids, which can be tailored to suitthe individual practices of each company. The model has been
'Asst. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Alberta, Edmonton, Alberta T6G 2G7, Canada; formerly, Grad. Res. Engr., Dept. ofCiv. and Envir. Engrg., Univ. of Melbourne, Parkville, Victoria, 3052,Australia.
implemented in the form of a prototype software systemnamed PRESTIO, which makes the model quick and easy touse (Fayek 1996a,b; Fayek et al. 1995).
The need for an additional competitive bidding strategymodel, despite the number of models already developed, isexplained. A brief description of fuzzy set theory and a discussion of the features of fuzzy set theory that make it suitablefor modeling the margin-size decision are provided. Each component of the competitive bidding strategy model is described,and the method of analysis based on fuzzy set theory is presented. A sample project, analyzed using the model, is provided to illustrate how the calculations are performed. ThePRESTIO software system is described and illustrated bysample screens. The benefits to be gained from the use of themodel and future developments are discussed.
NEED FOR AN ADDITIONAL COMPETITIVE BIDDINGSTRATEGY MODEL
Research in the area of competitive bidding (tendering)strategy models has been in progress since the 1950s [e.g.,Friedman (1956)]. Numerous models have been developed,some of which are designed specifically for the constructionindustry (Stark and Rothkopf 1979). Despite the number ofcompetitive bidding strategy models that have been developed,few of these are used in practice, largely because they do notsuit the actual practices of construction contractors (Ahmadand Minkarah 1988; Hegazy and Moselhi 1995; Shash 1995;Ting and Mills 1996). A need remains for models that aredesigned to suit the actual practices of construction contractorsso that they will be more readily accepted and used.
The following features need to be addressed in a competitive bidding strategy model to make it more suitable in practice:
• Consideration of a wide range of factors, besides profitmaximization and the competition, that affect the marginsize decision, to more realistically capture the decisionmaking process
• Consideration of multiple objectives in bidding, in addition to profit maximization
• The use of qualitative and subjective contractor judgmentand heuristic logic, rather than extensive mathematical orstatistical techniques
• Consideration of other factors, besides price, that affect acontractor's success in winning projects, since contractsare not always awarded to the lowest bidder (Odusote andFellows 1992; Ferguson et al. 1995)
• Less reliance on historical project and competitor data for
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training or use, since data of sufficient quality and quantity are difficult and time-consuming to obtain (Benjamin1972) or may not be available (Fayek 1996a)
• A method not based on population-specific data, trainingexamples, or rules, for wide applicability to other construction environments besides the one for which themodel is designed
• Quickness and ease of use, to suit the time-constrainednature of the competitive bidding process
by the user, while simultaneously accounting for the effects offactors internal and external to the company. The model doesnot assume that the lowest bidder will necessarily be awardedthe contract, rather, it considers the effect of other, qualitativecriteria that may influence the client's choice of the winningbidder and consequently the most suitable margin size.
COMPONENTS OF COMPETITIVE BIDDINGSTRATEGY MODEL
Objectives in Bidding
The components of the competitive bidding strategy modelare illustrated in Fig. 1 and described next.
~ SJn • W]*An'f}n + "n,P ·1FIG. 1. Components of Competitive Bidding Strategy Modeland Their Relationship
MARGIN SIZES
(lip)FACTORS AT GIVEN LEVELS
(Fn)
1. To win the project (0 1)
In this case, the company has a large need for work and/or a great desire for the project. The company may bid theproject at the lowest acceptable margin in order to increaseits chances of winning, particularly if the contract is likelyto be awarded to the lowest bidder. Other objectives in bidding that may lead a company to bid at the lowest acceptable margin are• To meet budgeted turnover requirements and/or to deploy
idle resources
A company may have more than one objective in bidding.Although a company aims at winning most projects it bids,winning mayor may not be the primary or only objective.
The company's objectives in bidding are influenced by factors internal to the company, such as the company's need forwork and its availability of resources, and external factors,such as the magnitude of the competition, the prevailing economic conditions, and the availability of future work. Theobjectives of the company may also be influenced by characteristics of the project that determine its desirability and suitability to the company, such as the project's location and itsstrategic value. The margin assigned to a bid is partly determined by the company's objectives in bidding.
The competitive bidding strategy model lists three objectives in bidding, which the user is asked to assess. Althoughthe model considers only these three objectives, it is recognized that there may be other objectives in bidding. The objectives considered by the model are denoted by OJ (see Fig.1). These three objectives are:
OBJECTIVES
(OD
USE OF FUZZY SET THEORY
This paper presents a competitive bidding strategy modelthat uses techniques of fuzzy set theory to address many ofthe features listed above. It builds on the advancements madeby previous models, in an effort to develop a realistic modelthat accurately captures the decision-making process used insetting a margin and suits the actual practices of constructioncontractors.
The concept of fuzzy set theory was first introduced by Zadeh (1965). A fuzzy set is characterized by its membershipfunction, which represents numerically the degree to which anelement belongs to a set. Unlike conventional (crisp) set theorywhere objects are either in or out of a set, fuzzy set theoryallows objects to have partial membership in a set. The fuzzyset introduces vagueness by eliminating the sharp boundarydividing members of the set from nonmembers, since the transition from member to nonmember is gradual rather thanabrupt (Klir and Folger 1988). Fuzzy set theory does not replace probability theory but rather provides solutions to problems that lack the mathematical rigor required by probabilitytheory (Nguyen 1985). Fuzzy sets describe vague conceptssuch as "long duration," "poor management," "high likelihood," and "good relationship," all of which are linguisticvariables. Fuzzy set theory is well explained by Schmucker(1984) and Klir and Folger (1988).
The conditions surrounding the margin-size decision are often imprecise and uncertain; assessments are consequentlymade using linguistic approximations. Fuzzy set theory provides a method of representing in numerical form the linguisticapproximations used to describe the relationships between dataitems, so that they can be manipulated by a computer. Fuzzyset theory can be used to generate solutions to problems thatcontain human subjectivity, such as the margin-size decision.Because fuzzy set theory is specifically designed to handlequalitative and linguistic data based on approximations, it naturally lends itself to the margin-size decision. The use of fuzzyset theory also provides a method of addressing the features,identified previously, that would make a competitive biddingstrategy model more suitable in practice. Fuzzy set theory wastherefore chosen to develop the competitive bidding strategymodel presented in this paper.
COMPETITIVE BIDDING STRATEGY MODEL
The competitive bidding strategy model described in thispaper is intended for use by civil engineering and buildingconstruction contractors in setting a margin on competitivelybid tenders (or bids). The goal of the model is to help a company to achieve its objectives in bidding. The model is basedon the single-bid situation. It is used after the decision to bidon the project has been made, and after the detailed estimatehas been completed. The basis of the margin-size recommendations of the model is not necessarily the margin that willmaximize the company's chances of winning the bid, unlesswinning is the sole objective of the company in bidding.Rather, the margin size recommended by the model will helpa company to achieve its objective(s) in bidding, as specified
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'Level of factor. as stated in competitive bidding strategy model. is in italics.
Category Examples'(1) (2)
TABLE 1. Examples of Factors Influencing Margin Size Considered in Competitive Bidding Strategy Model
Fig. 1). They are classified according to 11 categories, listedin Table 1. An example from each category is given in Table1. Each factor is stated in the model with a correspondinglevel. Non-price criteria that may be considered by the clientin selecting the winning bidder, such as the company's strengthin the industry and the quality of the company's relationshipwith the client, are included in the list of factors influencingmargin size.
The user selects the factors that are relevant to the bid underanalysis from the predefined list provided by the model. Theuser can choose a subset of any size of the 93 factors, to tailorthe extent and complexity of the analysis to suit his or herrequirements. The user can also add additional factors he orshe wishes to consider that are not listed in the model.
Range of Margin
The range of margin under consideration for a bid is therange within which the most suitable margin lies. The userspecifies the range of margin by defining the minimum marginand the maximum margin being considered for the bid. Theoretically, the minimum margin is equal to the project's requiredcontribution to corporate (head and branch office) overheads,which is usually set by the corporate budget based on a predicted level of turnover. Included in the corporate overheadcost is the cost of estimating and preparing bids. A companywould "break even" at the minimum margin, provided theestimated costs match the actual costs on the project. Onlyunder very special circumstances would a company bid at amargin below its minimum, such as in a very competitive market or in difficult economic times. A company may also bidbelow its minimum margin to keep its equipment and personnel working between large projects; in this case, the companycan recover direct construction costs, including project siteoverheads, and make a contribution to corporate overheads,which are predominately a fixed cost and do not vary significantly with annual construction volume. Anything above theminimum margin contributes to pure pretax profit and maycover project risks (if they have not been accounted for elsewhere in the bid). The maximum margin is usually determinedby what the market will bear, based on an analysis of suchthings as the current market conditions, the availability of projects, and the amount of competition.
A company may have a target margin within the range ofmargin, based on a desired profit contribution from each project for the predicted level of turnover. This target margin maypartly be determined by what the company considers an adequate return on its investment of capital and management personnel in the project. Margin should reflect the magnitude ofperceived project risk and opportunity in the project (Bacarreza 1973). A project with a higher risk should have the potential for a higher return. The target margin may be adjustedto reflect the company's strategy or business plan for the market in which it is bidding. F0r example, if the company istrying to break into a new market or build a reputation in amarket, the margin on projects in this market would be set low(perhaps to cover only corporate overheads). The companymay temporarily sacrifice profits in an attempt to win morework and build a reputation. A low margin may also be usedon projects the company is targeting for their strategic value,their high profile, a desire to work with a client, or potentialfuture work.
In the competitive bidding strategy model, the user sets therange of margin by specifying the minimum margin and themaximum margin under consideration for the bid. The rangeof margin is divided into six margin sizes, denoted by M p ,
with equal increments between them (see Fig. 1). Six marginsizes were chosen for the model because it is generally difficultfor a person to distinguish subjectively between more than
JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / JANUARY/FEBRUARY 1998/3
• To be seen as competItIve and/or to build a reputationwith the client and/or with consultants
• To break into a new market and/or to win the project forits strategic valueAll of the objectives in this category correspond to the
choice of the minimum margin size from the range of margin under consideration (explained later.)2. To test a new geographical area, and to give the esti
mating team experience in the new area (02)
In this case, the company may be bidding to test a newgeographical area or market in which it will be bidding forseveral future projects, and it wishes to give its estimatingteam experience in the new area. In this case, the companymay bid the project with a medium margin size in order toassess its position relative to its competitors for the project.This objective corresponds to the choice of a medium margin size from the range of margin under consideration (explained later).3. To maximize the project's contribution to profit (03),
In this case, the company may have a sufficient amountof work on hand and may already be seen as a major competitor in the market in which it is bidding. The companymay be bidding to maintain its feel for the market and toremain competitive. The company would therefore bid theproject at a relatively high margin, so that if it wins, it cananticipate a large profit on the project. Furthermore, if thecompany is at its maximum workload capacity, its financialor construction resources may be completely in use in existing projects; any additional work would require the company to pay a premium in order to obtain the resources toperform the work. As a result, the company would be bidding at a high margin to cover the premium it would haveto pay if it won the project. This objective corresponds tothe choice of the maximum margin size from the range ofmargin under consideration (explained later).
Any combination of these objectives is possible on anygiven bid.
Factors Influencing Margin Size
A number of factors internal to and external to the companyinfluence the most suitable margin size for a bid. A list of 93such factors is provided in the model. These factors were compiled from previous research on competitive bidding (Ahmadand Minkarah 1988; Sanders and Cooper 1990; Shash 1993;Shash and Abdul-Hadi 1992) and from the author's own industry experience (Fayek 1996a).
The factors influencing margin size are denoted by Fn (see
Project characteristics Large size of project (dollar value)Design characteristics Large degree of contractor involvement in
design phaseCost estimate characteristics Large proportion of time-based overheads
to contract valueProject-related risks High likelihood of unexpected climatic
conditions (e.g.• inclement weather)Project-related opportunities Large innovation in designCompany characteristics Large need for workCorporate and budgetary High actual versus budgeted turnover to
considerations dateThe client Good company relationship with clientCompetition Large number of competitors for projectCharacteristics of subcontractors High likelihood of negotiating a lower
and suppliers price on supply and/or subcontractsEconomic and political conditions High current unemployment rate
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seven alternatives (Saaty 1977). The six margin sizes are calculated using (1).
M p = [x + (p - l)z]% for p =1 to 6 (1)
where x =minimum margin size under consideration for bid(%), as specified by user; y = maximum margin size underconsideration for bid (%), as specified by user; and z = (y x)/5. Therefore
MI=x%
M2 = (x + z)%
M 3 = (x + 2z)%
M4 = (x + 3z)%
M~ = (x + 4z)%
M6 = (x + 5z)% =y%
The output of the model, based on its analysis, consists ofa varying degree of recommendation of each of these six margin sizes.
WEIGHTINGS IN COMPETITIVE BIDDING STRATEGYMODEL
The following weightings are specified by the user and areused in the analysis performed by the model (see Fig. 1).
Degree to which Objective is Desired in Bid Situation
The weighting ~ indicates the degree to which achievingobjective OJ is desired in the bid situation under analysis (seeFig. 1). This weighting is in the form of a scale ranging fromo for "not applicable" to 100 for "strong." The user canevaluate the weighting in linguistic terms and choose a numberon the scale that corresponds to that weighting. For example,if the company has a very strong desire to win the project,then the weighting WI of objective 0 1 would be 100 (for"strong").
The user is provided with a range of values from 0 to 100;however, since the membership value of a fuzzy set must rangefrom 0 to 1, the user input value is divided by 100 for furthercalculations. The user is provided with a scale of 0 to 100 toallow the user to be as precise as he or she wishes. It would,however, be unrealistic to grade a scale of 0 to 100 accurately.The user can effectively treat the scale as having incrementsof 10. Values in-between are available for fine-tuning of theevaluations, perhaps as a second iteration through the bid analysis.
Degree of Applicability of Factor at Given Level to BidSituation
The weighting An indicates the degree to which each factorFn, at the level stated in the model, applies to the bid underevaluation (see Fig. 1). The degree of applicability is in theform of a scale ranging from 0 for "false" to 100 for "true."Again, the user can evaluate the degree of applicability in linguistic terms and choose a number on the scale that corresponds to that degree of applicability. For example, if thereare a large number of competitors for the project, then thedegree of applicability, A.. of the factor F.. "large number ofcompetitors for project," would be 100 (for "true"). Themodel converts the value of 100 to a fuzzy set membershipvalue of 1.00.
Degree of Influence of Factor on Margin Size
The weighting ~n indicates the degree of influence that eachfactor F n has in setting margin, in order to achieve each ob-
jective OJ in turn (see Fig. 1). This evaluation is made assuming that the factor exists at full strength (i.e., at the level specified in the model) and that achieving the objective is desiredat full strength. The degree of influence is in the form of ascale ranging from 0 for "no influence" to 100 for "a highdegree of influence." The degree of influence can be evaluatedin linguistic terms and the corresponding value on the scalechosen. For example, given that the company's objective is towin the project, the existence of a large number of competitorsfor the project may influence the choice of margin to a veryhigh degree; therefore, the degree of influence, Iln, on marginsize of this factor, F.. paired with this objective, 01> would be100 (for "high degree of influence"). The value of 100 isconverted in the model to a fuzzy set membership value of1.00.
Degree to which Margin Size Would OptimizeObjective
The weighting Rjn•p is calculated by the model based on theuser's choice of the most suitable margin size that each factorwould indicate in order to achieve each objective in turn, assuming that both the factor and the objective exist at fullstrength (see Fig. 1). The most suitable margin size for a givenfactor would differ for different construction markets and classes of work. The user chooses the most suitable margin sizefrom the six system-calculated margin sizes, Mp , within theuser-specified range of margin. For example, given a largenumber of competitors, in order to win the project the minimum margin would be chosen in order to have a low bid priceand increase the chances of winning against a large numberof competitors. In this case M1 would be selected by the useras being the most suitable margin size to help the companyachieve the objective of winning the project.
The most suitable margin size (from M I to M 6 ) chosen bythe user for each factor and objective pair is given a weightingof 1.00 in the model. The other margin sizes are given weightings that decrease by 0.20 in either direction from the chosenmargin size. For example, if M4 is selected by the user as themost suitable margin size, then M 4 gets a weighting of 1.00;M~ and M 3 both get a weighting of 0.80; M 6 and M 2 both geta weighting of 0.60; and M1 gets a weighting of 0040. Thisweighting is Rjn •p , which is the weighting associated with objective OJ> factor F.. and margin size Mp •
METHOD OF ANALYSIS
Fuzzy Binary Relations
A relation was required to link two sets of data-objectivesand margin sizes-directly to each other through their respective relationship to a third and common set, factors influencingmargin size. The fuzzy binary relation approximates the relationship between two sets of data and can be represented as amatrix (Klir and Folger 1988). The elements of the matrixrepresent the fuzzy degrees of membership of each link between two data items.
Let the relation between the objective set, 0, and the factorset, F, be denoted by S(O, F), where S(O, F) is a fuzzy binaryrelation. Each element of S(O, F) corresponds to the strengthof the linkage between objective OJ and factor Fn and is represented by S(Oj' F n ). The element S(Oj, F n) corresponds tothe value of Sj.. calculated using (2) (see Fig. 1).
(2)
Each element of S(O, F) corresponds to how much a factorinfluences margin size in order to achieve an objective, discounted by the objective's degree of desirability and the factor's degree of applicability.
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Let the relation between the factor set, F, and the marginset, M, be represented by R(F, M), where R(F, M) is a fuzzybinary relation. Each element of R(F, M) represents thestrength of the linkage between factor F. and margin Mp , andis represented by R(F.. Mp ). The element R(F.. Mp ) corresponds to the value of Rj ••p (see Fig. 1).
(3)
Rj ••p is calculated by the model based on the user's choice ofthe most suitable margin size for each factor and objectivepair.
Fuzzy Composition Operations
A composition operation, performed on the two fuzzy binary relations S(O, F) and R(F, M), was required to determinethe relationship between objectives in bidding, 0, and marginsizes, M, through their respective relationships to factors influencing margin size, F. Let the composition of these tworelations be denoted by Q(O, M).
Q(O, M) =S(O, F)oR(F, M) =SoR(O, M) (4)
evidence that exists, the more highly a margin size is recommended using the cum-min composition operation. The cummin composition is therefore used to determine the most suitable margin size based on all supporting evidence (i.e., basedon the summation of the strength of all chains between a margin size and an objective in bidding).
Through either the max-min or the cum-min compositionoperation, each of the three objectives yields a fuzzy binaryrelation Q(Oj, Mp ), describing the relationship between the objective OJ and the margin sizes M1 to M 6• For each of the sixmargin sizes, M] to M 6 , each objective recommends that margin size to a different degree, based on the Q(OJ' Mp ) relation.A method was required to combine the results so as to recommend one set of margin sizes based on all three objectives.Each objective influences the recommendation of margin sizein proportion to its weighting, "'}, or in other words, in proportion to "'}/~ "'}. To determine the degree to which eachmargin size is recommended, the three recommendationstrengths (from the three objectives) for a given Mp aresummed and divided by ~ "'}.
Thus, for any given margin size, Mp , the total strength withwhich it is recommended is calculated using
where M* = recommended margin size based on a combination of all recommendations; p = number of margin sizes (p= 6); Mp = margin size (from M1 to M6); and J.LQ = membershipvalue of Mp in Q(O, M) (i.e, strength of the recommendation).
Using (9), a single margin size, M*, is recommended based
This operation of combining the recommendations fromeach objective is analogous to the statistical concept ofweighted means (Dixon and Massey 1969).
Eq. (8) yields recommendations of margin size ranging from0.00 to 1.00, the range of fuzzy set membership values. Thedegree to which a margin size, Mp , is recommended is calculated by multiplying Q(O, Mp ) by 100, to obtain a percentagerecommendation.
Using the cumulative-minimum composition operation, it ispossible to obtain margin-size recommendations [i.e., valuesof Q(O, Mp )] that are greater than 1.00 (i.e., greater than100%). In this case, the values of Q(O, Mp ) for all Mp arenormalized so as to obtain recommendations lying between0.00 (0%) and 1.00 (100%), since a margin size can not berecommended by more than 100%.
Margin sizes can be ranked in terms of their suitability tothe bid situation, based on their degree of membership in theQ(O, M) relation. Q(O, M) is a fuzzy decision set, and theranking of margin sizes is a fuzzy decision. Once a fuzzydecision has been made, it may be necessary to choose thebest single crisp alternative from the fuzzy decision set. Onemethod of choosing a single alternative is to choose the alternative that attains the highest membership grade in Q(O, M)(i.e., the most highly recommended margin size). Since thismethod ignores information regarding any of the other alternatives, it may not be desirable in all situations. Defuzzification methods that calculate the mean or center of area of afuzzy decision set may therefore be used instead to recommend a single margin size (Klir and Folger 1988). The centerof-area method of defuzzification combines the recommendations of margin sizes according to (9) (Berenji 1992).
(where 0 denotes the composition operation)Each element of Q(0, M) corresponds to the strength of the
linkage between objective OJ and margin size M p , and is represented by Q(Oj, M p).
Q(Oj, M p) =SoR(Oj, M p) =S(Oj, F.)oR(F., M p) (5)
SoR(Oj, M p ) defines the membership grade for the elements OJand M p of Q(O, M).
One common composition operation for fuzzy relations isthe maximum-minimum (max-min) composition operation(Klir and Folger 1988). This operation is defined, for a givenOJ and Mp , by
SoR(Oj, M p) = max min [S(Oj, F.), R(F., M p)] for all F. (6)
The max-min composition operation indicates the strengthof the relational chain between elements of ° and M, represented by the membership grade of the pair (OJ' Mp) in theQ(O, M) relation [calculated using (6)]. The strength of eachchain between OJ and M p (through each factor F.) equals thestrength of its weakest link (i.e., the minimum value); thestrength of the relation between elements OJ and Mp equals thestrength of the strongest chain between them (i.e., the maximum value). The max-min composition determines the mostsuitable margin size based on the strongest indicator or pieceof evidence, since margins are suggested with a strength equaling that of the strongest chain between them and the objectivesin bidding.
An alternative composition operation-that is, a variationof the max-min composition-is the cumulative-minimum(cum-min) composition (Russell and Fayek 1994). This operation is defined, for a given OJ and M p , by
SoR(Oj, Mp ) =sum min [S(Oj, F.), R(F., Mp )] for all F. (7)
The cum-min composition indicates the strength of a relational chain between elements of ° and M in the same wayas the max-min composition. In the cum-min operation, thestrength of each chain between any two elements of° and Mequals the strength of its weakest link (i.e., the minimumvalue, as in the max-min composition), but the strength of therelation between the two elements equals the summation ofthe strength of all chains between them (i.e., the sum of thevalues). The reasoning behind this rule is that each indicatorthat points to a margin size increases the strength with whichthat margin size is recommended. Various items of informationcan suggest that a margin size is suitable. The more supporting
p
2: MpfJ,Q(Mp)M* = ~.-:.:,Jp=-- _
2: fJ,Q(Mp)x-J
(9)
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TABLE 3. Applicability of Factors to Bid Situation
TABLE 2. Degree to Which Objectives Are Desired in Bid Situation
TABLE 5. Calculation of Elements of S(0, F) Relation for Sample Project
TABLE 4. Influence of Factors on Margin Size and Most Suitable Margin Size for Each Objective-Factor Pair
0, = win the projectO2 = test new geographical area0, = maximize project's contribution to profit
Applying Maximum-Minimum Composition Operation
The elements of the Q(O, M) relation are calculated usingthe maximum-minimum composition operation in (6) and (8)and are displayed in Table 7. For example, using (6)
Factors (Fn)
(1 )
Degree of Influence of Factors on Margin Size andMost Suitable Margin Size for Each Objective-FactorPair
Table 4 shows the influence of the factors on margin size(column 3) and the most suitable margin size for the objectivefactor pairs (column 4).
The elements of the 8(0, F) relation are calculated using(2) and are displayed in Table 5. The elements of the R(F,M) relation are calculated using (3) and are displayed in Table6.
F, = large proportion of design complete at timeof bidding
F2 = large innovation in construction methodsF, = large past profit on similar projectsF, = good company relationship with clientF, = large commercial advantages over competi
tors in quoted supply and/or subcontract prices
Most SuitableFactor Influence (ljn) of Margin Size
0, F, /11 =0.80 M, =20, F2 /12 = 1.00 M, =20, F, /" =0.60 M, =20, F, /" = 1.00 M 2 =40, F, /15 =0.90 M,=2O2 F, /21 =0.20 M, = 6O2 F2 /22 =0.60 M, = 6O2 F, /" =0.40 M, = 8O2 F, /24 =0.60 M, = 6O2 F, /2' = 0.70 M, = 80, F, /31 =0.80 M. = 120, F2 /32 = 1.00 M, = 80, F, /" = 1.00 M, = 80, F, /34 =0.80 M. = 120, F, /" =0.80 M, = 10
Range of Margin and Margin Sizes
Minimum margin (x) =2%
Maximum margin (y) = 12%
Using (1)
A sample project is analyzed using the competitive biddingstrategy model to illustrate how the calculations are performedand how the model is used in practice.
A civil engineering construction contractor is submitting alump-sum bid price for a roadworks project. The chief estimator has completed the estimate of project direct costs andproject overhead costs and has assigned an allowance to account for project risks and opportunities. The chief estimatorand the general manager of the company meet to determinean appropriate margin to add to the bid price.
The minimum margin, x, under consideration for the bid is2%, and the maximum margin, y, under consideration is 12%.The objectives of the company in bidding are as follows: avery strong desire to win the project (WI = 100), no desire totest a new geographical area (W2 = 0), and a weak desire tomaximize the project's contribution to profit (W3 = 20).
Five factors influence the margin-size decision on this bid:the proportion of design complete at the time of bidding, theinnovation in construction methods, the past profit on similarprojects, the company's relationship with the client, and thecommercial advantages the company may have over its competitors in quoted supply and/or subcontract prices. Almost allof the design is complete at the time of bidding (AI =80). Thecompany anticipates a large amount of innovation in its construction methods over its competitors (A2 = 80). The companyhas experienced a very large amount of past profit on similarprojects (A 3 = 100). The company has an excellent relationshipwith the client (A4 = 100). The company anticipates large commercial advantages over its competitors in its quoted supplyand/or subcontract prices (As = 80).
Based on these conditions, the company would like to determine the most suitable margin to add to the bid price inorder to achieve its objectives in bidding and to account forthe five factors influencing margin size. The company uses thecompetitive bidding strategy model to help choose the mostsuitable margin size. The following calculations are performedby the model based on the user-input assessments.
SAMPLE PROJECT
on a combination of all the margin sizes and the strength withwhich each is recommended.
The output of the model consists of a ranking of the marginsizes and the degree with which each is recommended, foreach of the max-min and the cum-min composition operations.The most highly recommended margin size(s) and the marginsize recommended based on the center-of-area method of defuzzification are indicated for each composition operation.
z = (y - x)/5 =2%
Therefore M, = 2%; M 2 =4%; M 3 =6%; M 4 =8%; M s = 10%;and M6 = 12%.
Degree to which Objectives are Desired in BidSituation
Table 2 shows the weights given to the different objectivesin the example bid situation.
Degree of Applicability of Factors at Given Levels toBid Situation
Table 3 shows the applicability of the factors in the examplebid situation.
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Q(OI' M.) = max min [(0.64, 1.00), (0.80, 1.00), (0.60, 1.00),
(1.00,0.80), (0.72, 1.00)] = max [0.64, 0.80, 0.60, 0.80, 0.72]
=0.80
Q(02' M 1) = max min [(0.00, 0.60), (0.00, 0.60), (0.00, 0.40),
Q(03' M1) = max min [(0.13, 0.00), (0.16, 0.40), (0.20, 0.40),
(0.16,0.00), (0.13, 0.20)] = max [0.00,0.16,0.20,0.00,0.13]
= 0.20
Using (8)
Q(O, M t ) = (0.80 + 0.00 + 0.20)/1.20 = 0.83
Q(Oh M1) = sum min [(0.64, 1.00), (0.80, 1.00), (0.60, 1.00),
(1.00,0.80), (0.72, 1.00)] = sum [0.64, 0.80, 0.60, 0.80, 0.72]
=3.56
Q(02' M 1) = sum min [(0.00, 0.60), (0.00, 0.60), (0.00, 0.40),
(0.00,0.60), (0.00, 0.40)] = sum [0.00, 0.00, 0.00, 0.00, 0.00]
=0.00
Q(03' M1) = sum min [(0.13, 0.00), (0.16, 0.40), (0.20,0.40),
(0.16,0.00), (0.13, 0.20)] = max [0.00, 0.16, 0.20, 0.00, 0.13]
=0.49
Using (8)
Q(O, M.) = (3.56 + 0.00 + 0.49)/1.20 = 4.05
Normalized
Q(O, M.) = 4.05/4.54 = 0.89
Applying Cumulative-Minimum CompositionOperation
The elements of the Q(O, M) relation are calculated usingthe cumulative-minimum composition operation in (7) and (8)and are displayed in Table 8. For example, using (7)
TABLE 6. Calculation of Elements of R(F, M) Relation forSample Project
The following output is produced by the model based on itsanalysis (see Tables 7 and 8). For the sample bid situation, thefollowing margins are recommended by the maximum-minimum (max-min) rule, based on the strongest evidence:
• A 4% margin is recommended by 100%.• A 2% margin is recommended by 83%.• A 6% margin is recommended by 83%.• An 8% margin is recommended by 67%.• A 10% margin is recommended by 50%.• A 12% margin is recommended by 33%.
Using the max-min rule, the most highly recommended marginsize is 4.00%. A 6.00% margin is recommended based on ananalysis of all the recommended margin sizes. The followingmargins are recommended by the cumulative-minimum (cummin) rule, based on all supporting evidence:
• A 4% margin is recommended by 100%.• A 2% margin is recommended by 89%.• A 6% margin is recommended by 88%.• An 8% margin is recommended by 66%.• A 10% margin is recommended by 44%.• A 12% margin is recommended by 22%.
Using the cum-min rule the most highly recommended marginsize is 4.00%. A 5.72% margin is recommended based on ananalysis of all the recommended margin sizes.
In this example, the most suitable margin size could have
JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT I JANUARYIFEBRUARY 1998 I 7
TABLE 8. Calculation of Elements of Q(O, M) Relation forSample Project Using Cumulative-Minimum Composition Operation
been detennined simply by inspection of the objectives in bidding and the factors influencing margin size, since a smallnumber of factors was chosen intentionally to maintain thesimplicity of the example. In an actual bid situation a largernumber of factors would influence the choice of margin size,which would make it difficult to assess their combined effectsimply by inspection. The use of the competitive bidding strategy model is therefore warranted under actual bidding conditions, in which a large number of factors must be taken intoaccount.
Since there is a certain degree of imprecision and subjectivity in the judgments made by the user, the final choice ofmargin is left to the decision-maker. The recommendations ofthe model act only as a guide in selecting the most suitablemargin size. By providing a number of margin-size recommendations based on different methods of analysis, the modelcan help the decision-maker to choose an appropriate marginsize that suits his or her risk attitude and philosophy in settinga margin.
PRESTTO: INTEGRATED ESTIMATING AND BIDDINGSOFTWARE SYSTEM
A prototype computer-aided estimating and bidding systemcalled PRESTIa, a PRoject EStimating and Tendering TOol,has been developed to implement the competitive biddingstrategy model (Fayek 1996a,b; Fayek et al. 1995). PRESTIais a UNIX-based system written in C++, which operates onan IBM-compatible personal computer through XWindows.
11=1 PRESTTO: Tendering Module 1-10Display Current ReportlGo BacklQuitl IHeip
Please answer each of the fallowing questions...Push Ih. 'n••I' bUllon 10 go on 10 Ih. nIXI qu.stion.
1. Nom. of proj.cl und.rovaluation: Highway 10'2. Th.lype of proj.cl und...valuation: RoadwDdrs3. Th. scop. of Ih. conl"",l: ConstnlCtOllly4. Th.lype of conl"",t: lump sum5. Th. m.lhod of lend.ring: Prequ.lifiod6. Does this project involve you in a joint venture? No7. On Ihls I.nd.r, whal do.s lho margin allowanc.lnclud.?
COfPOIIte overheads,Pu,.pretaxprofit
8. Consld.ring only your company's sltualion, Ih. margin rang. b.ing considenld Is:2-12%
g. for.ach objective Iisl.d, pl.... indical.lo whal d.g... achieVing il is desi..d in Ihistender situation. kty combination of objectives is possible. Please select anumber on thescale, ranging from 0 [N/Al 10100 [slrong):
01, Win the project: I _I95
02, Test a new geographical area: I - I15
03, Maximise project's contribution to profit: -5 ,Next..
FIG. 2. PRESTTO Data-Entry Screen: General Questions,Range of Margin, and Objectives in Bidding
PRESTIa comprises separate estimating and bidding modules, integrated in one system. The estimating module followsa "first principles" approach to detailed estimating. The bidding module is the implementation of the competitive biddingstrategy model described in this paper.
The bidding module is accessed through the user interfaceof the estimating module. The user can access the biddingmodule at any time during estimate preparation. The results ofthe bidding module analysis can be input to the estimatingmodule for distribution over the direct cost items in the estimate.
The first step in the bidding module requires the user torespond to a series of questions regarding the project underevaluation. The user's responses provide the name of the project; the type of project; the scope of the contract; the type ofcontract; the method of tendering (bidding); whether or notthe project involves a joint venture; and which items are included in the margin allowance [e.g., risk and opportunity allowance, corporate overheads, pure pretax profit (see Fig. 2)].These responses are not used in the analysis perfonned by thebidding module, but are included for the user's reference sincethey may affect the margin-size decision.
The next step requires the user to define the range of marginunder consideration for the bid by specifying the minimumallowable margin and the maximum feasible margin (see Fig.2). Next, the user assesses his or her objectives in bidding bymoving a visual control on a scale ranging from a for "notapplicable" to 100 for "strong" for each of the three objectives (see Fig. 2).
The user selects the factors influencing margin size that heor she wishes to consider from the predefined list of 93 factorsprovided by the bidding module. The user can specify additional factors he or she wishes to consider that are not listedby the module. For each factor, the user indicates to whatdegree it holds true or is applicable to the bid situation underanalysis, by moving a visual control on a scale ranging froma for "false" to 100 for "true" (see Fig. 3).
The user assesses the degree to which each factor, at thegiven level, influences the choice of margin size, in order toachieve each objective in turn. Again, the user moves a visualcontrol on a scale ranging from a for "no influence" to 100for "a high degree of influence" (see Fig. 4).
Next, the user selects the most suitable margin size that eachfactor at its given level, considered independently of all others,would indicate in order to achieve each objective in turn. Theuser chooses one of the six system-calculated margin sizes,ranging from the minimum to the maximum margin size, displayed on a visual scale (see Fig. 5).
IIII QuitOk
Select degree ofapplicability offactors
IIIL-------"';"........
34
11I1--~:~;;;3::-----J
FIG. 3. PRESTIO Data-Entry Screen: Degree of Applicability of Factors Influencing Margin Size
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=1 select degree of Influence of factors on margin cllolce
For the objective: 'Win the project",lndlcate the degree to which each factorinfluences the margin choice, given that achieving this objective Is 100% desired.Please seiect a number on the scale, ranging from 0 (None) to 100(Hlgh).
INext Page II Prev Page II Go Back II Ok II Quit II Helpl
1·10
FIG. 4. PRESTTO Data-Entry Screen: Degree of Influence of Factors on Margin-Size Decision
Select most suitable margin for each factor
For the objective: 'Win the project", indicate the most suitable margin that willoptimise the likelihood of achieving this obJective, given that achieving thisobjective Is 100% desired, and the factor at this level exists at full strength. Pleaseselect a number on the scale ranging from the minimum to the maximum margin.
• 0
Ok II Quit II Helpl
FIG. 5. PRESTTO Data-Entry Screen: Most Suitable Margin Size for Factors to Achieve Objective in Bidding
Finally, the user chooses the method of analysis from thefollowing options: the maximum-minimum (max-min) composition operation, the cumulative-minimum (cum-min) composition operation, or both methods (for comparison).
For each analysis method chosen by the user, the biddingmodule ranks the six margin sizes in terms of their suitabilityto the bid situation and indicates the percentage with whicheach is recommended. The bidding module also indicates themost highly ranked margin size (or sizes), and the margin sizerecommended based on the center-of-area method of defuzzification. The results of the bidding module analysis are displayed in a bid analysis report, which can be saved in ASCIIformat (see Fig. 6).
Implementation of the competitive bidding strategy modelin the form of the PRESTIO software system makes themodel quick and easy to use and therefore suitable to the timeconstrained, competitive bidding environment.
SIGNIFICANCE AND CONCLUSION
A competitive bidding strategy model that uses techniquesof fuzzy set theory to help in setting margins on civil engineering and building construction projects has been developedand implemented in the form of a prototype software systemnamed PRESTIO. Fuzzy set theory can be successfully applied to develop a model that suits the actual practices of construction contractors and that provides a realistic tool for setting margins. The use of fuzzy set theory allows assessmentsto be made in qualitative and approximate terms that suit thesubjective nature of the margin-size decision. The resultantmodel is quick and easy to use, does not rely on historical
project or competitor data, is not population- or context-specific, and captures many of the issues and factors that affect acontractor's margin-size decision. The competitive biddingstrategy model presented in this paper improves on previouslydeveloped models by addressing many of their disadvantagesthat hinder their use in the construction industry.
The competitive bidding strategy model can help a companyto assess its objectives in bidding and to account for the effectof numerous corporate, commercial, project, client, and competitive factors on the margin-size decision. By helping thecompany to logically consider all of its objectives in biddingand factors influencing margin size, the model can reducesome of the uncertainty associated with setting margin andhelp a company achieve its objectives in bidding.
The model provides a standard methodology for settingmargins on civil engineering and building projects that is independent of any company or organization. Experienced personnel can perform the analysis and obtain a reliable resulteach time. The model enables experts to express their experience in a formalized manner and provides a basis for discussion of the most appropriate margin size with other decision-makers. The model can be used to validate the user'sintuitive choice of margin size, to clarify the goals of the decision-maker, and to document the factors considered. Themodel is therefore useful as a quality assurance tool. Use ofthe model can improve the quality and efficiency of the decision-making process used in setting a margin, resulting in amore competitive bid.
The model can also be used as a training tool to help inexperienced personnel to understand the corporate decisionmaking process used in setting margin. Because it has the
JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT I JANUARY/FEBRUARY 1998/9
I- IL reviewers of this paper and Richard Larew of Ohio State University fortheir valuable comments and insights, which helped to enhance this paper.The writer also wishes to acknowledge the students from the Departmentof Computer Science at the University of Melbourne who perfonned theprogramming of the PRESTIO software system. The writer is grateful tothe University of Melbourne, the Commonwealth Government of Australia, and the Australian Research Council for the scholarships and grantsthat enabled the writer to conduct this research.
APPENDIX. REFERENCES
~ummary Of Results
FIG. 6. PRESTIO Bid Analysis Report
ACKNOWLEDGMENTS
The writer wishes to thank David Young and Colin Duffield of theUniversity of Melbourne for their ideas, comments, and supervisionthroughout the course of this research. The writer wishes to thank the
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SaveIIPrintIIOK
For this tender situation. the following margins are recommended.:
~~~o~th~:~~::~d~~:n rule,
A 2.00% margin Is recommended by 99%A 4.00% margin is recommended by 86%A 6.00% margin Is recommended by 86%
i~~~~~~sis~Jty6:"A 12.00% margin is recommended by 56%
The most highly recommended margin size is 2.00%,
The margin size recommended based on an analysisof all the recommended margin sizes is 6.41%.
Using the cumulative-minumum rule,based on all supporting evidence:
A 4.00% margin is recommended by 100%A 2.00% margin is recommended by 96%A 6.00% margin is recommended by 92%A 8.00% margin is recommended by 84%A 10.00% margin Is recommended by 69%A 12.00% margin Is recommended by 41%
The most highly recommended margin size Is 4.009'0.
The margin size recommended. based on an analysisof aU the recommended margin sizes Is 6.20%.
built-in flexibility to allow the user to specify the relevantfactors influencing margin choice, the model can be tailoredto suit any project and any company's individual practices.
Because the competitive bidding strategy model is quickand easy to use, particularly in its implemented form in thePRESTIO software system, it is suitable to the time-constrained competitive bidding environment. Numerous risk andopportunity scenarios and commercial and competitive scenarios can be modeled, and their impact on the most suitablemargin size quickly assessed. The model can therefore increasethe efficient use of the limited time available for setting margin.
Future development of the model includes the addition ofexplanation facilities regarding how the output was obtained;a set of expert rules to recommend modifications to the inputdata in cases where the output is not definitive; the additionof other objectives in bidding; the ability to allow the user tospecify the number of increments in which to divide the rangeof margin under consideration; and a set of expert rules guiding the user to the most suitable margin size for different levelsof each factor influencing margin, derived from a database ofcompany experience in bidding.
The degree to which the competitive bidding strategy modelmirrors actual industry practices is demonstrated through itsvalidation with data from actual project bids, collected from asurvey of the Australian construction industry. The validationof the competitive bidding strategy model will be presented ina companion paper.
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