Integration of Simulation-Based Cost Model
and Multi-Criteria Evaluation Model
for Bid Price Decisions
Wei-Chih Wang,
∗Ren-Jye Dzeng & Yu-Huang Lu
Department of Civil Engineering, National Chiao Tung University, TaiwanAbstract: Several criteria affect bidding decisions. Cur-rent bidding models determine a markup based on a fixed project construction cost. This work presents a novel bid price determination procedure that is built by integrating a simulation-based cost model and a multi-criteria eval-uation model. The cost model is used to consider cost uncertainties and generate a bid price cumulative distri-bution, whereas the multi-criteria evaluation model ap-plies pairwise comparisons and fuzzy integrals to reflect bidder preferences regarding decision criteria. The rela-tionship between the two models is based on a practi-cal phenomenon in that a bidder has a high probability of winning when criteria evaluations favor his bid, and, consequently, the bidder would bid a low price, and vice versa. The merits of the proposed procedure are demon-strated by its application to two construction projects in Taiwan.
1 INTRODUCTION
Bidding decisions often include whether to bid (Han and Diekmann, 2001; Wanous et al., 2000, 2003; Lin and Chen, 2004) and what bid markup to allocate (or what bid price to use). This study focuses on the sec-ond decision. Making suitable decisions regarding the bid price of a lump-sum-based construction project is essential for a bidder to win the project contract and achieve a reasonable profit, regardless of the type of bid-award method used (e.g., lowest bid versus multi-criteria evaluation bid). A high bid price that maximizes profit conflicts with the interest of the bidder in winning the
∗To whom correspondence should be addressed. E-mail: weichih@ mail.nctu.edu.tw.
contract. On the other hand, a low bid price that in-creases the probability of winning the contract jeopar-dizes profit (if awarded). The dilemma for the bidder is to set a bid price that is sufficiently high to maximize profit, while simultaneously being sufficiently low to suc-cessfully win the contract.
In practice, the markup (or bid price) of a construc-tion project is frequently determined based on intuiconstruc-tion and experience, and involves emotional responses to current pressures (Fayek, 1998; Xu and Tiong, 2001). Nevertheless, this experience-based bid price decision explicitly or implicitly considers numerous criteria re-lated to environmental conditions, company conditions, and project conditions (Dozzi et al., 1996; Chua and Li, 2000; Dulaima and Shan, 2002). Consequently, a suitable bid price decision must deal with the evaluations of these criteria.
Current bidding models determine bid markup by as-suming that project construction cost is fixed. However, construction costs typically vary due to variations in sev-eral cost uncertainties such as inflation rate, financing interest rate, quantity takeoff and price quotes. By con-sidering project construction cost as probabilistic and assuming that bid price decisions should go through a va-riety of criteria evaluations, this investigation proposes a novel hybrid bid price determination procedure that combines a simulation-based cost model and a multi-criteria evaluation model. The cost model considers the criteria involving cost uncertainties and derives a cumu-lative distribution of project bid price. The multi-criteria evaluation model is utilized to identify the preferences for other decision criteria. A bid price is recommended from the bid price distribution according to a project expected utility value as assessed by the multi-criteria evaluation model.
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2007 Computer-Aided Civil and Infrastructure Engineering. Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ, UK.
The rest of this article is organized as follows. The next section reviews the literature on bidding and tendering practices, and then describes the proposed procedure. The detailed workings of the proposed procedure are demonstrated using two projects (i.e., case studies I and II). Finally, research significance is discussed, and direc-tions for future research are suggested.
2 REVIEW OF PERTINENT RESEARCH Relevant bidding and tendering research addresses as-sessment of bidder capability to complete a contract (Russell and Skibniewski, 1988; Lo et al., 1999), selec-tion of a method for awarding contracts (Herbsman and Ellis, 1992; Ioannou and Leu, 1993), tests to minimize subjective bias in best value procurement (Kashiwagi and Byfield, 2002a, 2002b), determination of the project ceiling price (Wang, 2002a; Wang, 2004), evaluation of competitive bids for examining the decision to accept or reject the lowest project bid (Crowley and Hancher, 1995; Skitmore et al., 2001), and determination of bid markup. The research most relevant to this work is that for determining project ceiling price and bid markup.
From the perspective of project clients, Wang (2002a) created a procedure (called SIM-UTILITY) to obtain a project ceiling price or cost threshold to use as a ref-erence for accepting and rejecting construction project bids. Any bid over this cost threshold was generally dis-qualified under the Taiwanese Procurement Law (Wang, 2002a). Wang’s procedure was based on a utility theory and facilitated by a cost simulation approach. The util-ity theory was applied to reflect client preferences re-garding the determination criteria affecting project cost threshold, whereas the simulation technique was utilized to yield objective project cost data to support the exe-cution of utility theory. For simplicity, Wang (2004) fur-ther devised a mathematically derived cost model that substituted the simulated-derived cost model to support SIM-UTILITY.
Existing models for determining bid markups can be classified into three groups (Marzouk and Moselhi, 2003): (1) statistical models, (2) artificial intelligence based models, and (3) multi-criteria utility models. Among the statistical models, for example, Carr (1983) designed a general bidding model by considering the influence of the number of involved bidders on the markup. Carr (1987) further illustrated how competitive bid analysis can include resource constraints and oppor-tunity costs.
Considering that markup decisions have difficulty in going through a sequence of deep reasoning steps, several bidding models using Artificial Neural Network (ANN) related tools have been designed to support markup decisions (Moselhi et al., 1993; Li and
Love, 1999). Additionally, believing that bidding deci-sion problems are highly unstructured and no clear rules can be found for delivering a bidding decision, Chua et al. (2001) devised a case-based-reasoning bidding model for helping contractors.
Several decision criteria guide bidders in determining how to price their work in relation to estimated con-struction costs (Ahmad and Minkarah, 1988; Dozzi et al., 1996; Chua and Li, 2000; Dulaima and Shan, 2002). For example, Dozzi et al. (1996) applied a multi-criteria util-ity theory to implement construction project bid markup decisions. Moreover, based on the analytic hierarchy process (AHP), Cagno et al. (2001) proposed a simu-lation model to assess the probability of winning in a competitive bidding process in which competing bids were evaluated based on multiple criteria. Furthermore, Marzouk and Moselhi (2003) designed a model for esti-mating markup and evaluating bid proposal using multi-attribute utility theory and AHP.
Generally, statistical models have difficulty capturing specific project characteristics (e.g., project complexity and market conditions); the ANN-related models re-quire numerous training cases or suitable rules to rep-resent the bidding strategies of individual bidders. The multi-criteria evaluations meet the real-life situations closely (Marzouk and Moselhi, 2003). Finally, all current models produce bid markups based on an assumption of fixed project costs.
3 PROPOSED PROCEDURE 3.1 Modeling strategies
The goal of most bidding models is to maximize the chance of winning a bid under the criterion of expected profit maximization (Car, 1987; Moselhi et al., 1993; Cagno et al., 2001; Chua et al., 2001). However, like other models (Dozzi et al., 1996; Li and Love, 1999; Marzouk and Moselhi, 2003), the proposed procedure attempts to improve the quality of a bid price decision-making pro-cess by incorporating the assessments of a variety of de-cision criteria and by treating project construction costs as variables to fit real-world situations.
This study divides bid price decision criteria into two groups: (1) the group-1 criteria (cost uncertainties) di-rectly influence estimations of project construction costs; and (2) the group-2 criteria address subjective prefer-ences of decision-makers. Based on a review of several current studies (Dozzi et al., 1996; Cagno et al., 2001; Du-laima and Shan, 2002), Figure 1 displays an example hier-archical structure for these two groups of criteria. Each group of criteria is classified into two levels: level-1 cri-teria and level-2 subcricri-teria. The level-1 cricri-teria for each group are related to environmental conditions, company
Fig. 1. Example of the hierarchical structure of criteria and subcriteria.
conditions, and project conditions. A simulation-based cost model is applied to assess the group-1 criteria, whereas a multi-criteria evaluation model is designed to evaluate the group-2 criteria. The integration of both models for supporting bid price decisions is described in the following section.
3.2 Modeling steps
Figure 2 shows the modeling steps of the proposed hy-brid procedure achieved by modifying the procedure in Wang (2002a). (The differences between the two proce-dures are described in Section 6.1.) The right of the figure illustrates a simulated cumulative probability distribu-tion of project bid price, whereas the left part presents a utility function generated based on the multi-criteria evaluation model. The proposed procedure is executed via the following three phases, which consist of nine steps.
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Phase I: cost model1. Estimate the construction costs, including the di-rect and indidi-rect costs.
2. Conduct a simulation analysis to include cost un-certainties and then generate a cumulative dis-tribution of bid price.
3. Identify the maximum and minimum bid prices of the project (namely, the upper and lower boundaries of the project bid price).
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Phase II: multi-criteria evaluation model4. Set the lowest expected utility value for the bid-der, Eu(w), to 0. Additionally, set the probabil-ity of not winning (PONW) for Eu(w) at 1. The point (Eu(w)= 0, 1) thus corresponds to the probability of 1 of the cumulative distribution of bid price, and then corresponds to the max-imum bid price. (See Figure 2.) Submitting the maximum bid price implies that probability of winning is zero (=1 − PONW = 1 − 1). This set-ting reflects a practical phenomenon: a bidder assumes a high risk if the criteria evaluations are unfavorable to him; and he would bid a high bid price (with less chance of winning the project contract).
Fig. 2. Proposed procedure.
5. Set the highest expected utility value for the bid-der, Eu(p), to 1. Furthermore, set the PONW with respect to Eu(p) at 0. Thus, the point (Eu(p)= 1, 0) corresponds to the probability of 0 for the cumulative distribution of bid price, and then corresponds to the minimum bid price. (See Figure 2.) Submitting the minimum bid price in-dicates that probability of winning is 1 (=1 − PONW=1 − 0). Restated, a bidder would pre-fer to make a lowest price bid to gain a high chance of winning the project contract in situ-ations where the criteria evalusitu-ations favor that bidder.
6. Set a particular value of PONW (= 1.0 − average winning probability= 1.0 − Pave) corresponding
to the threshold expected utility value (Eu(t)). The value of Pave equals the number of earned
bids divided by total number of submitted bids in a given period for the bidder. The value of Eu(t) is calculated using threshold utility scores for the bidder’s subcriteria. The threshold utility score of a subcriterion is considered as the acceptable utility score for the subcriterion for the bidder to bid on a project. It is assumed that the bidder would submit a bid if the criteria evaluation of the project was Eu(t).
7. Assuming a straight-line relationship, develop the PONW utility function based on the follow-ing three points; that is, (Eu(w)= 0, 1), (Eu(t), 1− Pave), and (Eu(p)= 1, 0).
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Phase III: integration of two models8. Calculate the expected utility value of project scenario x, Eu(x) after assessing the utility value of each criterion of the project. According to the PONW utility function developed above, a value of PONW, Px, is identified with respect to Eu(x).
9. Based on the value of Px, find a recommended bid price from the cumulative distribution of the project bid price.
In establishing the PONW utility function, the two points, ((Eu(w)= 0, 1) and (Eu(p) = 1, 0)), are applica-ble to all bidders, whereas the threshold point (Eu(t), 1− Pave) is used to reflect a particular bidder’s uniqueness.
The PONW utility function assumes that the relation between the PONW values and the expected utility val-ues for previously submitted bids (notably, the PONW utility function) does not consider profitability of histor-ical projects. Restated, this utility function represents a way to transform a particular expected utility value for a given project (Eu(x)) into a predicted value of proba-bility of not wining (Px).
The relationship between the cost model and multi-criteria evaluation model is constructed based on practi-cal phenomenon (refer to steps (4) and (5)): a bidder has a high probability of winning (low Px) when the criteria evaluations are favorable, thus, the bid price would be low, and vice versa. Moreover, the meaning of Px is con-sistent in both models. That is, on the right of Figure 2, there is also a Px chance that a bid price will be below the recommended bid price.
3.3 Cost model
3.3.1 Project construction cost. The total cost of a con-struction project includes direct costs, indirect costs and markup (Adeli and Wu, 1998; Wang, 2002b; Wang et al., 2005). In this investigation, the total construc-tion cost (i.e., the bid price), CTot, of a project is
represented as,
CTot= (C1+ . . . + Cj+ . . . + CJ)
× (1 + C1+ . . . + Ck+ . . . + Ck)× (1 + t)
= J j=1 Cj × 1+ K k=1 Ck × (1 + t) (2) = J j=1 Cj+ J j=1 Cj× K k=1 Ck × (1 + t) (3) where Cj is the cost of direct cost component j, and J
denotes the number of direct cost components. Ckis the
cost of indirect cost component k, and K denotes the number of indirect cost components. ThusJj=1Cjand
J j=1Cj×
K
k=1Ckrepresent the total direct and
indi-rect project costs, respectively. The value t represents the tax as a percentage (constant value, usually 5% in Taiwan) of the sum of the total direct costs and the indi-rect costs.
The direct costs, measured in dollar terms, are such as excavation, structure, finishes, doors, windows, paint-ing, and furnishing. The indirect costs, measured in per-centage terms, include costs such as installing temporary water and electricity supplies, field and home office over-heads, insurance, and markup. Notably, markup can be expressed as a percentage of CTot (Dozzi et al., 1996;
Wang et al., 2005). In this study, according to the typ-ical practice in Taiwan, markup is treated as an indi-rect cost and measured as a percentage of total diindi-rect cost.
Notably, modeling step (1) develops a bid estimate according to bid documents (such as bid forms, draw-ings, and specifications) and the construction proce-dures devised by the bidder (Peurifoy and Oberlender, 2002). This bid estimate encompasses estimating tasks of quantity takeoffs and vender/subcontractor quotes for estimating labor, materials, equipment, and subcontract-ing costs for each detailed cost item in the bid project. The cost of each Cj(e.g., sitework) in Equation (1)
rep-resents the sum of costs of several detailed cost items (e.g., clearing, excavation, compaction, etc.).
3.3.2 Cost uncertainty. The proposed cost model as-sesses the first group of criteria and subcriteria that di-rectly affect estimations of project construction costs. The subcriteria are, for example, inflation, interest rates, historical markups, quantity takeoffs, payment terms, and cash flow requirements. These subcriteria are treated as cost uncertainties, and variations of such subcriteria impact direct and indirect cost components. Thus, Cj s
and Cks are variables in costs and percentages,
respec-tively. This cost model uses three point estimates (op-timistic, most likely, and pessimistic costs) to acquire a Beta distribution for each cost component. For example, the optimistic cost for Cjis the cost that would be lowest
once out of 20 times if the cost component could be re-peated under the same conditions (Moder et al., 1983). Similar definitions can be applied to the pessimistic cost. Furthermore, each indirect cost component is evaluated in terms of optimistic, most likely, and pessimistic per-centages.
This study suggests that costs (or percentages) esti-mated in modeling step (1) can be considered the most likely costs (or percentages) of Cj (or Ck). Moreover,
a bidder subjectively estimates the optimistic and pes-simistic costs (or percentages) for each Cj(or Ck) based
on experience or knowledge of the requirements of Cj
(or Ck) learned from the bid estimation process in
mod-eling step (1).
3.3.3 Simulation and computer implementation. Monte Carlo simulation involves the generation of random costs according to Cj and Ck distributions, and then totals
these costs to derive the project bid price (CTot)
ac-cording to Equations (1)–(3). This process is repeated several hundred times, with CTotbeing calculated each
time. A cumulative probability distribution of bid price can then be constructed based on the values of CTot.
Notably, the simulated maximum and minimum project construction costs are assumed to be maximum and min-imum bid prices, respectively. Additionally, in modeling step (5), the probability of zero (Px= 0) is assumed to be mapped to the simulated minimum value. This as-sumption is made for simplicity as the probability for this minimum value is only 0.02% (= 1/5,000 simulation iterations).
The cost model is implemented in a simulation lan-guage, Stroboscope (Martinez, 1996). Stroboscope can define probabilistic cost data concerning each cost com-ponent, and generate a cumulative distribution of project bid price. The cost model is implemented on a Pentium III PC with 768 MB of RAM in a Windows XP environ-ment. It took approximately 2 minutes to analyze the example projects 5,000 times.
3.4 Multi-criteria evaluation model
The multi-criteria evaluation model assesses the group-2 criteria mentioned earlier, which are divided into three categories of level-1 criteria (see Figure 1), namely en-vironmental conditions (R1), company conditions (R2), and project conditions (R3). Each criterion then includes several level-2 subcriteria. For example, the criteria and subcriteria shown in the bottom part of Figure 1 are iden-tified by the bidder for the example project (case study I) and are elucidated in Section 4.2. Notably, the pro-posed model does not restrict the number of criteria and subcriteria involved.
In the proposed multi-criteria evaluation model, cri-teria are assumed to be independent, and the impor-tance of criteria is pairwisely compared to derive the criteria weights according to AHP algorithms (Saaty, 1978). Then, assuming that the subcriteria under a crite-rion are mutually dependent, the fuzzy integral is em-ployed to support subcriteria assessments (Chen and Tzeng, 2001). The assessment result for a subcriterion is a utility score of the subcriterion. The evaluation re-sult for the level-2 subcriteria (e.g., r5, r6, r7, and r8) for a given level-1 criterion (e.g., R2) is a utility value for the criterion. Multiplying the utility value by a corre-sponding weight yields a weighted utility value for each criterion. The sum of all of the weighted utility values of the criteria is the expected utility value for a specific project scenario. Further details of these utility-related definitions can be found in Clemen (1996).
3.4.1 Weight of criteria. The importance of the three group-2 level-1 criteria is pairwisely compared. The scale used to derive the relative importance from ma-trices of pairwise comparisons ranges from 1 to 9, as follows (Saaty, 1978): 1—equally important; 3— slightly more important; 5—strongly more important; 7—demonstratedly more important; 9—absolutely more important. 2, 4, 6, 8 denote a degree of importance lying between 1 and 3, 3 and 5, 5 and 7, and 7 and 9, respec-tively. The matrix of preferences is manipulated via a method that determines the eigenvector corresponding to the maximum eigenvalue of a matrix (Saaty, 1978). The sum of the weights of criteria equals 1.
3.4.2 Fuzzy integral. As mentioned previously, the sub-criteria for a criterion are assumed to be interdepen-dent. Thus, unlike criteria evaluations (an additive sit-uation), subcriteria evaluations are non-additive. This work employs a fuzzy integral value to express the util-ity value (hdg) of each criterion that is evaluated based on fuzzy measure (g(·)) and the utility score (h(·)) of each subcriterion.
The fuzzy measure is frequently used with a fuzzy inte-gral for aggregating information evaluation. Theλ fuzzy measure is applied to evaluate the importance of the de-pendent subcriteria (Chen and Tzeng, 2001). The fuzzy measure g is a set of function defined using a power set β(X) of X, and g:β(X) → [0, 1]. The function g must pos-sess the following properties (Chen and Tzeng, 2001):
(A) g(φ) = 0, g(X) = 1.
(B) if A, B∈ β (X) and A ⊂ B, then g(A) ≤ g(B) Aλ fuzzy measure gλ has the following properties: ∀A, B ∈ β(X), A∩ B = φ; gλ( A∪ B) = gλ( A)+ gλ(B)+
λgλ( A)gλ(B); and−1 < λ < ∞. Then for the definite set
X= {x1, x2,. . . , xn}, the density of fuzzy measure
gi= gλ({xi}) (gλ({x1, x2,. . . , xn}) can be viewed as
the importance of considering various subcriteria), can be formulated as follows (Chiou et al., 2005):
gλ({x1, x2, . . . . ., xn}) = n i=1 gi+ λ n−1 i 1=1 n i 2=i1+1 gi 1gi 2 + . . . . + λn−1g 1g2, . . . , gn, for − 1 < λ < ∞ (4)
In a specific case involving two subcriteria, A and B, if λ > 0, namely, gλ({A, B}) >gλ({A}) + gλ({B}), then A
and B have multiplicative effects; ifλ < 0, namely, gλ({A, B}) < gλ({A}) + gλ({B}), then A and B have
substitu-tive effects; if λ = 0, namely, gλ({A, B}) = gλ({A}) + gλ({B}), then the evaluation of the set {A, B} equals the sum of assessments for sets{A} and {B}.
Let h be a measurable set function defined on a mea-surable space, and suppose h(x1)≥ h(x2)≥ . . . ≥ h(xn),
then the fuzzy integral (i.e., hdg= utility value of a criterion) of fuzzy measure g(·) with respect to h(·) can be defined as follows (Ishii and Sugeno, 1985).
hdg= h(xn)g(Hn)+ [h(xn−1)− h(xn)]g(Hn−1)
+ . . . + [h(x1)− h(x2)]g(H1)
= h(xn)[g(Hn)− g(Hn−1)]+ h(xn−1)[g(Hn−1)
− g(Hn−2)]+ . . . + h(x1)g(H1) (5)
where h(xi) is the utility score of subcriterion xi; H1 =
{x1}, H2= {x1, x2}, . . . , Hn= {x1, x2, x3,. . . , xn} = X.
Figure 3 illustrates the concept of Equation (5). Namely, the value of hdg is the area in Figure 3. The details of g({x1, x2,. . . , xn}) and
hdg can also be found in (Chen and Tzeng, 2001; Lin, 2005); an example is pre-sented in Section 4.2.
4 CASE STUDY I
The mechanical/electrical subproject (termed M/E project herein) of a public construction project in northern Taiwan is used to demonstrate the proposed procedure. Besides two underground floors, the project includes a 5-story high-tech facility building and a 10-story office building. The project was completed by mid-2004. The project was awarded based on a multi-criteria evaluation bid-award method. The bid-award criteria en-compassed bid price, technology, quality, function, and commercial terms of a bid. The proposed procedure was applied to support a bidder in determining bid price. This application was conducted following the awarding of the M/E project (namely, after the submission of the bid price). A cost manager who was fully involved in the bid decision-making process for the bidder provided the inputs for executing the proposed procedure. The follow-ing subsections describe the assessments of the modelfollow-ing steps.
4.1 Evaluations of the cost model
Based on bid documents and planned construction pro-cedures, the bidder conducted a bid estimation based on the quantity takeoff and a vender/subcontractor’s quote for each detailed cost item in the project. Then, the costs of numerous detailed cost items are aggre-gated to a summary sheet that includes 11 cost compo-nents. Table 1 lists the description and three point cost estimates (optimistic, most likely and pessimistic costs or percentages) for each cost component. Following 5,000 simulations, the minimum and maximum bid prices are NT$387,345,043 and NT$419,265,473, respectively. (thirty New Taiwan dollars∼=1US dollars. Thereafter, NT
Table 1
Three-point estimates for each cost component of the M/E project
(Currency: NT$30 ∼= US$1)
Cost components Optimistic cost ($NT) Most likely cost ($NT) Pessimistic cost ($NT)
C1. Electrical systems 71,200,000 71,386,677 78,000,000
C2. Water supply/disposal systems 7,100,000 7,434,321 8,500,000
C3. Mechanical systems 41,800,000 41,966,401 47,600,000
C4. Fire protection systems 36,600,000 36,724,514 41,600,000
C5. Clean room and special systems 193,000,000 194,373,567 219,700,000 Optimistic % Most likely % Pessimistic % C6. Drawing compositions and quality inspection 0.23% 0.25% 0.50%
C7. Temporary water & electricity 0.70% 0.75% 0.90%
C8. Site safety management 0.25% 0.30% 0.60%
C9. Insurance 0.15% 0.20% 0.35%
C10. Markup 3% 4.05% 6.00%
C11. Tax 5% 5% 5%
dollar is used.) Notably, the generated cumulative prob-ability distribution of the project bid price is displayed on the right of Figure 5.
4.2 Assessments of the multi-criteria evaluation model The bottom part of Figure 1 shows the group-2 level-2 subcriteria that are qualitatively assessed for the M/E project. Table 2 describes the utility and range of the utility scores for each subcriterion. The subcriterion of r1 (future projects) provides an example. If the bidder forecasts that several new projects are being marketed, then he will have a high chance of obtaining project con-tracts. Restated, the bidder can still find opportunities to compete for other projects if he does not win the contract of the current project. Consequently, the bidder will sub-mit a comparatively high bid price, leading him to assign a low utility score to subcriterion r1.
Table 3 shows a pairwise comparison and lists the im-portance of the level-1 criteria. These inputs of impor-tance have passed the consistency index and consistency ratio tests (Saaty, 1978). The eigenvector for the matrix of Table 3 (preferences of criteria) is (0.9628, 0.1067, 0.2483) using the maximum eigenvalue of 3.0649. The normalized weights of the three criteria then are 0.7306, 0.0810, and 0.1884. The sum of the normalized weights of the criteria equals 1.
Next, the fuzzy integral is utilized to evaluate the sub-criteria and generate the utility value of each criterion. Table 4 displays the threshold and project utility scores (h(xi)) assigned to subcriteria for computing the
thresh-old expected utility value (Eu(t)) and expected utility value for the project (Eu(x)). For example, the bidder assigns utility scores of 1.0, 0.9, 1.0, and 0.8 of h(xi)
Table 2
Description of utility and range of utility scores for subcriteria of the M/E project
Subcriteria Description of utility Range of utility scores
R1. Environmental conditions
r1. Future projects Forecast of upcoming projects on the market. Many future projects→ more opportunities for bidders → low current project value→ high bid price → low utility score
(0, 1); Many= 0, Few = 1
r2. Market conditions Other projects currently being tendered for. Good
construction economy→ more opportunities for bidders → low current project value → high bid price → low utility score
(0, 1); Good= 0, Poor = 1
r3. Competition Expected number of competitors bidding for the project. Many competitors→ high current project value → low price→ high utility score
(0, 1); Few= 0, Many = 1
r4. Labor availability Is local labor available or difficult to obtain? Many laborers are available→ high current project value → low price → high utility score
(0, 1); Few= 0, Many = 1
R2. Company conditions
r5. Current work load Volume of all current projects relative to company capacity. High current load→ high bid price → low utility score
(0, 1); High= 1, Low = 0 r6. Need for public exposure High exposure→ high current project value → low bid price
to win project contract→ high utility score
(0, 1); Low= 0, High = 1 r7. Need for work High need for work→ high current project value → low bid
price→ high utility score
(0, 1); Low= 0, High = 1 r8. Experience in similar projects Good experience→ high current project value → low bid
price→ high utility score
(0, 1); Poor= 0, Good = 1 R3. Project conditions
r9. Project complexity Does the project complexity exceed current firm capabilities? High project complexity→ high risk → low current project value→ high bid price to meet project specifications→ low utility score
(0, 1); High= 0, Low = 1
r10. Location Is the project located within company operating area? Close location→ high current project value → low bid price → high utility score
(0, 1); Far= 0, Close = 1
r11. Project duration Tight duration→ high risk → low current project value → high bid price to meet project deadline→ low utility score
(0, 1); Tight= 0, Loose = 1 r12. Relationship with owner Good relationship→ Good communication → high current
project value→ low bid price → high utility score
(0, 1); Poor= 0, Good = 1
h(r5)= 1.0, h(r7) = 1.0, h(r6) = 0.9, and h(r8) = 0.8. And h(r5)≥ h(r7) ≥ h(r6) ≥ h(r8).
Then, based on Equation (4), the fuzzy measure g({x1,
x2,. . . , xn}) (namely, the importance considering
var-ious subcriteria) is assessed. The criterion R2 (company conditions) provides an example. The evaluation re-sults demonstrate that the importance of r5= gλ({r5}) = 0.0619, the importance of r56 (i.e., considering both subcriteria r5 and r6)= gλ({r5, r6}) = 0.3966, the im-portance of r567= gλ({r5, r6, r7}) = 0.6572, and the importance of r5678= gλ({r5, r6, r7, r8}) = 1. (The detailed computations for g({x1, x2,. . . , xn}) in this
case study can be found in Lin (2005).) The utility value of the criterion R2 (including subcriteria r5, r6, r7, and
r8),hdg, is calculated according to Equation (5) (see Figure 4), namely:
hdg= utility value of criterion R2 (= the area shown in Figure 4)
= 0.8 × 1 + (0.9 − 0.8) × 0.6572 + (1.0 − 0.9) × 0.3966 + (1.0 − 1.0) × 0.0619 = 0.91
(6) The left of Table 5 shows the weight and utility value for each criterion. The weighted utility value (i.e., weight multiplied by utility value) then can be obtained, and the expected utility value of the project (Eu(x)) equals
Table 3
Pairwise comparisons of group-2 level-1 criteria for the M/E project
Criteria R1. Environmental conditions R2. Company conditions R3. Project conditions
R1. Environmental conditions 1 7 5
R2. Company conditions 1/7 1 1/3
R3. Project conditions 1/5 3 1
Table 4
Threshold and project utility scores assigned to each subcriterion of the M/E project
Threshold Utility score
Subcriteria utility score of the project
r1 0.6 0.6 r2 0.4 0.5 r3 0.5 0.5 r4 0.6 0.6 r5 0.6 1.0 r6 0.6 0.9 r7 0.6 1.0 r8 0.7 0.8 r9 0.5 0.9 r10 0.5 0.9 r11 0.5 0.9 r12 0.5 0.8
0.6175 (= 0.3799 + 0.0737 + 0.1639; the sum of the weighted utility values of the three criteria). Similarly, the threshold expected utility value (Eu(t)) equals 0.4870 using the threshold utility scores assigned to subcriteria. (See Table 4.) Additionally, the average winning prob-ability for this bidder was just 10% per year (namely, the bidder won around 10 project contracts out of 100 projects). Thus, Pave= 0.1 (i.e., 1 − Pave= 0.9).
Fig. 4. Fuzzy integral of criterion R2 of the M/E project.
4.3 Results
Figure 5 presents the modeling results based on the eval-uations of the cost model and the multi-criteria evalua-tion model. According to the PONW utility funcevalua-tion, the probability Px can be estimated from the following relationship, and Px= 0.671.
Px
0.9=
(1− 0.6175)
(1− 0.4870) (7)
By mapping the value of Px (0.671) to the cumu-lative distribution of bid price (i.e., the right part of Figure 5), the probabilities of 0.6668 (with a bid price of NT$400,200,000) and 0.6724 (with a bid price of NT$400,300,000) are closest to Px. Then, assuming a linear relationship, the recommended bid price (RBP) corresponding to Px can be determined using the fol-lowing relationship, and the recommended bid price is NT$400,281,132.
RBP− 400,200,000 400,300,000 − 400,200,000 =
(0.6710 − 0.6668) (0.6724 − 0.6668) (8) In this project, the bidder’s submitted bid price was ex-actly NT$390,000,000, which was approximately 2.64% less than the recommended bid price (=(400,281,132 − 390,000,000)/390,000,000). However, the cost manager indicated that the initial estimate exceeded $400 million. If NT$400 million is used as another comparison base,
Table 5
Multi-criteria evaluation results of the M/E project
Threshold Utility Weighted threshold Weighted
Weight utility value value utility value utility value
Criteria (m) (n ) (n) (z = m × n ) (z= m × n)
R1. Environmental conditions 73.06% 0.47 0.52 0.3434 0.3799
R2. Company conditions 8.10% 0.61 0.91 0.0494 0.0737
R3. Project conditions 18.84% 0.50 0.87 0.0942 0.1639
Expected utility value Eu(t)= 0.4870 Eu(x)= 0.6175
the bid price recommended using the proposed proce-dure is around 0.07% above the initial estimate of the bidder (=(400,281,132 − 400,000,000)/400,000,000). Re-stated, the difference in the estimates (estimated by the procedure and the bidder) is marginal (2.64% or 0.07%). Notably, NT$390 million (estimated by the project ar-chitect/engineer) was the project budget announced in the tendering documents. Any bid price over that budget would be disqualified. The bidder regarded the project budget as tight. However, the bidder decided to sub-mit a bid price of $390 million (instead of the initially estimated $400 million) as the bidder perceived that a chance existed for reducing project construction costs by efficiently allocating resources (primarily laborers) and using certain material equivalents or substitutions to decrease equipment costs. Furthermore, this bidder, who used the project budget as a bid price, could still earn the project contract because he gained favorable re-sults for other bid criteria (i.e., technology, quality, func-tion, and commercial terms) evaluations for the project. Overall, the proposed procedure adds value for this case study because it improves the quality of the bid price decision-making process (in considering multi-criteria evaluations and cost uncertainties) while generating a recommended bid price close to submitted estimates (ei-ther NT$390 million or NT$400 million).
Fig. 5. Modeling results of the M/E project (case study I).
5 CASE STUDY II
To examine further the feasibility of the proposed procedure, this study applied the proposed procedure to another case project with characteristics that dif-fer from the first case. This project is related to the civil/structure/architect part of a high-tech construction project (called C/S/A project herein). The C/S/A project is located in southern Taiwan, and was constructed be-tween May 2003 and February 2004 (duration = 10 months). The project was tendered according to a low-bid method. Again, the proposed procedure was applied after the project bid price had been submitted. This app-lication came from a different contractor. The project budget was not made known in advance. A project man-ager involved in the project bidding process provided the inputs for the proposed procedure.
Following the above modeling steps, Figure 6 displays the evaluation results of this C/S/A project. Namely, after simulating the cost model 5,000 times, the minimum and maximum bid prices of this project are NT$118,866,465 and NT$131,123,626, respectively. In the multi-criteria evaluations, the expected utility values of Eu(t) and Eu(x) are 0.5979 and 0.7990, respectively. Moreover, Pave= 0.43 (namely, winning nine project contracts from
Fig. 6. Modeling results of the C/S/A project (case study II).
average winning probability was comparatively high, because this contractor generally did not compete for a project unless they were highly confident of win-ning the contract. For example, the bidder considered the location of this project (such as subcriterion r10 in Table 2) favorable owing to having a nearby project that was nearing completion and simply being able to reallo-cate existing resources (including laborers and equip-ment) to this C/S/A project, thus saving mobilization costs if awarded the project contract. Additionally, the bidder had considerable experience in similar projects (subcriterion r8 in Table 2). Most importantly, the bid-der had a good relationship with the owner of the project (subcriterion r12). The assessments of these subcriteria provided the bidder with an edge, and provided them with increased confidence relative to other potential competitors.
The probability, Px, can be estimated based on the following PONW utility function, and Px= 0.285.
Px
0.57=
(1− 0.7990)
(1− 0.5979) (9)
By mapping the value of Px (0.285) to the cumu-lative distribution of bid price (i.e., the right portion of Figure 6), the recommended bid price is around NT$123,597,917 with a winning probability of 0.715 (=1 − 0.285). Meanwhile, the bid price submitted by the bidder totaled NT$120,000,000. These two prices only differ by around 3% (=(123,597,917 − 120,000,000)/ $120,000,000). Thus, this C/S/A project achieves reliable application results.
6 RESEARCH SIGNIFICANCE AND FUTURE WORK 6.1 Research significance
As indicated earlier, this proposed procedure modi-fies the SIM-UTILITY procedure developed by Wang
(2004). Both procedures have a cost model and a multi-criteria evaluation model. However, the primary dif-ferences in the two procedures are as follows. First, the proposed procedure supports contractors in select-ing bid prices, whereas SIM-UTILITY assists clients in determining project cost thresholds. Second, the proposed procedure evaluates bid criteria, whereas the SIM-UTILITY addresses tendering criteria. The proposed procedure includes a markup in cost esti-mation, and SIM-UTILITY does not. Third, the pro-posed procedure applies fuzzy integrals, whereas the SIM-UTILITY uses utility theory for multi-criteria evaluations. Fourth, the Y-axis value in the pro-posed procedure represents the probability of not win-ning. Conversely, the Y-axis value in SIM-UTILITY is the likelihood of a bidder completing the project profitably.
Three key contributions of this proposed procedure are as follows:
r
Although the cost model and multi-criteria evalua-tion model are not original, integraevalua-tion of these two models is novel within bid decision research.r
The proposed procedure derives bid price decisions considering that project construction costs are uncer-tain, thereby fitting real-world practices more closely than existing bid models.r
The proposed procedure determines bid prices for meeting a practical decision-making process, whereas current bidding models focus on markups. In Taiwan, a considerable number of decision-makers typically look for methods of reducing construc-tion costs to attain an edge over other bidders. Eventually, such bidders submit low bids with-out sacrificing a percentage markup. Focusing on percentage markup is not central to winning a project contract. Namely, the bidders look at the to-tal bid price rather than markup when making bid decisions.6.2 Future work
During the course of this work, the following future re-search directions arose that may improve the proposed procedure.
r
To reduce the computational complexity in the simu-lation, a statistic-based cost model can be employed. Based on χ2 (chi-square) tests, the Lognormal andWeibuill distributions have the best goodness of fit to the bid price distributions for case studies I and II, respectively. A normal distribution fails theχ2 tests
in both case studies. Nevertheless, a normal distribu-tion deserves special consideradistribu-tion as it only requires estimating means and standard deviations.
r
Previous studies have indicated that correlations be-tween cost components affect construction project costs (Touran and Wiser, 1992; Wang, 2002b). The correlated effects on bid price should be considered to improve cost scheme modeling.r
The proposed procedure suggests a total bid price. However, the procedure does not indicate how direct and indirect costs should be adjusted to arrive at this suggested total bid price. Therefore, future research can explore strategies for cost adjustments.r
The multi-criteria evaluation model uses AHP algo-rithms to assess the weights of independent criteria and fuzzy integrals to examine mutually-dependent subcriteria. To simplify the modeling, the AHP algorithms can be applied throughout the crite-ria/subcriteria evaluations by assuming that the sub-criteria are also independent. Notably, the consistency measure for inputs of relative criteria and subcriteria importance requires further investigation.r
In the PONW utility function, the value of threshold point (Eu(t), 1− Pave) is devised to obtain theunique-ness of a specific bidder. Future research should up-date the values of Eu(t) and Pavewhen using the
pro-posed procedure for additional projects.
r
In the two cases studies, the difference between rec-ommended bid price and actual bid price is utilized to demonstrate the benefits of the proposed proce-dure in addressing real-world situations. The recom-mended bid price corresponds to a probability of win-ning (1− Px). Future research should extend the cur-rent procedure to derive a bid price that meets the goal of maximizing the probability of winning and ex-pected profit.7 CONCLUSION
To fit real-world situations closely, bid price decisions should be considered via a series of criteria evaluations
given that project construction costs are variable. Thus, this study presents a new bid price determination pro-cedure that comprises a simulation-based cost model to assess cost uncertainties and a multi-criteria evaluation model to evaluate numerous decision criteria.
The proposed procedure adds value for the two appli-cation projects as it improves the bid price decision qual-ity (in considering multi-criteria evaluations and cost un-certainties) while producing a recommended bid price close to the submitted estimate. However, the effect of the tendering method or the project type (e.g., M/E ver-sus C/S/A) on procedure performance warrants further investigation. For instance, is the proposed procedure more suited to a project tendered using the lowest-bid method (e.g., case study II) than one tendered with a multi-criteria evaluation bid-award method (e.g., case study I)? Furthermore, as indicated earlier, the two ap-plications of the proposed procedure were conducted af-ter bid prices were submitted. Future work should apply this procedure to other projects prior to bid submission.
ACKNOWLEDGMENTS
The authors would like to thank the reviewers for their careful evaluation and thoughtful comments. This re-search is supported in part by the Ministry of Education, Aim for the Top University (MOU-ATU) program in Taiwan. Additionally, Mr. W. C. Chen and C. S. Ni are appreciated for providing sample project data. Two grad-uate students at National Chiao Tung University—Mr. C. L. Lin and Mr. J. J. Liu, are also appreciated for assisting in applying the procedure to the example projects.
REFERENCES
Adeli, H. & Wu, M. (1998), Regularization neural network for construction cost estimation, Journal of Construction
Engi-neering and Management, ASCE, 124(1), 18–24.
Ahmad, I. & Minkarah, I. (1988), Questionnaire survey on bid-ding in construction, Journal of Management in Engineering,
4(3), 229–43.
Cagno, E., Caron, F. & Perego, A. (2001), Multi-criteria assess-ment of the probability of winning in the competitive bidding process, International Journal of Project Management, 19(6), 313–24.
Carr, R. I. (1983), Impact of number of bidding on competi-tion, Journal of Construction Engineering and Management,
109(1), 61–73.
Carr, R. I. (1987), Competitive bidding and opportunity costs, Journal of Construction Engineering and Management,
113(1), 151–65.
Chen, Y. W. & Tzeng, G. H. (2001), Using fuzzy integral for evaluating subjectively perceived travel costs in a traffic as-signment model, European Journal of Operational Research,
130, 653–64.
Chiou, H. K., Tzeng, G. H. & Cheng, D. C. (2005), Evaluat-ing sustainable fishEvaluat-ing development strategies usEvaluat-ing fuzzy
MCDM approach, The International Journal of Management
Science, 33, 223–34.
Chua, D. K. H. & Li, D. (2000), Key factors in bid reasoning models, Journal of Construction Engineering and
Manage-ment, 126(5), 349–57.
Chua, D. K. H., Li, D. Z. & Chan, W. T. (2001), Case-based reasoning approach in bid decision making, Journal
of Construction Engineering and Management, 27(1), 35–
45.
Clemen, R. T. (1996), Making Hard Decisions, 2nd edn. Duxbury Press, Pacific Grove.
Crowley, L. G. & Hancher, D. E. (1995), Evaluation of com-petitive bids, Journal of Construction Engineering and
Man-agement, 121(2), 238–45.
Dozzi, S. P., AbouRizk, A. M. & Schroeder, S. L. (1996), Utility-theory model for bid markup decisions, Journal of
Construc-tion Engineering and Management, 122(2), 119–24.
Dulaima, M. F. & Shan, H. G. (2002), The factors influencing bid markup decisions of large- and medium-size contractors in Singapore, Construction Management and Economics, 20, 601–10.
Fayek, A. (1998), Competitive bidding strategy model and soft-ware system for bid preparation, Journal of Construction
Engineering and Management, 124(1), 1–10.
Han, S. H. & Diekmann, J. E. (2001), Making a risk-based bid decision for oversees construction projects, Construction
Management and Economics, 19, 765–76.
Herbsman, Z. J. & Ellis, R. D. (1992), Multiparameter bid-ding system – innovation in contract administration, Journal
of Construction Engineering and Management, 118(1), 142–
50.
Ioannou, P. G. & Leu, S. S. (1993), Average-bid method — competitive bidding strategy, Journal of Construction
Engi-neering and Management, 119(1), 131–47.
Ishii, K. & Sugeno, M. (1985), A model of human evaluation process using fuzzy integral, International Journal of
Man-Machine Studies, 22(1), 19–38.
Kashiwagi, D. & Byfield, R. (2002a), State of Utah perfor-mance information procurement system tests, Journal of
Construction Engineering and Management, 128(4), 338–
47.
Kashiwagi, D. & Byfield, R. (2002b), Testing of minimization of subjectivity in best value procurement by using artificial intelligence systems in state of Utah procurement, Journal
of Construction Engineering and Management, 128(6), 496–
505.
Li, H. & Love, P. E. D. (1999), Combining rule-based expert systems and artificial neural networks for mark-up estima-tion, Construction Management and Economics, 17, 169– 76.
Lin, C. L. (2005), Determination of bid price considering project value, MS thesis, University of Chiao Tung Univer-sity, Hsin-Chu, Taiwan. (in Chinese)
Lin, C. T. & Chen, Y. T. (2004), Bid/no-bid decision-making – a fuzzy linguistic approach, International Journal of Project
Management, 22, 585–93.
Lo, W., Krizek, R. J. & Hadavi, A. (1999), Effects of high pre-qualification requirements, Construction Management and
Economics, 17(5), 603–12.
Martinez, J. C. (1996), Stroboscope: State and resource based simulation of construction processes, Ph.D. dissertation, University of Michigan, Ann Arbor, MI.
Marzouk, M. & Moselhi, O. (2003), A decision support tool for construction bidding, Construction Innovation, 3, 111–24. Moder, J. J., Philips, C. R. & Davis, E. W. (1983), Project
Man-agement with CPM, PERT and Precedence Diagramming,
3rd edn. Van Nostrand Reinhold, New York.
Moselhi, O., Hegazy, T. & Fazio, P. (1993), DBID: Analogy-based DSS for bidding in construction, Journal of
Construc-tion Engineering and Management, 119(3), 466–70.
Peurifoy, R. L. & Oberlender, G. D. (2002), Estimating
Con-struction Costs, 5th edn. McGraw Hill, New York.
Russell, J. S. & Skibniewski, M. J. (1988), Decision criteria in contractor prequalification, Journal of Management in
En-gineering, 4(2), 148–64.
Saaty, T. L. (1978), Exploring the interface between the hier-archies, multiple objectives and fuzzy sets, Fuzzy Sets and
Systems, 1, 57–68.
Skitmore, M., Drew, D. & Ngai, S. (2001), Bid-spread, Journal
of Construction Engineering and Management, 127(2), 149–
53.
Touran, A. & Wiser, E. P. (1992), Monte carlo technique with correlated random variables, Journal of Construction
Engi-neering and Management, 118(2), 258–72.
Wang, W. C. (2002a), SIM-UTILITY: Model for project ceil-ing price determination, Journal of Construction
Engineer-ing and Management, 128(1), 76–84.
Wang, W. C. (2002b), Simulation-facilitated model for assess-ing cost correlations, Journal of Computer-Aided Civil and
Infrastructure Engineering, 17, 368–80.
Wang, W. C. (2004), Supporting project cost threshold deci-sions via a mathematical cost model, International Journal
of Project Management, 22(2), 99–108.
Wang, W. C., Lin, C. L. & Lu, Y. H. (2005), Bid-price determi-nation considering cash-flow effects, in Proceedings of the
Tenth International Conference on Civil, Structural and En-vironmental Engineering Computing, Rome, Italy.
Wanous, M., Boussabaine, A. H. & Lewis, I. (2000), To bid or not to bid: A parametric solution, Construction Management
and Economics, 18, 457–66.
Wanous, M., Boussabaine, A. H. & Lewis, I. (2003), A neural network bid/no bid model: The case for contractors in Syria,
Construction Management and Economics, 21, 737–44.
Xu, T. & Tiong, R. (2001), Risk assessment on contractors’ pric-ing strategies, Construction Management and Economics, 19, 77–84.
