A knowledge-based method for bid/no-bid decision-making in project management



Projects and project management are the wave of the future. The development of a comprehensive proposal for a large project should itself be treated as a project itself for a contractor whose business depends on creating winning proposals in response to business or government requests for proposals (RFP). Thus, it is important to develop a winning proposal in project management. However, the development and preparation of a proposal takes time and can be costly. Kerzner and Thamhain (1986) observed that most bidders are merely wasting time and money. Furthermore, submitting a lot of non-winning proposals in response to RFP can damage a contractor’s reputation (Gido & Clements, 1999). In addition, a project that is inconsistent with an organization’s long-term goals or current and near-term resources will limit the organization’s continued growth and success. For a contractor, success is winning the contract-not merely submitting a proposal. Therefore, the basis of a successful strategy is to filter out losing projects, and concentrate proposal efforts on projects that assist in their success by satisfying the objectives of the organization. With regard to preventing an organization from dissipating its energies in preparing a losing proposal, Rosenau (1998) even asserted that the bid/no-bid decision must be made within the context of the organization’s strategic framework.

A bid/no-bid decision is usually made on the basis of a set of criteria, such as nature, competition, value of the project, and resource capabilities, reputation of the company. Due to the unpredictability of the complexity of the competition as well as the ill-defined criteria existing in project assessment, and the human capability of understanding and analyzing obscure or imprecise events which are not easily incorporated into existing analytical methods, the experts’ judgments are the vital elements in evaluation of the bidding strategies. Thus, in most projects the bid/no-bid evaluation is dependent on subjective expertise in judgment based on a certain number of elements in the criteria.

In the past, there have been two approaches dedicated to the problem of effective bid/no-bid evaluation: (1) Gido and Clements (1999) proposed a method that use linguistics, such as high, medium, low to measure all criteria. But, theirs is an incomplete approach since it does not deal with how to translate and aggregate the linguistic measurement into a usable term for decision making. (2) On the basis of fuzzy sets theory, Eldukair (1990) proposed a fuzzy bidding decision method. In that method, it is assumed that the experts are capable of making an adequate scale of a given factor. However, in many cases it is virtually impractical for experts to directly determine the scale of a vague factor (Karwowski & Mital, 1986). Moreover, when a factor is ill defined, the experts simply adjudge that the score of a given factor is “low,” “high,” “fairly high.” It is natural to use linguistic expressions to estimate ill-defined factors. Furthermore, Eldukair’s method deals with only the bidding selection. In fact, in most situations, contractors must implement a bid/no-bid decision for only one project.

Fuzzy sets theory provides a useful tool for dealing with decisions in which the phenomena are imprecise and vague. Using fuzzy concepts, evaluators can use linguistic variables to assess the factors in a natural language expression; and the importance and effect of the factors can be approximated by their membership functions. Thus, fuzzy concepts are well suited for decision making with uncertainty. Furthermore, such concepts have been applied to the evaluation of multi-criteria decision problems (Chen, 1997; Kangari & Riggs, 1989; Tsourveloudis, 1998).

From this review a method for bid/no-bid decision using fuzzy sets is proposed. In this approach the importance of weights and the effect ratings of different criteria assigned by decision-makers are expressed in linguistic terms. Then appropriate fuzzy numbers are used to present the linguistic terms, and a simple fuzzy arithmetical operation is employed to aggregate these fuzzy numbers into one fuzzy number, which is called the fuzzy possible success rating. Finally, the fuzzy success rating is translated back into linguistics and the suggestion for a bid/no-bid decision is expressed in linguistic terms. This method, which not only efficiently and effectively handles vague environments and ill-defined data, can also easily be used by most real-world managers in a bid/no-bid decision. In addition, it is worth pointing out that the proposed method do not deny former approaches, but represent an upgrade in those segments which by it nature or complexity lead to inconsistency, vague and unfeasibility.

Exhibit 1. Fuzzy Numbers for Approximate Linguistic Rating Values

Fuzzy Numbers for Approximate Linguistic Rating Values

Basic Concept of Fuzzy Sets Theory

For the purpose of application, the basic properties of fuzzy sets theory needed in this study are introduced, and more discussion can be found in Kaufmann and Gupta (1991).

Fuzzy Numbers

Fuzzy sets theory was introduced by Zadeh (1965) to deal with problems in which the phenomena are imprecise and vague. Let X be a collection of objects, called the universe, whose elements are denoted by x. A fuzzy subset A in X is characterized by a membership function fA (X) which is associated with each element x in X, a real number in the interval 0,1. The function value fA (X) represents the grade of membership of x in A. The larger fA (X) is, the stronger the degree of belongingness for x in A.

A real fuzzy number A is a fuzzy subset of the real line R with membership function fA (X), which possesses the following properties:


where a, b, c, and d are real numbers. Unless elsewhere specified, it is assumed that A is convex, normal and bounded (i.e.,-∞ < a, d < ∞). For convenience, the fuzzy number in this definition can be denoted by (a, b, c, d). There are many forms of fuzzy numbers for representing imprecise information. As used here, triangular fuzzy numbers are applied.

Let x, a, b, c ∈ R (real line); hence a triangular fuzzy number is a fuzzy number A in R, if its membership function fA :R [0,1] is


The triangular fuzzy number is parameterized by the triplet A=(a, b, c). The parameter “b” gives the maximal grade of fA (x), i.e., fA(b)=1, which is the most probable value of the evaluation data. The parameters “a” and “c” are the lower and upper bounds of the available area for the evaluation data. For example, the triangular fuzzy number to represent “close to 5” can be parameterized by A=(2, 5, 7). This kind of fuzzy number is used because, under some weak assumptions, such use immediately complies with the relevant optimization criteria (Pedrycz, 1993). Furthermore, using triangular fuzzy numbers makes an evaluation intuitively easy for a decision-maker to perform (Liang & Wang, 1993; Lin & Wang, 1997).

Linguistic Variables

The concept of a linguistic variable is very useful in dealing with situations that are too complex or too ill defined to be reasonably described in conventional quantitative expressions. A linguistic variable is a variable whose values are words or sentences in natural or artificial language. For example, “ low” is a linguistic variable if its value is linguistic rather than numerical. Furthermore, by the approximate reasoning of fuzzy sets theory, the linguistic value can be represented by a fuzzy number. For example, for the linguistic variables (Worst, Very Poor, Poor, Fair, Good, Very Good, Best), the fuzzy numbers approximate to these linguistic rating values are represented in Exhibit 1. In this study the weight of importance and the rating of effect of each criteria are assessed by linguistic variables.

Fuzzy Number Arithmetical Operations

Let X, Y and Z be fuzzy sets, and let f be a mapping from X * Y to Z such that Z = f(x, y). Give the fuzzy numbers A and B in X and Y the membership functions fA and fB, respectively. The membership function of the fuzzy number C = f(A, B) is defined as:

Exhibit 2. The Bid/No-Bid Decision-Making Algorithm

The Bid/No-Bid Decision-Making Algorithm

By the extension principle, the fuzzy number arithmetical operations can be summarized as follows:

Let A = (a1, a2, a3) and B = (b1, b2, b3) be two triangular fuzzy numbers; then


The fuzzy number (Y, Q, Z; H1, T1, H2, U1 ) has its membership function expressed as:


Exhibit 3. Main Criteria for Bid/No-Bid Decisions

Main Criteria for Bid/No-Bid Decisions



It is obvious that (Y, Q, Z; H1, T1; H2, U1 ) is not a triangular fuzzy number. However, when fA and fB are in the neighborhood of 1, then A ⊗ B ≅ (a1b1, a2b2, a3b3).

Method and Algorithm

In this section, a method for bid/no-bid decision using fuzzy sets is proposed. This approach can take into account the decision-makers’ rating the effect of each factor and tradeoff importance among various evaluation criteria in the aggregation process to assure a more convincing and accurate decision-making. The first part is to evaluate and obtain a fuzzy success rating, and the second part is to translate it into an appropriate linguistic. The procedure is shown in Exhibit 2, and a stepwise description is given as follows:

1. Form a committee of decision-makers and select criteria for decision-making.

2. Determine the appropriate preference scale to assess the effect ratings and the importance weights of the selected criteria.

3. Evaluate the criteria rating and weight using linguistic terms.

4. Approximate the linguistic ratings and weights by fuzzy numbers.

5. Aggregate these fuzzy numbers to obtain a fuzzy possible success rating.

6. Translate the fuzzy success rating into an appropriate linguistic term.

Select Criteria for Decision-Making

A suitable project is typically characterized by a variety of features and traits. Moreover, a bid/no-bid decision depends not only on project characteristics but also company mission and project competition. Since the situations and requirements vary from project to project, there is a high probability that there is no single set of factors that reflects all situations and requirements.

By referring to the factors proposed in previous studies (Eldukair, 1999; Gido & Clements, 1999; Rosenau, 1998; Thamhain, 1988), the main criteria for bid/no-bid decision and subcriteria are listed in Exhibit 3. They are broadly categorized into six groups: resources, reputation, and mission of the company, probability of project go-ahead, and risk and competition of the project.

Preference Rating System

Since in many cases it is virtually impractical for experts to directly determine the score of a vague factor, in this paper linguistic terms are used to assess the effect rating and importance weight. Many linguistic terms have been proposed for linguistic assessment (Chen & Hwang, 1992). In general, it is suggested that one not exceed nine levels, which represent the limits of human discrimination. Thus, it is suggested that decision-makers choose a set R, R = {Worst (W), Very Poor (VP), Poor (P), Fair (F), Good (G), Very Good (VG), Best (B)}, to evaluate the effects of various factors on the success of the bidding. Meanwhile, the set W, W = {Very Low (VL), Low (L), Fairly Low (FL), Fairly High (FH), High (H), Very High (VH)}, is chosen to evaluate the relative importance of different criteria. According to the customer’s RFP and project-related information and on the basis of experts’ experience and knowledge, the experts can directly use the linguistic terms above to assess the rating that characterizes the degree of the effect of various factors. Furthermore, the weight that characterizes the degree of importance of various factors can be obtained by direct assignment or indirect pair comparisons.

Exhibit 4. Fuzzy Numbers for Approximate Linguistic Weighting Values

Fuzzy Numbers for Approximate Linguistic Weighting Values

After rating the factors and evaluating the weight, the linguistic values are approximated by fuzzy numbers. The fuzzy numbers for approximating the linguistic values in the rating set R are shown in Exhibit 1, and the fuzzy numbers for approximating the linguistic values in the weighting set W are shown in Exhibit 4.

Aggregate Criteria Effect Ratings and Importance Weightings and Calculate Fuzzy Possible Success Rating

It is important to aggregate the different decision-makers’ opinions at group decision-making. Many methods can be used to aggregate the decision-makers’ fuzzy assessments, such as mean, median, maximum, minimum, and mixed operators. Since the average operation is the most commonly used aggregation method, the mean operator is used here to pool the decision-makers’ opinions.

Suppose a committee of m evaluators (i.e., Et, t = 1, 2,…, m) conducts the bid/no-bid evaluation. Let Fj, j = 1,2, …, n be factors for bid/no-bid evaluation, Rtj = (atj, btj, ctj), the fuzzy numbers approximating the linguistic effect rating given to Ft by evaluator Et, and Wtj = (xtj, ytj, ztj) the fuzzy numbers approximating the linguistic importance weighting given to Ft by evaluator Et. Then the average effect rating Rj and the average importance weighting Wj are computed as:


where on the basis of the extension principle, Rj and Wj are also triangular fuzzy numbers.


Finally, the fuzzy possible success rating (FPSR) is computed as:

FPSR=(1/n)⊗ [(R1⊗W1)⊕(R2⊗W2)⊕…⊕(Rn⊗Wn)](4)

Exhibit 5. Effect Ratings of Criteria Assigned by Experts

Effect Ratings of Criteria Assigned by Experts

PR: Project Resources; ER: Execution Resources; PE: Past Experience; MP: Market Position; FLG: Fulfillment of Long-Range Goals; EC: Extension of Capabilities; PPGA: Probability of Project Go-Ahead; TR: Technical Risk; SR: Schedule Risk; CR: Cost Risk; PC: Preferred Contractors; SC: Special Competitors

Exhibit 6. Importance Weighting of Criteria Assessed by Experts Using Linguistic Terms

Importance Weighting of Criteria Assessed by Experts Using Linguistic Terms

By the extension principle, FSR is a fuzzy number with membership function as




Furthermore, the fuzzy number FPSR can be represented as FPSR = (Y, Q, Z; H1, T1; H2, U1).

Translate Back to Linguistics

Once the estimated project’s fuzzy possible success rating has been obtained, one can further approximate a linguistic label whose meaning is the same as (or closest to) the meaning of FPSR from the natural language expression set of possible success (PS). There are basically three techniques: (a) Euclidean distance, (b) successive approximation, and (c) piecewise decomposition. It is recommended that the Euclidean distance method be utilized because the other methods are difficult to implement (Kangari & Riggs, 1989).

The Euclidean method consists of calculating the Euclidean distance from the given fuzzy number to each of the fuzzy numbers representing the natural-language expressions set. Suppose the natural-language expression set PS = {Very Low, Low, Fairly Low, Fairly High, High, Very High}, then the distance between fuzzy number FPSR (known) and each fuzzy number member PSi (unknown) ∈ PS can be calculated as follows:

Exhibit 7. Importance Weighting of Criteria Approximated by Fuzzy Numbers

Importance Weighting of Criteria Approximated by Fuzzy Numbers

where p = {x0, x1 …, xm} ⊂ [0, 1] such that 0 = x0 < x1 < …< xm = 1. Let p = {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,1}. Then the distance from FSR to each of the members in the set SP can be calculated, and the closest natural expression with the minimum d can be identified.

An Illustrative Example

In this section a bid/no-bid decision is cited to demonstrate how the proposed method can be implemented numerically.

Suppose a committee comprised of three experts is formed to conduct the bid/no-bid decision. The first step that the committee has to do is to identify and classify the criteria for decision-making. Suppose the committee selects the criteria as shown in Exhibit 3 for evaluating.

The next step is to determine the appropriate preference rating scale to assess the effect rating and the importance weighting of the selected criteria. Before the assessment proceeds, the committee members will survey the client’s request for a proposal and project-related information or data.

After RFP and related information are surveyed, the evaluation committee applies the rating scale (i.e., Worst (W), Very Poor (VP), Poor (P), Fair (F), Good (G), Very Good (VG), Best (B)) to assess the evaluating criteria. Exhibit 5 shows the results of assessment under the 12 criteria given by evaluators E1, E2 and E3 respectively. At the same time, the committee members apply the weighting scale (i.e., Very Low (VL), Low (L), Fairly Low (FL), Fairly High (FH), High (H), Very High (VH)) to evaluate the relative importance of each evaluating criterion, based on their experience and knowledge. The results are shown in Exhibit 6.

On the basis of Exhibit 4, the linguistic terms of importance weighting shown in Exhibit 6 can be approximated by fuzzy numbers parameterized by quadruples as shown in Exhibit 7. Similarly, on the basis of Exhibit 1, the linguistic terms of effect ratings of 12 criteria assessed by each evaluator shown in Exhibit 5 can be approximated by fuzzy numbers parameterized by quadruples as shown in Exhibit 8.

By applying Eq. (2) and Eq. (3), the fuzzy numbers of the effect ratings shown in Exhibit 8 and the fuzzy numbers of the importance weights shown in Exhibit 7 can be aggregated under the same criteria. The results are shown in Exhibit 7 and Exhibit8 respectively.

Exhibit 8. Effect Ratings of Criteria Approximated by Fuzzy Numbers

Effect Ratings of Criteria Approximated by Fuzzy Numbers

Furthermore, by using the formula in Eq. (4), the fuzzy success rating for bidding this project is obtained as:

FPSR = (0.2674,0.5081,0.7273; 2.7236,0.0373; 6.1770,0.0193).

Finally, suppose the natural-language expression of possible success set, PS = {Very Low (VL), Low (L), Fairly Low (FL), Fairly High (FH), high (H), Very High (VH)}, is chosen for labeling. Furthermore, to simplify, suppose the membership functions shown in Exhibit 4 are chosen for matching. (One can choose other membership functions if necessary.) Then by using formula (5), the Euclidean distance D from FPSR to each member in set PS can be calculated:

D(FPSR, VL) = 1.6997, D(FPSR, L) =1.7271, D(FPSR, FL) = 0.9139,

D(FPSR, FH) = 0.9665, D(FPSR, H) = 1.7387, D(FPSR, VH) = 1.6997.

Then, by matching a linguistic label with the minimum D, the possible success of the bid for this project is fairly low.


The development and preparation of a proposal takes time and can be costly. Furthermore, submitting a lot of non-winning proposals in response to request for a proposals can damage a contractor’s reputation. To prevent dissipating an organization’s energies in preparing losing proposals, a bid/no-bid decision must be made within the context of the organization’s strategic framework.

Due to the ill-defined and ambiguous criteria that exist in project assessments, the conventional “crisp” evaluation approaches not can handle such assessments suitably and effectively. Thus, a method for bid/no-bid decision-making using fuzzy sets has been proposed. In this approach a natural framework for representation and manipulation in a situation under ill-defined and vague environments is constituted. The experts assess the vendors’ project using a set of linguistic terms. Then the term values are approximated by their membership functions; and by using fuzzy set operations, the values from different evaluation assessors can be aggregated under different criteria. Thus, these imprecise criteria for bid/no-bid decision are allowed to assume exact values. Even though six and seven levels of linguistic values are designated in the weighting and rating scales respectively, on the basis of the needs of cognitive perspectives and available data characteristics, the number of levels can be adjusted correspondingly. In general, it is suggested that one not exceed the human discrimination capacity consisting of nine levels. Furthermore, an example has been cited to illustrate the performance evaluation process of a vendor’s project. The results indicate the proposed approach is very useful in a bid/no-bid decision. This method, which not only efficiently and effectively handles bid/no-bid decision in project management, can also be easily used in most real-world managerial decisions in which there is uncertainty.

In addition to the previous example, this approach resolves some of the problems in traditional methods of evaluation and has several advantages when compared to numerical or strict qualitative methods.

1. The method is simple and intuitive in terms of evaluation and computation. It allows the analyst to evaluate the success and importance index directly using linguistic terms, and fuzzy numbers can easily approximate the linguistic terms.

2. The analyst can obtain a more reliable assessment, particularly in a situation with ill-defined, inaccurate as well as qualitative data in a management consultant evaluation.

Moreover, the algorithm of the proposed method can be computerized. Thus, by the decision-makers’ providing linguistic assessments through a menu-driven interface design, the decision-makers can make a bid or no-bid decision.


The author wishes to express appreciation to Dr. Cheryl Rutledge for her editorial assistance.

Chen, S.J., & Hwang, C.L. (1992). Fuzzy multiple attribute decision making methods and applications. New York: Springer-Verlag.

Chen, S.M. (1997). A new method for tool steel material selection under fuzzy environment. Fuzzy Sets and Systems 92, 265–274.

Gido, J. & Clements, J.P. (1999). Successful project management. Ohio: South-Western College Publishing.

Eldukair, Z.A. (1990). Fuzzy decisions in bidding strategies. Uncertainty Modeling and Analysis 1990 Proceeding. First International Symposium on IEEE: 591–594.

Kangari, R., & Riggs, L.S. (1989). Construction risk assessment by linguistic. IEEE Transactions on Engineering Management, 36 (2), 126–131.

Karwowski, W., & Mital, A. (1986). Applications of approximate reasoning in risk analysis. In Karwowski, W. & Mital, A. (Eds.), Applications of fuzzy set theory in human factors. Netherlands, Amsterdam.

Kaufmann, A., & Gupta, M.M. (1991). Introduction to fuzzy arithmetic theory and applications. New York: Van Nostrand.

Liang, G.S., & Wang, M.J. (1993). Fuzzy fault-tree analysis using failure possibility. Microelectron. Reliab, 33 (4), 583–597.

Lin, C.T., & Wang, M.J. (1997). Hybrid fault tree analysis using fuzzy sets. Reliability Engineering and System Safety 58, 205–213.

Pedrycz, W. (1994). Why triangular membership functions? Fuzzy Sets and System 64, 21–30.

Rosenau, M.D. (1998). Successful project management: A step-by-step approach with practical examples. New York: John Wiley & Sons.

Thamhain, H.J. (1998). Developing winning proposals. In Cleland, D.I. & King, W.R. (Eds.), Project Management Handbook. New York: Van Nostrand.

Tsourveloudis, N.C., & Phillis, Y.A. (1998). Fuzzy assessment of machine flexibility. IEEE Transactions on Engineering Management, 45 (1),78–87.

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Proceedings of PMI Research Conference 2000



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