Using fuzzy decision making for supplier selection in public procurement

4 downloads 9464 Views 549KB Size Report
Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, e- ..... Obviously, different design choices for the fuzzification process by the ...... Salomon R., EU public procurement directive and utilities directive, DBDH Newsletter, n.4, ...
Using fuzzy decision making for supplier selection in public procurement Nicola Costantino1, Mariagrazia Dotoli2, Marco Falagario3, Maria Pia Fanti4 1

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, email: [email protected] 2

Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, e-mail: [email protected] 3

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Via Japigia 182, 70126 Bari, Italy, e-mail: [email protected], phone +39 080 5962754 fax +39 080 5963312 (corresponding author) 4

Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, e-mail: [email protected]

Abstract: We address the strategic issue of supplier selection in the public procurement sector. The aim of the paper is providing a decision making tool that mimics the intuitive behavior of the public tender committee in evaluating the (quantitative and qualitative) performance indices characterizing suppliers and yet results in a strict and transparent selection procedure, in accordance with governmental procurement regulations and requirements. After discussing the peculiarities and similarities of governmental purchasing with respect to the procurement of services and goods in the private sector, we formalize the process of supplier selection for public procurement. We apply to this decision problem a well-known fuzzy multiple criteria decision making approach, able to incorporate imprecise information in vendor selection while keeping the necessary transparency features requested in public procurement. We enlighten the characteristics of the presented technique by way of a case study involving an Italian public administration, showing the effectiveness and efficiency of the proposed method.

Keywords: Public procurement, supplier selection, decision analysis, multiple criteria evaluation, fuzzy decision making.

1

1. Introduction Nowadays organizations tend to focus on their core business and resort to outsourcing their nonessential functions. Consequently, the supplier or vendor selection process receives considerable attention in the business management literature (Chen et al. 2004, de Boer et al. 2001, Huang and Keshar 2007). A study carried on by Bruno et al. (2009) shows the interest of the Supplier Selection Problem in the literature: by analyzing several important journal the authors underline the increasing interest in such a problem. Indeed, incorrect decisions about supplier selection may lead to disruptions in the supply of product/services, and therefore to serious troubles in the organization operation (Piramuthu 2005). As a result, in the last decade many organizations have changed their focus from the classical purchasing concept to an effective tactical management of the procurement task, including identification of supplier selection criteria, supplier selection decisions and monitoring of supplier performance (Karpak et al. 2001). The vendor rating process is a critical step in the choice of the supplier, which is in turn perhaps the most important responsibility of the purchasing function for any organization. Vendor rating systems identify top suppliers, i.e., the candidate partners that are best equipped to meet the customer’s expected level of performance, and check them periodically (Baily et al. 2005). With the aim of achieving benefits already accomplished by private companies, in most countries the public sector has recently started using innovative methodologies for supplier selection and, more generally, for the procurement of services and goods (de Boer et al. 2001, Panayiotou et al. 2004). Recently, Erridge and Callender (2005) recognized, together with the necessary concern with

2

transparency and the need of formal tendering procedures, opportunities for innovation, more competitive supply and higher levels of service in the public procurement sector.

1.1. Vendor Rating in Private and Public Purchasing The vendor selection process is continuously developing and numerous approaches to this decision problem have been proposed in the related literature. Since 1966, when Dickson reported about 23 criteria for vendors’ evaluation (Dickson 1966), numerous steps have been made to innovate this important process. As early as 1968, Wind and Robinson (1968) proposed one of the first linear weighting models in which suppliers are rated based on several criteria and ratings are combined into a single score. Later on, advanced statistics methods have been proposed: Petroni and Braglia (2000) discuss the principal component analysis method, which is a multi-objective approach for vendor selection attempting to provide a decision support system for multiple sourcing. Subsequently, mathematical programming approaches have been extensively used for vendor selection. They include linear programming, mixed integer programming and goal programming (see Kumar et al. (2006) for a discussion on these techniques). Numerous additional innovative methodologies have been suggested. However, a thorough enumeration and discussion of the many techniques for vendor rating available in the related literature is not the aim of this paper: the interested reader is referred to de Boer et al. (2001) for a comprehensive discussion on this topic. This paper focuses on vendor rating in the public procurement area. Some common points may be found between procedures for supplier selection in the public and private sectors. In a review of 74 articles Weber et al. (1991) conclude 3

that by nature supplier selection is a multi-objective problem. Indeed, both for private and public organizations vendor selection is a multi-objective decision problem that includes conflicting objectives such as, besides the obvious goal of (low) price: quality, quantity, delivery, performance, capacity, communication, service, geographical location etc. (Araz et al. 2007, Degraeve et al. 2000, Morlacchi 1999). Recently proposed methods take into account other factors such as the assessment of risk, which may significantly influence a transaction (Costantino et al. 2006). Despite the similarities between private and public (or governmental) purchasing, the latter type of procurement exhibits some peculiarities (Panayiotou et al. 2004). In most countries, the public sector is covered by a number of public procurement regulations, bringing legislative requirements into force: for instance, in the European Union the 2004/18/EC Directive, also called the Public Procurement Directive, is effective (The European Parliament 2004). As a consequence, although governmental and private procurement share the same essential purpose of finding supply sources at the cheapest price and at acceptable quality, several dissimilarities arise between these two procurement systems. In particular, public procurement differs from the private one in the fact that prescribed procedures are to be followed and transparency is imperative (Panayiotou et al. 2004) for the so called public tender committee (usually a commission of experts, named by the public authority) that substitutes the buyer of a private contract. In other words, it is crucial that public procurement follows strict and clear business models that optimize the specific service objectives and considers the impact on processes across the considered governmental organization, avoiding subjective evaluations of vendors: all suppliers participating to the public procurement procedures are equal in principle and preference must be given by the public organization based 4

on the rigorous ranking obtained by the application of the said transparent business models. Usually, in both the public and private sectors the vendor rating decision problem is characterized by conflicting objectives and imprecise and qualitative information. From a conceptual point of view, Ellram (1990) underlines the importance of qualitative issues in the vendor selection process, particularly of financial concerns, organizational culture, strategic issues and technological capability concerns. Also Patton (1996), by sampling 1500 different buyers, points out the necessity of qualitative judgments in selecting the right vendor. Although the public sector has a long tradition of using the lowest bid as the only award criterion for contracts, recently, reliance on additional nonprice criteria is increasing (Waara et al. 2006) and public procurement regulations are being changed accordingly. For instance, the Public Procurement Directive (The European Parliament 2004) explicitly states that supplier selection may be performed according to, apart from price, qualitative factors such as technical merit, aesthetic and functional characteristics, environmental characteristics, etc. In this directive, the application of either of the following two award criteria is considered: the Lowest Price (LP) and the Most Economically Advantageous Tender (MEAT) criterion. Typically, the LP principle is significant in case the sole purpose is to save money. On the contrary, when the contract is awarded on the basis of the MEAT criterion, various criteria (concerning both quantitative and qualitative factors) are simultaneously considered to award the contract in question, depending on the object of the contract. Regardless of the chosen principles for supplier selection, in most governmental areas selecting one of the numerous alternative vendors bidding for a transaction may turn out to be a deeply complex task, since usually the dimension of the 5

vendor set is excessively large and such a decision process typically incorporates a variety of uncontrollable and unpredictable factors affecting decisions (Bevilacqua et al. 2006). Often the supplier selection process has to deal with imprecise and qualitative information, e.g., enhancement plans, quality and performance. The need in the public sector for vendor rating procedures able to deal with qualitative factors appears to be potentially in contrast with the necessity for transparency: in public procurement decisions have to be based on a strict and unambiguous ranking of the available bidding suppliers. Fuzzy multi-criteria optimization was proposed in the related literature to enhance traditional vendor rating and purchasing management techniques in the private procurement sector. In fact, fuzzy logic provides a natural framework to incorporate qualitative judgments with quantitative information. Some early contributions in this field are proposed by Albino et al. (1998), Li et al. (1997), Morlacchi (1999), Nassimbeni and Battain (2003). In particular, Morlacchi (1999) presents a first investigation on the advantages and limitations in the use of fuzzy logic for vendor evaluation and selection. Li et al. (1997) employ the fuzzy bag method to compensate for blindness in human judgment and combine scores for quantitative and qualitative criteria in an intuitive sum of weighted averages called the vendor performance index. Albino et al. (1998) propose a Sugeno fuzzy inference system for vendor rating taking into account three criteria, namely economic competitiveness, technical and management level as well as supply timeliness, and compare the obtained system with a neural network in order to evaluate the different performances. In the same direction, Nassimbeni and Battain (2003) develop a supplier selection tool based on fuzzy logic and refine it using a neural application, subsequently comparing the obtained tool with an ordinary least squares regression method, which reproduces a more traditional 6

method for supplier evaluation. More recently, Jain et al. (2004) and Ohdar and Ray (2004) propose to enhance fuzzy inference systems evaluating suppliers by adopting a genetic algorithm based methodology that lets the fuzzy rule base evolve in an optimal and automatic way depending on the problem at hand. Later contributions to the issue of supplier ranking for private procurement based on fuzzy logic are proposed in Amid et al. (2006), Bevilacqua et al. (2006), Chen et al. (2006), Noorul Haq and Kannan (2006), Costantino et al. (2006). Bevilacqua et al. (2006) apply the fuzzy quality function deployment decision method to a supplier selection problem regarding a manufacturing industry. Chen et al. (2006) extend the so called Technique for Order Preference by Similarity to Ideal Solution in a fuzzy logic framework for supplier evaluation and selection. Similarly, Noorul Haq and Kannan (2006) apply the Fuzzy Analytic Hierarchy Process (FAHP) to vendor evaluation and selection for the private procurement sector. A fuzzy logic based model for suppliers ranking and selection is proposed by Costantino et al. (2006), taking into account classical concepts such as the knowledge of the product price as well as more innovative notions such as the suppliers’ risk evaluation: the obtained vendor performance rating index is linear, so that the resulting technique is compensatory in nature. Amid et al. (2006) develop a fuzzy multi-objective linear model for vendor evaluation that is able to deal with multiple sourcing supplier selection. Finally, Kumar et al. (2006) propose a fuzzy multi-objective integer programming approach for vendor selection.

1.2 Contribution This paper focuses on supplier selection in public procurement based on multiple criteria (just like the MEAT award procedure included in the Public Procurement 7

Directive), disregarding the trivial case of the price-only award criterion. In the MEAT criterion, the most widespread decision making technique for ranking the pool of supplier candidates is the Linear Weighting (LW) technique (Dulmin and Minimmo 2004, Sonmez 2006). In this approach, the vendors set is ranked according to an overall performance index that is the weighted sum of the linear normalization of each performance index characterizing the considered suppliers. The LW methodology is effective, simple and rapid to apply. However, such a technique is structurally unable to model the intuitive behavior of the buyer that chooses the best bidding supplier according to his synthetic experience, as it usually happens in the private sector. In such a case, the buyer evaluates in a nonlinear fashion the selected performance indices characterizing the vendors. While the price index is typically linearly assessed, so that even a low difference in the offered prices is relevant for the evaluation, other factors such as for instance the reduction in the execution time are evaluated in a non linear way, e.g., only a definite difference in the offered execution time reductions is viewed as significant by the buyer. While in the private procurement area such a nonlinearity is usually embedded in the buyer holistic experience, in the public sector it has to be explicited in formal and transparent rules. To our knowledge, fuzzy multi-objective optimization (Bellmann and Zadeh 1970) has never before been applied for evaluating and ranking the available bids in governmental procurement. As a matter of fact, fuzzy decision making is particularly suitable for dealing with conflicting objectives and qualitative performance indices, while mimicking the intuitive behavior of the tender committee in assessing in a nonlinear fashion the considered objectives. Moreover, fuzzy optimization is based on unambiguous rules that address the need for strict and transparent procedures in vendor selection in the public 8

procurement sector, e.g., as nowadays prescribed by the European directives (The European Parliament 2004). The paper proposes the application to supplier selection in the public procurement area of a well-known decision making approach based on fuzzy logic, i.e. the FAHP methodology (Saaty 1990, Triantaphyllou and Lin 1996). The FAHP decision making technique is selected among the numerous available alternatives for the following reasons: i) it is a renowned optimization technique; ii) it is compatible with the widespread current European Union directives. In FAHP, the elements involved in the decision problem (overall goal, criteria, alternatives) are arranged in a hierarchical structure, with objectives that are of varying degrees of importance. The ranking is achieved by assigning to each available alternative a power indicative of its importance and then raising each fuzzy value to the appropriate power (Saaty 1990, Triantaphyllou and Lin 1996). The advantages in the use of this method for governmental purchasing are discussed analyzing a case study, namely the contract regarding the renovation of a building facility of Politecnico di Bari, Italy. The presented model for supplier selection in the public procurement sector is implemented in the MATLAB framework (The Mathworks 2004a, The Mathworks 2004b) and is a typical case of a multiple source singleitem vendor selection problem taking into account four performance indices: price, reduction in the execution time, free maintenance time and enhancement plans (proposed design changes). Thanks to the simplicity and effectiveness of the presented vendor evaluation and selection tool, we envision extending it into a decision support system, e.g., a web automatic tool that supports the public tender committee in the vendor evaluation and selection process, as well as the supplier in a simulated pre-evaluation of his own bid. The remainder of the paper is structured as follows. Section 2 defines the vendor 9

rating and selection problem for the public procurement sector and presents and discusses the fuzzy decision making model. Section 3 presents the case study and illustrates the application of the chosen technique. The Conclusions Section summarizes the paper objectives and results and proposes some future research perspectives. Finally, an up-to-date reference list concludes the paper.

2. Fuzzy Logic Based Vendor Rating for Public Procurement 2.1 The Input Data to the Supplier Selection Problem In the public procurement sector, governmental regulations typically impose that all the potential suppliers satisfying the requirements specified in the public tender call may bid; public agencies have thus to evaluate and rank all the different bids, according to the offered prices and/or to a prefixed set of parameters (price, delivery time, quality, etc.) in a transparent way and on the basis of strict procedures. Accordingly, in the public procurement sector a vendor selection decision problem can be defined through the set of bidding suppliers S={s1,s2,…,sm} and the given set of conflicting criteria C={c1,c2,…,cn} (defined beforehand by the tender committee). Hence, vendors in S have to be ranked based on several parameters connected to the supplier characteristics and the product/service features. Consequently, each supplier si∈S is associated the following n-tuple: (di1, di2,…,din), where dij represents the value of the performance index characterizing the i-th vendor with i=1,…,m with respect to the j-th criterion with j=1,…,n. For example, the first performance index di1 associated to the i-th supplier with i=1,…,m typically represents the price of the received bid. These performance indices are collected in a m×n decision matrix D,

10

where m is the number of available vendors and n is the number of criteria. Therefore, the generic element dij of D, with i=1,…,m and j=1,…,n, represents the j-th performance value of the i-th alternative supplier. The decision problem data are completed by the criteria importance, i.e., each criterion cj with j=1,…,n is n

associated a given weight wj, with ∑ w j = 1 , assigned by the public tender j =1

committee and specified in the call. Typically, in a vendor selection problem of the public procurement area using the MEAT approach, the n considered criteria include price and other indices such as reduction in the planned work execution time, free maintenance period post delivery, certified supplier quality, enhancement plans (proposed changes to the designed work and/or to the requested supply that can improve the purchasing results), etc. Accordingly, since the most important factor in a vendor selection problem is typically price, particularly in the case of public procurement, its corresponding weight is usually the highest one, while the others are equal or lower and correspond to less crucial criteria. For the sake of simplicity and to take into account the typical public procurement regulations, e.g., the European Public Procurement Directive, in the sequel we assume that the criteria and their weights are known and assigned by the public tender committee. However, it is noteworthy that soft computing methods and in particular fuzzy logic techniques may be straightforwardly employed to address the issue of obtaining in an automatic and objective way the criteria weights.

2.2 The Fuzzification Process The well-known fuzzy multi-objective technique Fuzzy Analytic Hierarchy Process (FAHP) (Saaty 1990, Triantaphyllou and Lin 1996) is proposed and 11

evaluated in this work for use in the decision problem of supplier selection for public procurement. FAHP requires as input data the sets S and C of suppliers and criteria, the mxn decision matrix D as well as the criteria weights wj with j=1,…,n. A fuzzification process associates to each element dij with i=1,…,m and j=1,…,n of D a fuzzy value d’ij, with 0≤d’ij≤1, defining the m×n fuzzified decision matrix D’ that models the committee satisfaction degree with respect to the bidding suppliers against each criterion. In particular, each j-th column of D’ for j=1,…,n is obtained by applying to the corresponding column of D a fuzzy membership function µj with j=1,…,n that mimics the tender committee evaluation of the j-th performance index. The choice of such functions that are n in number is subjective and has to be performed by the tender committee before the award. If necessary, the membership function selection may take place with the help of experts joining the committee to this purpose. The definition of the membership functions is a key point in the fuzzification process, because the only restriction that a membership function has to satisfy is that its values must be in the [0,1] range. A fuzzy set can therefore, unlike a crisp one, be represented by an infinite number of membership functions: a whole variety of possibilities exist, including triangular, trapezoidal or Gaussian membership functions, as well as sinusoidal, exponential shapes and so forth (The Mathworks 2004b). The fact that a fuzzy set can be described by an infinite number of membership functions is at the same time a weakness and a strong point: uniqueness is sacrificed at the advantage of flexibility, thus making the “adjustment” of a fuzzy model possible. From the point of view of using fuzzy decision making in public procurement, this subjectivity feature is an added value of fuzzy decision making, since it allows closely mimicking the intuitive tender committee behavior in the criteria evaluation. Note that in the related literature 12

numerous methods exist for determining the membership functions that are essentially based on direct methods of inquiry made on human beings and corrected using indirect methods, through which we try to eliminate the casual and the systematic deformations affecting the membership functions because of the low reliability of man as a measuring device (see Bouchon-Meunier et al. 1996 for a discussion on the topic). In the private procurement area, the most common choices for the membership functions shape are the piece-wise linear outline and other strongly nonlinear functions (typically sigmoidal), see Chen et al. 2006 and Ohdar and Ray 2004 for some examples. In particular, linear membership functions model the fact that all the variations in the considered performance criterion (even negligible ones) are equally significant and as such are taken into account by the tender committee in the vendor rating process, in a proportional way. While some criteria are linearly assessed, others often have to be evaluated in a non linear way, e.g., for some performance indices and for some values ranges, only a considerable difference in the offered bids is viewed as significant by the buyer. In the private procurement area such a non-linearity is usually embedded in the buyer holistic experience; on the contrary, in the public sector it has to be explicited in formal and transparent rules. Therefore, custom nonlinear membership functions can be used to model the intuitive tender committee behavior. We remark that, regardless of the choice of the membership function shape, some criteria values (e.g., prices) have to be minimized, whereas others have to be maximized (e.g., the values of free maintenance post delivery). Accordingly, the chosen membership functions are respectively monotonically decreasing and monotonically increasing. In addition, in particular cases some criteria (e.g., reduction in execution time) may be evaluated by way of a custom membership 13

function, exhibiting local maxima in a particular region of the offered bids range, to closely model the buyer evaluation that may take into account the trustworthiness of the offered bids. This is for instance the case of the reduction in the execution time criterion, for which too high offered values may be penalized by the tender committee, i.e., judged not credible. Obviously, different design choices for the fuzzification process by the experts modeling the tender committee evaluation may result in different solutions of the decision problem, e.g., involving different final choices. It is important to remark that a commission of experts may easily reveal what type of membership functions best fit the public tender committee evaluating preferences by simply interviewing its members, thus enhancing the efficiency of the evaluation process while preserving its transparency.

2.3. The FAHP Approach In the FAHP approach all the elements involved in the decision problem (overall goal, criteria and alternatives) are arranged in a hierarchical structure and objectives are of varying degrees of importance. The ranking is achieved by assigning to each available alternative (the generic supplier in the vendor rating case) a power indicative of its importance and then raising each fuzzy value to the appropriate power. Such powers are obtained by determining the eigenvector of the maximum eigenvalue of the so-called comparison matrix. The technique consists of the following steps (Triantaphyllou and Lin 1996).

Step 1. Structuring the decision problem as a hierarchy. Select the first level of the hierarchical structure as the overall goal “Supplier Efficiency”. Define the second level that is composed by the n considered criteria contributing to the goal. 14

Moreover, determine the third level as the m alternative supplier configurations to be ranked in terms of the criteria defined in the second level.

Step 2. Determining the fuzzified decision matrix. Determine the mxn fuzzified decision matrix D’ applying column by column the chosen membership functions to the decision matrix D.

Step 3. Constructing the pairwise comparison matrix CM. Compare the n criteria that define the second level of the hierarchical structure with each other and construct the n×n pairwise comparison matrix CM by Saaty’s original AHP scale in Table 1. More precisely, determine each element cmij of CM with i,j=1,…,n, representing the relative importance of the i-th criterion compared to the j-th one, by evaluating the difference 100|wi-wj| of the respective performance indices weights and associating it an integer value from 1 to 9 according to Table 1.

Step 4. Determining the eigenvector associated to the maximum eigenvalue of the comparison matrix. Calculate the eigenvalues set { λ 1, λ 2,…, λ R} of CM, where R is the matrix rank. Let λ max be the maximum eigenvalue of CM, then determine its eigenvector vmax. Compute the priority vector: P = vmax ⋅ n = [π1 ... πn ]T ,

(1)

where each element πj with j=1,…,n of P represents the importance degree of the j-th performance index associated to the j-th column of D’: the greater πj, the more important the j-th performance index.

15

Pairwise differences AHP Scale

0÷5

5 ÷ 15

1

2

15 ÷ 25 25 ÷ 35 35 ÷ 45 45 ÷ 55 55 ÷ 65 65 ÷ 75 75 ÷ 100 3

4

5

6

7

8

9

Table 1: Saaty’s original AHP scale.

Step 5. Raising alternatives to the criteria power. Determine the alternative values associated to each j-th performance index as follows: CRITj = [ d '1 j ... d 'mj ]

(2)

for each j=1,…,n. Determine the following vectors: Γj=[γ1j … γmj]= ( CRITj )

πj

π π ⎤ ⎡ = ⎢ d '1 j j ... d 'mj j ⎥ ⎣ ⎦

(

)

(

)

(3)

for each j=1,…,n.

Step 6. Determining the decision model. For each alternative or bidding supplier si∈S with i=1,…,m, determine: PIi _ FAHP = min ( γ i1,..., γ in )

(4)

so that PIi_FAHP provides information about the overall satisfaction of alternative si with respect to the performance indices and their importance degree.

Step 7. Ranking the alternatives. Rank the alternatives or bidding suppliers according to their overall performance index PIi_FAHP with i=1,…,m. Obviously, the best supplier is the one showing the highest index PIi_FAHP obtained by (4). Therefore, the ranked vector of alternatives is σ=[σ1 … σm]T, where σi for i=1,…,m is the generic i-th supplier and exhibits a performance index PIi_FAHP>PIi+1_ FAHP: thus, σ1 is the best supplier and σm is the worst vendor.

16

2.4 Discussion on the Presented Vendor Evaluation and Selection Technique Usually, in most public tenders adopting a MEAT approach the top-ranked vendor happens to be the one showing the highest overall index using the LW method. The main objective of this paper is to test an alternative approach (more detailed than the linear weighting one) able to support the tender public committee in its important choice while taking into account also qualitative factors, e.g., as prescribed by the European Union directives. The multiple criteria decision making approach previously described may be successfully employed to model and solve a vendor selection problem for public procurement. Note that several key differences may be remarked between the considered approach and the standard LW method, nowadays the most widespread vendor rating approach for MEAT awards. First, the LW technique is compensatory in essence, since it simply determines a crisp or non-fuzzy weighted sum of the normalized performance indices associated to each supplier. Hence, a good performance of an alternative with respect to a particular criterion may easily balance another second-rate performance index of the supplier, which in many cases is not realistic. On the contrary, the FAHP decision making approach is non-compensatory in nature, partly due to the considered nonlinear rules in the vendors evaluation (i.e. Steps 1 to 7) but mostly because of the nonlinear transformation or fuzzification of the alternatives performance indices by way of the membership functions, a process that tends to reward suppliers exhibiting the best performance indices with respect to all criteria and to penalize the worst ones, and that is – in our opinion – more fitting with the overall preferences and behavior of a tender committee in governmental purchasing.

17

Second, it is noteworthy that the considered fuzzy logic based technique is characterized by an algorithmic approach that is more complex than the LW technique. Nevertheless, the use of the FAHP decision making technique for vendor evaluation and selection is enabled by the exploitation of simple computational platforms, nowadays available to any outsourcing organization, so that this technique can be easily managed by any purchasing department in the public sector. Referring to the considered fuzzy multi-objective optimization technique, the following remarks are also worth mentioning. The FAHP technique relies on pairwise comparisons of the solutions, providing an approach to rank alternatives based on their reciprocal assessment. Therefore, FAHP may be preferred to other fuzzy decision making techniques because of its enhanced accuracy. However, setting up the pairwise comparison matrix may be a difficult task, especially when the decision problem dimension includes an excessively large number of criteria, and in such cases (actually not so common in usual public procurement) alternative fuzzy decision making techniques may be selected. Finally, note that the FAHP method, being based on the Saaty’s comparison scale, produces a stepwise ranking of the bidding suppliers. Although such a feature is advisable when a multiple sourcing approach is preferred, the presence of two (or more) equally ranked best suppliers can be a problem in public procurement (where, usually, only one supplier has to be chosen); nevertheless, this problem can be easily solved: equally ranked suppliers may be further classified based on a predefined rule, for instance on the basis of one criterion only, e.g., price.

18

Reduction in Free maintenance execution time post delivery

Enhancement plans

Vendor

Price

si

di1 [€]

di2 [weeks]

di3 [months]

di4

s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20 s21 s22 s23 s24 s25 s26 s27 s28 s29 s30 s31 s32 s33 s34 s35 s36 s37 s38 s39 s40 s41 s42 s43 s44 s45

110238.11 110963.63 109514.93 110484.45 110681.87 111092.92 112930.37 112783.38 131714.23 109920.87 110821.52 109775.89 108511.70 111457.61 111127.97 108990.13 115299.67 111242.01 112036.06 111461.96 111009.58 110504.87 110247.06 110438.76 112457.83 108469.71 110667.84 111660.57 110500.76 110918.29 115520.49 119535.68 110183.27 109839.68 110583.74 110186.17 125075.21 111151.44 109224.97 110556.28 110575.67 107967.74 111367.66 116276.03 118868.15

8.00 4.00 20.00 8.00 13.00 4.00 15.00 7.00 16.00 17.00 19.00 11.00 2.00 6.00 23.00 4.00 21.00 13.00 25.00 2.00 11.00 3.00 24.00 0.00 19.00 20.00 22.00 2.00 10.00 6.00 20.00 11.00 23.00 5.00 7.00 4.00 3.00 22.00 14.00 14.00 4.00 21.00 16.00 9.00 13.00

48.00 9.00 29.00 15.00 22.00 29.00 50.00 6.00 108.00 113.00 59.00 59.00 41.00 108.00 44.00 13.00 94.00 47.00 29.00 48.00 12.00 16.00 113.00 120.00 69.00 7.00 28.00 42.00 99.00 0.00 5.00 20.00 78.00 88.00 78.00 54.00 66.00 36.00 89.00 23.00 82.00 22.00 44.00 75.00 94.00

8.00 9.00 1.00 9.00 6.00 1.00 3.00 5.00 10.00 10.00 2.00 10.00 10.00 5.00 8.00 1.00 4.00 9.00 8.00 10.00 7.00 0.00 8.00 9.00 7.00 8.00 7.00 4.00 7.00 2.00 7.00 0.00 3.00 0.00 1.00 8.00 7.00 3.00 10.00 0.00 4.00 4.00 8.00 8.00 2.00

Table 2: Case study bids and corresponding decision matrix elements.

3. The Case Study The presented decision making approach for supplier selection in the public procurement area is applied to a case study. We consider the contract regarding 19

the renovation of a building facility of Politecnico of Bari, Italy.

3.1 The Public Tender Data The tender amount based auction is € 148500 plus VAT and the maximum acceptable work duration is 35 weeks. The number of bidding suppliers is m=45, each offering a bid evaluated by way of n=4 criteria, specified in the tender call. According to one of the options offered by the European legislation regulating public procurement under the MEAT award procedure, the following n=4 criteria are selected: 1) offered price c1 (with the corresponding performance value di1 measured in € for the i-th supplier and i=1,…,m); 2) offered reduction in the planned work execution time c2 (with di2 measured in weeks and i=1,…,m); 3) offered free maintenance period post delivery c3 (with di3 measured in months and i=1,…,m); 4) quality of enhancement plans c4 (with di4 and i=1,…,m evaluated by the tender committee in a 0-10 scale estimating the quality of changes proposed by the buyer to the designed work and/or to the requested supply that can improve it). We remark that three of the selected criteria (i.e., c1, c2 and c4) measure price and efficiency of the bids, while criterion c3 may be classified as belonging to the class of after sales services parameters. Some additional classes of parameters may be taken into account, e.g. technological solutions and environmental conditions (see Salomon (2004) for further examples on this topic); most of them can anyway be evaluated analogously to the enhancement plans criterion. In addition, note that the criteria according to which the contract is awarded are partly quantitative (as it is the case with c1, c2 and c3) and partly qualitative (as with criterion c4, since the tender award committee has to evaluate the actual enhancements to the supply/service that the proposed changes would produce). Evidently, taking into 20

account additional (qualitative) criteria, e.g., product standardization level, vendor dimension and reliability, other technical improvements etc., to personalize the vendor rating process is always possible with the proposed method. Hence, to each bidding supplier si∈S we associate the following four-tuple collecting the elements of the i-th row of the decision matrix: (di1,di2,di3,di4). We select the weight wj for criterion cj with j=1,…,4, respectively. To show the effectiveness of the technique, we evaluate two alternative rankings obtained in the following cases: case a) w1=0.55, w2=w3=w4=0.15; case b) w1=w2=w3=w4=0.25. In other words, case a) corresponds to the usual public procurement situation in which the offered price is the main performance index according to which the contract is awarded, while the other criteria are assigned minor importance. Case b) corresponds to the less frequent situation in which all criteria are equally significant. The different vendors and their bids are evaluated and ranked implementing the FAHP technique in the MATLAB framework (The Mathworks 2004a, Venkataraman 2001). The vendor bids for the case study are reported in Table 2. More precisely, the vendor labels si with i=1,..,m and their bids di1 are collected in the first two columns of Table 2. Note that prices range from bids of about 108 k€ to about 132 k€. In particular, according to the LP principle only, supplier s42, offering the lowest bid and highlighted in bold in the table, is the top-ranked supplier, while the worst one is s9, providing the highest price and also highlighted in bold. Moreover, the offered suppliers reductions in the planned work execution time di2 for i=1,…,m are collected in the third column of Table 2. We remark that 21

reductions in execution time range from 0 weeks (supplier s24, highlighted in bold in the table), to 25 weeks (s19, also highlighted in bold). In addition, the vendors offered maintenance times di3 for i=1,…,m are collected in the second last column of Table 2. These range from 0 months (s30, in bold), to 120 months (s24, in bold). Finally, the last column of Table 2 reports the enhancement plans performance indices, ranging from votes of 0 (s22, s32, s34, s40, in bold), to 10 (s9, s10, s12, s13, s20, s39, also in bold), as assigned by the committee to the free of charge enhancement plans to the requested service offered by the bidding vendors.

3.2 The Fuzzification Process After interviewing the commission members for the tender case study described in the sequel, we select for the fuzzification process the well-known piecewise linear and sigmoidal membership functions. In particular, for the price criterion we choose a linear membership function that models the fact that even negligible price variations are taken into account by the tender committee in the vendor rating process, in a proportional way. Accordingly, the generic element of the first column of the fuzzified decision matrix D’ is obtained as follows: d 'i1 =

d1max − di1 , for i=1,…m, d1max − d1min

with d1min = min

i =1,..., m

( di1 ) =107967.74 € and

(5) d1max = max

i =1,..., m

( di1 ) =131714.23 €,

respectively representing the minimum and maximum bids offered by the m suppliers (see Table 2). Note that (5) defines a monotonically decreasing linear membership function that rewards (penalizes) low (high) values, associating a performance index of 1 (0) to suppliers that exhibit a performance value equal to d jmin ( d jmax ). Bids in 22

between these two values are evaluated in a linear way. Figure 1 depicts the price membership function defined by (5). The chosen membership function of the second ranking criterion (i.e., the reduction in the execution time) is piece-wise linear and triangularly shaped, so that the generic element of the second column of the fuzzified decision matrix D’ is obtained as follows: ⎧ di 2 − d 2min ⎪ ⎪ d 2* − d 2min d 'i 2 = ⎨ ⎪ d 2max − di 2 ⎪d − d 2* ⎩ 2max

for di 2 ∈ [d 2min , d 2* ]

, for i=1,…m,

(6)

for di 2 ∈ [d 2* , d 2max ]

1

Degree of membership

0.8

0.6

0.4

0.2

0 1.1

1.15

1.2 Price [€]

1.25

1.3 5

x 10

Fig. 1 The price membership function.

1

Degree of membership

0.8

0.6

0.4

0.2

0 0

5

10 15 20 Reduction time in the execution [weeks]

25

Fig. 2 The reduction in the execution time membership function.

23

with

d 2min = min

i =1,..., m

( di 2 ) =0 weeks and

d2max = max

i =1,..., m

( di 2 ) =25 weeks,

respectively representing the minimum and maximum reduction times offered by the m suppliers (see Table 2). Moreover, we set d 2* =

d 2min + 3d 2max 4

=18.75

weeks, representing the most suitable value of reduction in the execution time according to the expert members of the commission. In other words, (6) defines a triangular membership function that rewards intermediate values of reduction in the execution times and penalizes suppliers that exhibit a performance value equal to d jmin (since too low indices are virtually useless) or d jmax (because too high values are judged unrealistic and therefore unreliable). Accordingly, while the index values belonging to the [d 2min , d 2* ] interval are evaluated in a monotonically increasing linear fashion, the remaining values are assessed in a decreasingly linear way. Figure 2 depicts the reduction time membership function defined by (6). The third criterion based on which the supplier ranking is performed is the free maintenance time, for which we select a sigmoidal and increasing membership function. In particular, the generic element of the third column of the fuzzified decision matrix D’ is obtained as follows: 0 ⎧ ⎪ ⎪ ⎛ d − d ⎞2 3* ⎪ 2 ⎜ i3 ⎟ − d d ⎪⎪ ⎝ 3** 3* ⎠ d 'i3 = ⎨ 2 ⎪ ⎛ d3** − di3 ⎞ − 1 2 ⎪ ⎜ ⎟ ⎪ ⎝ d3** − d3* ⎠ ⎪ 1 ⎪⎩

with

d3min = min

i =1,..., m

if di3 ∈ [d3min , d3* ] + d3max ⎤ d3 ⎡ if di3 ∈ ⎢ d3* , min ⎥ 2 ⎥⎦ ⎣⎢ + d3max ⎡ d3 ⎤ if di3 ∈ ⎢ min , d3** ⎥ 2 ⎢⎣ ⎥⎦ if di3 ∈ [d3** , d3max ]

( di3 ) =0 months and

, for i=1,…m,

d3max = max

i =1,..., m

(7)

( di3 ) =120 months,

respectively representing the minimum and maximum free maintenance times 24

offered by the m suppliers (see Table 2). Furthermore, d3* =

3d3min + d3max =30 4

months represents the minimum acceptable value in the free maintenance time according to the buyer. In addition, suppliers offering a free maintenance time equal to or higher than d3** =

d3min + 3d3max 4

=90 months are all ranked at the

same (top) level by the buyer. In other words, (7) defines a monotonically increasing sigmoidal membership function that penalizes (rewards) low (high) values of the free maintenance times, with index values in the [ d3* , d3** ] interval evaluated in a nonlinear fashion. This membership function models the fact that free maintenance is almost useless in the first months after the award (because the supplier has to assure anyway assistance in the guarantee time) and that in the long range increases in the free maintenance time are disregarded by the committee (since the usual need for refurbishment of the facility makes it useless to increase the free maintenance period over some years). Figure 3 depicts the free maintenance time membership function defined by (7). Similarly to (5), we determine the elements of the fourth column of the fuzzified decision matrix D’ by a monotonic linear membership function. However, enhancement plans are evaluated in a monotonically increasing linear fashion, since this performance index has to be maximized, as follows: d 'i 4 =

di 4 − d 4max d 4max − d 4min

with d 4min = min

i =1,..., m

, for i=1,…m,

( di 4 ) =0 and

(8)

d4max = max

i =1,..., m

( di 4 ) = 10 (see Table 2). Figure 4

depicts the enhancement plans membership function (8). Note that the abscissa represents the vote that the tender committee assigns to the free of charge number of variations proposed by the supplier to improve the product/service quality. 25

1

Degree of membership

0.8

0.6

0.4

0.2

0 0

20

40 60 80 Free maintenance time [months]

100

120

Fig. 3 The free maintenance time membership function.

1

Degree of membership

0.8

0.6

0.4

0.2

0 0

1

2

3

4 5 6 7 Enhancement plans score

8

9

10

Fig. 4 The enhancement plans membership function.

3.3 The Supplier Selection by FAHP Table 3 shows the results obtained applying the FAHP technique to the case study in case a) (second column of the table) and in case b) (last column), reporting the overall performance index of each supplier PIi_FAHP for i=1,…,m obtained under the considered methodology. The highest overall performance indices are highlighted in bold in both cases. Table 4 reports the corresponding ordered list of the top-ten vendors in the two cases. Note that, when an identical performance index value is obtained for two or more suppliers, these are classified according to the LP principle (e.g., this is the case of suppliers s36 and s41 in case a, respectively ranked ninth and tenth since s36 offers a lower price than s41). 26

Vendor si s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20 s21 s22 s23 s24 s25 s26 s27 s28 s29 s30 s31 s32 s33 s34 s35 s36 s37 s38 s39 s40 s41 s42 s43 s44 s45

PIi_FAHP Case a) 0.4243 0 0 0 0 0 0.4714 0 0 0.8069 0.4472 0.6835 0.2593 0.5657 0.3300 0 0.3973 0.4007 0 0.3266 0 0 0.400 0 0.5922 0 0 0.2828 0.7303 0 0 0 0.5477 0 0.3162 0.4619 0.0413 0.1414 0.8641 0 0.4619 0 0.3300 0.3408 0.2152

Case b) 0.1800 0 0 0 0 0 0.2222 0 0 0.9067 0.2000 0.4672 0.0672 0.3200 0.1089 0 0.4000 0.1606 0 0.1067 0 0 0.1600 0 0.7000 0 0 0.0800 0.5333 0 0 0 0.3000 0 0.1000 0.2133 0.1600 0.0200 0.7467 0 0.2133 0 0.1089 0.4800 0.200

Table 3: Vendor performance indices for the case study for cases a) and b).

Table 4 shows that in case a) the fuzzy decision making method chooses vendor s39 as the best solution. Indeed, this supplier is characterized by one of the lowest values of price; moreover, among the low price solutions, it exhibits intermediate values of the less important criterion reduction in execution time, and very high 27

performance in terms of the minor criteria free maintenance time and enhancement plans (see Table 2). As regards case b), FAHP selects s10 as the best solution. In fact, such a vendor exhibits satisfactory values of the first two performance indices and maximum values for the last two criteria (all criteria are now equally weighed due to the particular choice of the assigned weights), see Table 2. Note that s10, evaluated as best supplier in case b), is ranked second in case a) (since it exhibits a higher price than solution s39 that is ranked as the best in this case), while the top ranked vendor in case a) s39 is evaluated as second in case b) since its values of reduction time and free maintenance time, now more significant than in case a), are worse than those offered by the top supplier s10. It is interesting to remark that in both cases the worst suppliers are assigned a zero overall performance index (see the second and third columns of Table 3), corresponding to the cases in which at least one of the fuzzified performance index d’ij is null (e.g. vendor s2 is assigned an index PI1_FAHP=0 since it holds d23=9< d3* = 30 , s9 is associated PI2_FAHP=0 since it holds d91=131714.23=d1max, etc. see Table 2). Finally, note that supplier s42, offering the lowest price (see Table 2), is assigned a zero overall performance index, due to the too low free maintenance time offered by the vendor and the non-compensatory nature of the technique. Position 1 2 3 4 5 6 7 8 9 10

Case a) s39 s10 s29 s12 s25 s14 s33 s7 s36 s41

Case b) s10 s39 s25 s29 s44 s12 s17 s14 s33 s7

Table 4: Top-ranked bidding vendors for the case study for cases a) and b).

28

3.4 Discussion on the Application of the Technique to the Case Study The following remarks refer to the proposed fuzzy decision making technique and its application to the case study. First, using a different multiple criteria decision making technique than FAHP may result in a different solution of the problem. However, it is well known that fuzzy multi-criteria optimization is quite tolerant of the particular optimization technique chosen for ranking a given set of candidates according to conflicting criteria (Triantaphyllou and Lin 1996). Additional investigations (not reported for the sake of brevity) employing different fuzzy decision making methods confirm that the obtained results are rather tolerant of the specific optimization technique. Note that further studies may refine the vendor ranking, defining a restricted subset of suppliers to be further assessed, e.g., by additional performance indices such as capacity, communication, service, geographical location etc. (Degraeve et al. 2000). Second, the FAHP technique has a non-compensatory nature, particularly visible in case b), in which all criteria are assigned the same weights, (evidently, in case a) price weighs so much that the taken decisions are close to those obtained in a single-objective decision problem). This is in contrast with the classical LW method, characterized by a compensatory essence that tends to counterbalance satisfactory and substandard values of different performance indices, and witnesses the capacity of the fuzzy technique to provide a satisfactory proxy of the synthetic global evaluation of a skilled tender committee. Third, the use of the proposed fuzzy multi-objective technique is advisable when some of the considered conflicting criteria refer to qualitative performance indices that cannot be treated by the crisp LW technique. These may be related to the requested goods or services (as it is the case with the enhancement plans criterion, 29

considered in the presented case study), e.g., in the case of product standardization level, quality, strategic importance and availability, or to the supplier, such as for instance risk level, vendor dimension and reliability, proposed technical improvements, experience and geographical location (Costantino et al. 2006, Degraeve et al. 2000). Finally, the obtained results were analyzed together with the purchasing manager responsible for the considered tender. Such an examination showed that the FAHP supplier ranking fits with the synthetic, holistic manager preferences resulting from his personal experience.

4. Conclusions The paper contributes to the field of purchasing in the public sector focusing on vendor assessment and selection in single-item multiple sourcing exchanges. We address the need for supplier selection procedures in the public sector that are able to deal with qualitative factors, as prescribed by the recent European legislation, while maintaining the necessity for transparency typical of public practices. We propose to enhance traditional vendor evaluation and selection techniques in the public procurement sector by employing fuzzy multiple criteria optimization and in particular the well-known FAHP technique. The approach is tested by way of a case study involving an Italian public administration, illustrating its effectiveness for application to governmental purchasing. Future work may consider additional qualitative factors related either to the requested product/service or to the particular supplier, as well as the more complex case of multi- items exchange. Moreover, fuzzy inference systems may be employed to determine the weights characterizing the performance scores in an

30

automated way depending on supplier characteristics. An additional perspective on future research is to implement the proposed vendor evaluation and selection framework as a decision support system. To this aim, the authors are developing a web automatic tool that supports the buyer in the vendor evaluation and selection process and may be employed by the bidding suppliers to evaluate their own offers before the actual bid takes place.

5. References Albino V., Garavelli A.C., Gorgoglione M., Fuzzy logic in vendor rating: a comparison between a fuzzy logic system and a neural network, Fuzzy Economic Review, Vol. 3, pp. 25-48, 1998. Amid A., Ghodsypour S.H., O’Brien C., Fuzzy multiobjective linear model for supplier selection in a supply chain, International Journal of Production Economics, Vol. 104, pp. 394-407, 2006. Araz C., Ozkarahan I., Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure, International Journal of Production Economics, Vol. 106, pp. 585-606, 2007. Baily P., Farmer D., Jessop D., Jones D., Purchasing, Principles and Management, Prentice Hall, London, UK, 9th ed., 2005. Bellmann R., Zadeh L.A., Decision making in a fuzzy environment, Management Science, Vol. 17, no. 4, pp. 141–164, 1970. Bevilacqua M., Ciarapica F.E., Giacchetta G., A fuzzy-QFD approach to supplier selection, Journal of Purchasing and Supply Management, Vol. 12, pp. 14-27, 2006. Bouchon-Meunier B., Dotoli M., Maione B., On the choice of membership functions in a Mamdani-type fuzzy controller, Proceedings of the First Online Workshop on Soft Computing, 1996, Nagoya, Japan. Bruno G., Esposito E., Genovese A., Passaro R, A supplier selection model based on a multicriteria analysis, Proceedings of the IPSERA 2009 Conference, Wiesbaden, Germany, April 5 – 8, 2009. Chen C.-C., Yeh T.-M., Yang C.-C., Customer-focused rating system of supplier quality performance, Journal of Manufacturing Technology Management, Vol. 15, no. 7, pp. 599-606, 2004. Chen C.T., Lin C.T., Huang S.F., A fuzzy approach for supplier evaluation and selection in supply chain management, International Journal of Production Economics, Vol. 102, pp. 289-301, 2006. Costantino N., Dotoli M., Falagario M., Fanti M. P., A fuzzy model for vendor rating with risk assessment, Proceedings of the 2006 International Workshop on Logistics & Transportation, Hammamet, Tunisia, April 30 – May 2 2006, pp. 212-217. de Boer L., Labro E., Morlacchi P., A review of methods supporting supplier selection, European Journal of Purchasing & Supply Management, Vol. 7, pp. 75-89, 2001. Degraeve Z., Labro E., Roodhooft F., An evaluation of vendor selection models from a total cost of ownership perspective, European Journal of Operational Research, Vol. 125, pp. 34-58, 2000. Dickson G., An analysis of vendor selection systems and decisions, Journal of Purchasing, Vol. 2, pp. 28–41, 1966. Dulmin R., Mininno V., Linear weighting per la vendor evaluation: alcune osservazioni sul metodo, RCS- Economia & Management Rivista on Line, available online at http://economiaemanagement.corriere.it/dynuni/dyn/Universita/UniPISA-DulminMininno.jhtml, 2004 (in Italian). Ellram L.M., The supplier selection decision in strategic partnerships, Journal of Purchasing and Material Management, Vol. 26, pp. 8-14, 1990. Erridge A., Callender G, Introduction to the special issue on public procurement, Journal of Purchasing & Supply Management, Vol. 11, No. 5-6, pp. 209-211, 2005.

31

Huang S.H., Keshar H., Comprehensive and configurable metrics for supplier selection, International Journal of Production Economics, Vol. 105, no. 2, pp. 510-523, 2007. Jain V., Tiwari M.K., Chan F.T.S., Evaluation of the supplier performance using an evolutionary fuzzy-based approach, Journal of Manufacturing Technology Management, Vol. 15, no. 8, pp. 735-744, 2004. Karpak B., Kumcu E., Kasuganti R. R., Purchasing materials in the supply chain: managing a multi-objective task, European Journal of Purchasing and Supply Chain Management, Vol. 7, pp. 209-216, 2001. Kumar M., Vrat P., Shankar R., A fuzzy programming approach for vendor selection problem in a supply chain, International Journal of Production Economics, Vol. 101, pp. 273-285, 2006. Li C.C., Fun Y.P., Hung J.S., A new measure for supplier performance evaluation, IIE Transactions on Operations Engineering, Vol. 29, no. 9, pp. 753-758, 1997. Morlacchi P., Vendor evaluation and selection: the design process and a fuzzy-hierarchical model, Proceedings of the 8th International Annual IPSERA Conference, Belfast/Dublin, Ireland, 1999. Nassimbeni G., Battain F., Evaluation of supplier contribution to product development: fuzzy and neuro-fuzzy based approaches, International Journal of Production Research, Vol. 41, no. 13, pp. 2933-2956, 2003. Noorul Haq A., Kannan G., Fuzzy analytical hierarchy process for evaluating and selecting a vendor in a supply chain model, International Journal of Advanced Manufacturing Technology, Vol. 29, No. 7-8, pp. 826-835, 2006. Ohdar R., Ray P.K., Performance measurement and evaluation of suppliers in supply chain: an evolutionary fuzzy-based approach, Journal of Manufacturing Technology Management, Vol. 15, no. 8, pp. 723-734, 2004. Panayiotou N. A., Gayialis S. P., Tatsiopoulos I.P., An e-procurement system for governmental purchasing, International Journal of Production Economics, Vol. 90, pp. 79–102, 2004. Patton W.W., Use of human judgment models in industrial buyer’s vendor selection decisions, Journal of Industrial Market Management, Vol. 25, pp. 135-149, 1996. Petroni A., Braglia M., Vendor selection using principal component analysis, Journal of Supply Chain Management, Vol. 36, No. 2, pp. 63-69, 2000. Piramuthu S., Knowledge-based framework for automated dynamic supply chain configuration, European Journal of Operational Research, Vol. 165, pp. 219-230, 2005. Saaty T.L., How to make a decision: the analytic hierarchy process, European Journal Operational Research, Vol. 48, pp. 9-26, 1990. Salomon R., EU public procurement directive and utilities directive, DBDH Newsletter, n.4, 3 pages, 2004, available online at http://dbdh.dk/images/uploads/pdf-eudir/News-4-2004-art1.pdf. Sonmez M., A review and critique of supplier selection process and practices, Business School Occasional Papers Series, Paper 2006:1, Loughborough University, ISBN 1-85901-197-7, available online at http://www.lboro.ac.uk/departments/bs/research/2006-1.pdf, 2006. The European Parliament, 2004. Directive 2004/18/EC on the coordination of procedures for the award of public works contracts, public supply contracts and public service contracts, Official Journal of the European Union, L 134/114 - L 134/240, April 30th 2004. The MathWorks Inc., MATLAB User’s Guide Version 7, Natick, MA, 2004. The MathWorks Inc., Fuzzy Logic Toolbox for Use with MATLAB User’s Guide Version 2, Natick, MA, 2004. Triantaphyllou E., Lin C., Development and evaluation of five fuzzy multiattribute decisionmaking methods, International Journal of Approximate Reasoning, Vol. 14, pp. 281-310, 1996. Venkataraman P., Applied Optimization with MATLAB Programming, Wiley Interscience, 2001. Waara F., Bröchner J., Price and nonprice criteria for contractor selection, Journal of Construction Engineering and Management, Vol. 132, pp. 797-804, 2006. Weber C., Current J.R., Benton W.C., Vendor selection criteria and methods, European Journal of Operational Research, Vol. 50, pp. 2-18, 1991. Wind Y., Robinson, P.J., The determinants of vendor selection: the evaluation function approach, Journal of Purchasing and Materials Management, Vol. 4, No.8, pp.29-41, 1968.

32