A fuzzy strategic alliance selection framework for supply chain partnering under limited evaluation resources

Computers in Industry 55 (2004) 159–179

A fuzzy strategic alliance selection framework for supply chain partnering under limited evaluation resources Chun-Wei R. Lin*, Hong-Yi S. Chen Department of Industrial Management, National Yunlin University of Science and Technology, Touliu, Yunlin 640, Taiwan, ROC Received 1 July 2003; accepted 20 February 2004 Available online 22 July 2004

Abstract Joining a global supply chain (SC) is a critical strategy to stay competitive for today’s business. However, numerous decision attributes, either subjective or objective, need to be considered; and these evaluation processes are always complicated and costly. This paper presents a fuzzy decision-making framework for selecting the most favourable strategic SC alliance under limited evaluation resources. Firstly, a generic configuration hierarchy (GCH) is identified which comprises 183 evaluation attributes for general industrial SC partnering consideration. Secondly, to target the specific industry of interest, a customized configuration hierarchy (CCH) is extracted from GCH with basic belief acceptability values for all attributes assigned by experts. Thirdly, adding the evaluation resource constraints to CCH, a 0–1 non-linear programming model is formulated to determine the optimal configuration hierarchy. Fourthly, a fuzzy-rule based relationship intensity function jointly with a fuzzy relationship hierarchy is then constructed to derive and rank the final fuzzy favorabilities for all candidate SCs. Lastly, an illustrative example for a personal computer company that intends to partner with one of three SCs is developed to demonstrate the applicability of the proposed framework. # 2004 Elsevier B.V. All rights reserved. Keywords: Supply chain partnering; Fuzzy decision-making; Belief acceptability

1. Introduction Individual businesses no longer compete as autonomous entities but rather by joining a supply chain (SC) alliance due to the highly competitive business situation. Therefore, suppliers, manufacturers, logistic companies, and retailers in the SC always forge stronger alliances, vertically or horizontally, to compete against other SCs. There are three immediate benefits: securing critical technologies and knowl* Corresponding author. Tel.: þ886 5 5342601x5102. E-mail address: [email protected] (C.-W.R. Lin).

edge, expanding market entry and share, dispersing costs and risks [1]. For example, IBM, Intel, and Microsoft formed a strategic alliance to speed up their product development process. As a result, they spent only 15 months to enter the personal computer (PC) business, replacing Apple’s position in the market [2]. Thus, selecting an appropriate SC is a critical and strategic decision-making process. Evaluation attributes include both quantitative indices, such as annual productivity and financial stability [3], as well as qualitative indices, such as trademark reputation and communication openness [4,5]. Sometimes evaluation attributes also include both subjective indices,

0166-3615/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.compind.2004.02.003

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Nomenclature

U

a

xp

~ aj;s A

bg ~ li;t B

cpg

h i, j k Kli l L m() m (Klik) P r SAb, SAa ~ Sbli T ui U Ui

layer index of the generic configuration hierarchy (GCH) of the supply chain evaluation attributes the linguistic term for describing yaj. s ¼ 1, 2, . . .. It is a fuzzy set defined Uaj the universe of discourse for yaj total available amount of evaluation resource g a linguistic term for yli and t ¼ 1, 2, . . .. It is a fuzzy set defined on Uli, the universe of discourse for yli the unit consumption rate of evaluation resource g to acquire information of evaluation attribute xp index for the fuzzy rule indices for the qualitative evaluation attributes index of the subordinate attributes set and k ¼ 1, 2, . . ., Kli the total number of subordinate attributes sets of evaluation attribute yli layer index of configuration hierarchy, l ¼ 1,2, . . ., L total number of layers in the configuration hierarchy the basic probability assignment function of a given proposition the belief acceptability for Klik of the master attribute yli index of the quantitative evaluation attribute which is directly measurable index of the fuzzy rule candidate supply chain alliances b and a, respectively the set of subordinate fuzzy performance values of the master attribute, ~ yli, of and SAb and Sbli ¼ ð~vbyaj jyaj 2 Zli Þ t-norm operator an incidence of the linguistic variable Ui the linguistic variables whose universe of discourse is U the linguistic variable whose universe of discourse is Ui, i ¼ 1, 2, . . ., n

y00

yaj yli Zli

|| de

8 kk

the universe of discourse for the fuzzy rule base the quantitative evaluation attribute p which is directly measurable and always located in the bottom layer of the attribute configuration hierarchy the final aggregate evaluation attribute, i.e. the favourability, of the SC and whose value is a fuzzy number the qualitative evaluation attribute j in layer a the qualitative evaluation attribute l in layer l the set of selected attributed to measure the utility of yli, which is called customized configuration hierarchy (CCH) for yli absolute function the ceiling function that returns a value of one plus the integer portion of the variable the sup-t composition the number of elements in a set

Greek letters alik the adjusting factor of m (Llik) d(aj)(li) the binary attribute selection variable that if the qualitative evaluation attribute yaj belongs to the subordinate attributes set of yli, i.e. yaj is used to measure the belief acceptability of yli, then d(aj)(li) ¼ 1; otherwise, d(aj)(li) ¼0 dp dp ffi 1 if xp is selected. Otherwise, dp ¼ 0 dp(li) the binary attribute selection variable that if the quantitative evaluation attribute xp belongs to the subordinate attributes set of yli, i.e. xp is used to measure the belief acceptability of yli, then dp(li) ¼ 1; otherwise, dp(li) ¼ 0. F a general notation to represent the relationship intensity function Fli the relationship intensity function containing a set of fuzzy rules to define the relationship between yli and its subordinate attributes, yaj 2 Zli

C.-W.R. Lin, H.-Y.S. Chen / Computers in Industry 55 (2004) 159–179

F(L

1)i

e Zlik K K00k

Klik r

~ ðÞ mA i b ~v00 , ~va00 ~vbxp ~vbyaj ~vbyli z xaj xli xli

intensity function containing a set of fuzzy rules to define the relationship between y(L-1)I and its subordinate quantitative attributes, xp 2 Z(L-1)i a very small number an alternative notation of m (Klik), i.e. the belief acceptability of Klik a general notation to represent the subordinate attributes set the kth subordinate attributes set of the final aggregate evaluation attribute, i.e. the favourability, y00 of the SC the kth subordinate attributes set of its master attribute yli and Klik ¼ {yaj |a ¼ l þ 1, j ¼ 1, 2, . . .} ~r the membership function of fuzzy set A i the fuzzy favourability of the candidate SC, i.e. the final fuzzy SC performance, of SAb and SAa, respectively the fuzzy performance value of the quantitative attribute, xp, of SAb the fuzzy performance value of the subordinate attribute, yaj, of SAb the fuzzy performance value of the master attribute, yli, of SAb a general notation to represent the acceptability of an evaluation attribute the belief acceptability of the subordinate evaluation attribute yaj the belief acceptability of master evaluation attribute y^ the belief acceptability of attribute xp

such as business cultural coherence and shareholder’s favourability, and objective indices, such as corporate image and geographic coverage [6–11]. Most of all, acquiring information on evaluation attributes is always complicated and costly. In addition, as the evaluation attributes increase, the interdependency among the attributes will also increase. As a general rule, the amount of evaluation resource constraints, both in time and money, which are put on the decision process will always affect the decision quality/acceptability in selecting the most favourable SC to join. For a qualitative approach to modelling the SC partner selection problem, Lewis [12] suggested several

161

criteria to measure whether a particular strategic alliance is appropriate for a firm, e.g. value added to products, operations and technologies strengthening, and improvement in market access. Lorange et. al. [3] developed a two-stage SC selection approach: first evaluating the matching degree with candidate partners and then analyzing the market potential, main competitors, and the worst-case scenarios simulation after allying. Regarding the quantitative modelling approach, Harvey and Lusch [9] constructed a ranking approach to evaluate potential international strategic alliances based on the weighted attributes, e.g. macro environment and industry environment. However, in that approach, the weights were subjectively assigned by the decision-maker. Kaslingam and Lee [13] developed an integer programming model to select suppliers with minimum total supplying costs including purchasing and transportation costs. Ip et. al. [4] developed a non-linear programming model to solve the partner selection problem in large-scale engineering projects, considering both costs and due dates. However, they failed to simultaneously consider both qualitative and quantitative evaluation attributes. Hajidimitriou and Georgiou [14] employed the goal programming technique for the SC partner selection problem that is able to achieve multiple goals for different performances of the corresponding attributes. Due to the hierarchical characteristics among the SC evaluation attributes, the analytical hierarchy process technique (AHP) has been widely adopted to model the ranking procedure of the alliance selection problem. Babic and Plazibat [15] employed AHP to rank candidate firms, considering multiple business efficiency indices, such as profit margin and debt ration. Mikhailov [11] extended AHP to cope with the fuzziness that occurs when a decision-maker compares the relative importance among attributes. For this, the rating scale in the pair-wise comparison matrix is relaxed to the interval rating scale. However, this method ignores the effects resulted from interdependent attributes. To consider the effect of multiple interdependent attributes, Efstathiou and Rajkovic [16] suggested fuzzy if-then rules to derive the utility function of the decision-maker. On the contrary, their approach can not be applied to a complex problem, such as that represented by a hierarchical structure of decision attributes.

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Fig. 1. The fuzzy strategic SC alliance selection framework.

Coping with the drawbacks in the previous researches, this paper aims to meet the following essential practical requirements for the SC alliance selection problem: (1) the decision attributes should include both quantitative and qualitative attributes (2) the interdependency among attributes should be considered; and (3) the resources, e.g. time and money, available to obtain the information on the evaluation attributes are limited. This paper develops a fuzzy decision-making framework to select the most favourable strategic SC alliance under limited evaluation resources, as shown in Fig. 1. Firstly in Section 2, a GCH is identified, including 183 evaluation attributes, both quantitative and qualitative, under eight categories for general industrial SC partnering consideration. Secondly in Section 3, targeting the specific industry of interest, a CCH is extracted from the GCH with basic belief acceptability values for all attributes assigned by experts. Thirdly, adding the evaluation resource constraints to the CCH, a 0–1 non-linear programming model is formulated to determine the optimal configuration hierarchy (OCH)

which contains decision attributes with maximum total belief acceptability. Fourthly, a fuzzy-rule based relationship intensity function is developed to build up the relationships among these resultant evaluation attributes. A fuzzy relationship hierarchy (FRH) is then constructed to derive and rank the final fuzzy favorabilities for all corresponding candidate SCs. Finally, an illustrative example for a PC maker that intends to partner with one of three candidate PC SCs is developed to demonstrate the applicability of the proposed fuzzy strategic alliance selection framework. Detailed design comparisons between the proposed fuzzy decision-making framework and other counterpart approaches are also summarized in Tables 1 and 2.

2. Development of the hierarchical representation for evaluation attributes The objective of this section is first to identify the evaluation attributes that need to be considered in the

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Table 1 Proposed approach vs. various SC partners selection approaches based on the evaluation framework and attributes Approaches

Model types

Structures of attributes

Attributes selected by

Types of attributes

Kaslingam and Lee [13] Ip et al. [4] Hajidimitriou and Georgiou [14] Talluri et al. [5] Babic and Plazibat [22] Mikhailov [11] Proposed approach

Lpa NLPb GPc GP AHPd Fuzzy AHP Hierarchial fuzz rules

Flat Flat Three levels Three levels Flat Hierarchial Hierarchial

Author Author Author Author Author Descision-maker OCHe

Quantitative Quantitative Quantitative Quantitative & qualitative Quantitative Quantitative & qualitative Quantitative and qualitative

5: Analytical network process. a Linear programming. b Non-linear programming. c Goal programming. d Analytical hierarchical process. e Optimal configuration hierarchy approach.

Table 2 Proposed approach vs. various SC partners selection approaches based on the candidate ranking mechanism Approaches Kaslingam and Lee [13] Ip et al. [4] Hajidimitriou and Georgiou [14] Talluri et al. [5] Babic and Plazibat [22] Mikhailov [11] Proposed approach

Attributes aggregation LAa mAb LA

Assignment of weights Coefficientd Coefficient By user

Interdependent attributes – – –

Verify ranking consistency – – –

Ranking quality of attributes – – –

LA LA LA FRHc

By user MCe Fuzzyf Fuzzy favourability

– – – Multiple

– CMg – CCRh

– – – Belief acceptability

a

Linear aggregation. Multiple aggregation. c Fuzzy relationship hierarchy. d As coefficient in the objective function. e Multiple paired comparison method in AHP. f Fuzzy preference programming method. g The eigenvalue of the comparison matrix. h Indices for completeness, consistency, and redundancy of fuzzy if-then rules. b

strategic SC alliance selection problem, based on the literature survey and practical suggestions of the authors. Secondly, based on the attributes identified, a GCH representation is developed for the general industry. Thirdly, a set of customized evaluation attributes related only to the industry of interest is extracted from the GCH by experts or decisionmakers. Since variations exist for assuring the exactness of the information of the decision attributes, a basic acceptability index, x, is assigned to every

evaluation attribute by the experts/decision-makers. A CCH containing selected evaluation attributes with assigned basic acceptabilities is then created to later formulate the optimal evaluation attributes model. 2.1. Compilation of evaluation attributes The prudent selection of evaluation attributes plays a critical role in the SC selection problem. An individual industry will use its own industrial-domain

164

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related decision attributes and very often it will have different emphases, even on the same attributes under a dynamically changing business environment. Inappropriate attributes not only waste valuable evaluation resources, e.g. time and money, but also may mislead the final decision on selecting the most favourable SC with which to partner. Most of all, as the number of evaluation attributes increases, the chance of having interdependency also tends to increase. An efficient fuzzy rule-based system is devised to solve this problem and a detailed discussion is in Section 3. From the literature review and the findings of this paper, 183 decision attributes are identified for general industries. They are categorized into eight different aspects while evaluating the favourability of candidate SC alliances: (1) finance [6,7,9–11,17] (2) human resource management [9,10,14,17] (3) industrial characteristics [7,9] (4) knowledge/technology acquiring and management [3,6–9,14,17] (5) marketing [6,9–11,14,17] (6) organizational competitiveness [7,9,10,17] (7) product development, production, and logistics management [6–9,14,17,18] and (8) relationship building and coordination [3,4,6–10,14,17,18]. Over 50% of the evaluation attributes are focused on two categories: ‘‘relationship building and coordination’’ and ‘‘product development, production, and logistics management’’, as shown in Table 3. 2.2. Construction of the generic configuration hierarchy The construction of a GCH to represent the relationships among evaluation attributes is a foundation for the SC selection problem. It is a common approach for solving the complex multiple-attribute decision-making problem by decomposing the problem into a hierarchical structure. The GCH compiles as many evaluation attributes as possible to describe the general characteristics for all industries. This paper first defines a fuzzy favourability index, ~v, as the resultant, i.e. the most aggregate, attribute to represent the final preference of the decision-maker to the candidate SCs. In the next lower layer down, the fuzzy favourability is then broken into several subordinate attributes sets, L, to represent its detailed evaluation attributes. This ‘‘hierarchy’’ construction procedure is repeated until all subordinate attributes sets in the same layer are directly measurable or

Table 3 Evaluation attributes for the strategic supply chain alliance selection problem Finance Ability to finance initial sales and subsequent growth [17] Ability to provide adequate promotion and advertising fnds [17] Ability to raise additional funding [17] Asset efficiency [10] Capital/assess to additional capital or debt [9] Corporate image [10] Financial assets [7] Financial conditions (assets and liabilities) [6] Financial stability [11] General reputation [9] Intangible assets [7] Leverage [10] Liquidity [10] Organization reputation [10] Profitability [10] Reputation among current and past customers [17] Human resource management Corporate culture [9] Entrepreneurial/creativity [9] Human resource management skill [10] Learning ability [10] Organizational leadership [10] Product and market expertise [17] Quality of local personnel [14] Quality of management team [17] Industrial characteristic Bargaining power of buyers [9] Bargaining power of suppliers [9] Industry attractiveness [7] Influence on industry [9] Relative power of organization [9] Rivalry among existing firms [9] Threat of substitute products [9] Knowledge/technology acquiring and management Ability to formulate and implement 2 to 3 year marketing plans [17] Ability to maintain inventory [17] Acquire partner’s local knowledge (local economic, local political, local cultural environments) [3] Capability for incremental improvements [6] Cost of alternatives [7] Experience with target customers [17] Familiarity with the product [17] Importance of technical advice [8] Knowledge of local business practices [14] Knowledge of US Business [17] Managerial capabilities [7] Managerial know-how [9] Marketing expertise/knowledge [9] Market knowledge access [7]

C.-W.R. Lin, H.-Y.S. Chen / Computers in Industry 55 (2004) 159–179 Table 3 (Continued ) Partner’s ability to acquire your firm’ special skills [7] Patent security [17] Proficiency in English [17] Quality of support personnel [8] Special skills that you can learn from your partner [7] Strrategic orientation [14] Technical capabilities [7] Technical capability [6] Technological level [14] Technology (existing base) [9] Technology expertise [9] The importance of new technology [8] Track record with past suppliers [17] Willingness to share expertise [7,14] Working experience with other exporters Marketing Better export opportunities [14] Brand/corporate loyalty [9] Changes in demand locations Customer base [9] Customer demand Change Customer loyalty [10] Market position [10] Market share [17] Marketing competence [10] Price [11] Product brand [10] Rapid market entry [14] Sales force [17] Supplier representative’s competence [6] Trademark/brands/logos [9] Variation in demand quantity Variation in price Variation in types of products or services Organizational competitiveness Complementarity of capabilities [7] Complementarity of product lines [17] Corporate market position [9] Functional competencies [9] Strategic orientation [10] Strategic position in the marketplace [9] Unique competencies [7] Product development, Production, and logistics management Ability and responsiveness of a supplier to customers’ needs [8] Ability to change production volumes rapidly [6] Ability to set up for new products at short notice [6] Accuracy of transactions [8] After-sales service [8] After-sales support [6] Average defect rate Average inventory level in the distributors Average inventory level in the producers Average WIP level Capabilities to provide quality product/service [7]

Table 3 (Continued ) Condition of physical facilities [17] Consistency in meeting of delivery deadlines [6] Consistent conformance to specifications [6] Cost-reduction capability [6] Credit facilities [8] Delivery capacity Delivery performance of a supplier [8] Delivery reliability [8] Design capability [6] Distributing network performance Distribution network quality [14] Flexibility in meeting customer needs [8] Flexible discount [8] Geographic coverage [17] Geographical location [6] Location of joint venture facilities [14] Manufacturing network performance Offer of the lowest of price [6] On time delivery [17,18] Order fulfil rate Order lead time of manufacturing Percentage business accounted by a single supplier [17] Price/cost [18] Product appearance [6] Product quality [18] Product reliability [6] Production and logistics management Production capabilities [9] Production locations [9] Professionalism of salesperson [18] Prompt response to requests [6] Quality and sophistication of product lines [17] Quality of product information [8] Quality philosophy [6] Quality stability [11] Responsiveness to create a service element [8] Responsiveness to customer needs [18] Service [8] Service level Short delivery lead time [6] Supplier performance [18] Supply network performance Time from order to delivery [8] Transportation cost Volatility of product mix [17] Relationship building and coordination Alliance experience [9] Available information of the supplier [8] Board-of-directors impact/influence [9] Closeness of past relationship [6] Commitment to achieving minimum sales targets [17] Communication openness [6] Company’s reputation to integrity [6] Compatible management styles [14] Compatible organization cultures [14]

165

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Table 3 (Continued ) Compatible strategic objectives [14] Connections with influential people [17] Cost to integration [4] Data/information [9] Distribution relationships [9] Financial institution relationship [9] Foreign experience [10] Government relationships [9] Industrial experience [10] Likelihood of long-term relationship [6] Market information [8] Member in trade associations [17] Participation in trade fairs [17] Performance awards received by the supplier [6] Relationship building Relative power/size to potential partner [9] Risk of failure of the project [4] Supplier relationships [9] The stability of the joint venture [3] Time needed to integration [4] Undivided attention to product [17] Willing to commit advertising dollars [17] Willing to invest in sales training [17] Willing to keep sufficient inventory [17] Willingness to resolve conflict [6] Willingness to reveal financial records [6] Wining to drop competing product lines [17]

quantifiable. This can be seen in Fig. 2, which shows an illustrative example of a GCH. Let yli represent the evaluation attribute i in the lth layer of the GCH, where l ¼ 1, 2, . . ., L and L is the total number of

layers in the GCH. Let Klik ¼ {yaj |a ¼ l þ 1, j ¼ 1, 2, . . . represent the kth subordinate attribute sets of attribute yli where k ¼ 1, 2, . . ., Kli and Kli is the total number of subordinate attributes set of attribute yli. The detailed procedures to construct the GCH of the SC evaluation attributes are as follows: Step 1. Let y00 represent the final aggregate evaluation attribute, i.e. the fuzzy favourability of the SC. Then 8k; k ¼ 1; 2; . . . ; K00 , develop L00k ¼ {y1j: j ¼ 1, 2, . . .} as the subordinate attributes set of y00. Let l ¼ 0. Step 2. Let a ¼ l þ 1, 8j and 8k, k ¼ 1, 2, . . ., kaj, develop Lajk ¼ {yaj|j ¼ 1, 2, . . .} as the subordinate attributes set of yaj. Step 3. If 8j, yaj is directly measurable/quantifiable, go to next step; otherwise let l ¼ l þ 1 and go to Step 2. Step 4. Let L ¼ l. xp ¼ yLj, p ¼ 1, 2, . . ., nL. nL is the total number of quantitative attributes in the bottom layer L of the GCH. Stop. There are two advantages of the GCH: adaptability and flexibility. For adaptability, considering the interests/characteristics of each individual industry, the GCH can be tailored and adapted to meet with special needs under timing and budgetary constraints. Furthermore, while the information of an qualitative

Fig. 2. Generic configuration hierarchy (GCH).

C.-W.R. Lin, H.-Y.S. Chen / Computers in Industry 55 (2004) 159–179

attribute is not completely certain, an attribute belief acceptability index, z is developed to represent the bias of the decision-maker. The detailed description of this adaptability advantage is depicted in Section 2.3. For flexibility, this paper relaxes the attributes dependency, which is a common phenomenon in the past multi-attribute decision-making problems. For a target attribute in the current layer, the decision-maker can form any meaningful combinations out of the attributes in the lower layer and generate the subordinate attributes sets for the target evaluation attributes. The relationship between the target attribute and attributes sets are bounded by the relationship intensity function, F. For example, as shown in Fig. 2, the final aggregate evaluation attribute, i.e. the favourability of the SC, y00, includes two subordinate attribute sets, K001 ¼ {y11, y12, y13} and K002 ¼ {y13, y14}, which have the same subordinate attribute, y13. Detailed discussions of the flexibility advantage of the GCH are provided in Section 3. 2.3. Construction of the customized configuration hierarchy Based on an individual industry’s business characteristics and the judgment bias caused by incomplete information used by the decision-maker, a CCH of the evaluation attributes is extracted from the GCH with assigned belief acceptabilities. An illustrative example of a CCH is shown in Fig. 3, and Zli ¼ [kKlik ¼ {yaj|yaj 2 Llik, a ¼ l þ 1,8k} represents the subordinate attributes set in the lower layer of the master evaluation attribute, yli. The evaluation attributes in the SC selection problem inherit two important practical

characteristics: uncertainty and ignorance. The former exists when the available information for decisionmaking is incomplete, imprecise, or unreliable. The latter results from lack of information while making decisions [19]. For instance, if the decision-maker is either not completely certain or it is too costly to obtain exact information about the distribution network performance of the candidate SC, a belief acceptability is then assigned by the decision-maker to represent his/her confidence in the information/ value of this evaluation attribute. The belief acceptability of an attribute in this paper is equal to the lower bound of the belief interval [20]. The value of the belief acceptability of an attribute is calculated from the summation of the adjusted basic acceptabilities of its all subordinate attributes sets, as follows: X

xli ¼

alik  mðKlik Þ

and

Kli X

mðKlik Þ ¼ 1

k¼1

Klik jZli Klik

(1) where xli is the belief acceptability of the master evaluation attribute, yli;alik the adjusting factor for the basic acceptability of Klik; Kli the total number of subordinate attributes sets of qualitative evaluation attribute, yli, Zli the customized set of all subordinate attributes of the master attribute, yli, Klik the kth subordinate attributes set of its master attribute, yli; m(Klik) is the basic acceptability of Klik, where m () is the basic probability assignment function The purpose of the adjusting factor is to equally normalize the contribution of the belief acceptabilities from all subordinate attributes in Klik of the master attribute, yli. The adjusting factor is defined as: alik ¼

X yaj 2Klik

Fig. 3. Customized configuration hierarchy (CCH).

167

X 1 1  xp þ  xlik jjKlik jj jjKlik jj y 2K p

(2)

lik

where yaj is the qualitative subordinate evaluation attribute j in layer a and yaj 2 Klik; xaj the belief acceptability of yaj; xp the quantitative subordinate evaluation attribute p that is directly measurable and always located in the bottom layer of the attribute configuration hierarchy, xp 2 Klik; xp the belief acceptability of xp; 1/||lik|| the normalized weight of attributes in Klik and Klik represents the total number of attributes in Klik

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Since xp is used to directly measure the performance of a candidate alliance, it is reasonable to assume that xp ¼ 1, 8p. Eq. (2) then can be rewritten as: X 1  xaj alik ¼ jjKlik jj yaj 2Klik 0 1 X 1 A (3) þ @1 jjKlik jj y 2K aj

lik

For the special case where Zli contains only quantitative, i.e. directly measurable, attributes, then all the adjusting factors are equal to one. Eq. (1) can be reduced to: X xli ¼ mðKlik Þ (4) Klik jZli Klik

The procedures to calculate the resultant belief acceptability of the CCH can be summarized as follows: Step 1. Let l ¼ L 1, where L is the total number of layers of the CCH. 8i, calculate the belief acceptability, xli, of yli.

of candidate alliances on various performance attributes. However, before deciding the most favourable SC to partner with, it is the decision-maker’s responsibility to ensure that the information acquired is as complete as possible, and certainly within the timing and budgetary constraints. The objective of this section is to determine the final evaluation attributes possessing the maximum total belief acceptabilities. A 0–1 non-linear programming model is developed to generate the OCH of evaluation attributes under limited evaluation resources. A fuzzy rule-based evaluation procedure based on the OCH will then be adopted to determine the resultant favorabilities of all candidate SCs. A detailed discussion of this fuzzy evaluation procedures is provided in Section 4. The optimal belief acceptability model and constraints for the evaluation attributes are introduced as follows: maxðZ ¼ the total belief acceptabilities of

¼

Step 2. Let l ¼ l 1. 8i, compute xli for yli according to the following situations:

attributes extracted from CCHÞ ( ! XX Y max dpððL 1ÞiÞ ZðL 1Þik

dpððL 1ÞiÞ ; dðajÞðliÞ

þ

L 2 XX X l¼1

Case I. If the subordinate attributes set of yli contains only quantitative, i.e. directly measurable, attributes, then calculate the belief acceptability, xli of yli based on Eq. (4). Case II. If the subordinate attributes set of yli contains both quantitative and qualitative, i.e. directly and indirectly measurable, attributes, then calculate the belief acceptability, xli, of yli based on Eq. (1). Step 3. 8i, repeat step 2 and calculate xli for y(L 3)j, y(L 4)j,. . ., y1j, and y00, respectively, y00 is the resultant favourability attribute of the candidate SC.

When conducting an actual SC evaluation process, there are costs to acquire the performance information

xp 2KðL 1Þik

k

Y

alik Zlik

!)

ddðajÞðliÞ

(5)

yaj 2Klik

k

and Zlik ¼ mðKlik Þ;

8l; i; k

(6)

8 X > > > for l ¼ L 1 Zlik  P dpðliÞ > > xp 2Klik < k xli ¼ > X > > > alik  Zlik  P dðajÞðliÞ for l ¼ 1; 2; . . . ; L 2 > : k

xp 2Klik

(7)

alik

X yaj 2Klik

3. Generating the optimal configuration hierarchy (OCH) under limited evaluation resources

i

i

0 1 X 1 1 A;  xaj þ @1 jjKlik jj jjKlik jj y 2K aj

lik

8l; i; k Subject to: ! P X l;i dpðliÞ cpg P  bg ; l;i dpðliÞ þ e p

8g

(8)

(9)

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  dðajÞðliÞ  xaj ; dpðliÞ 2 f0; 1g;

8a; j and

8l; i

dðliÞðajÞ 2 f0; 1g;

(10) 8p; a; j; l; i

169

Eq. (11) constrains the values of the attribute selection variables to be binary.

(11)

where de is the ceiling function that returns a value of one plus the integer portion of the variable; bg total available amount of evaluation resource g; cpg the unit consumption rate of evaluation resource g to acquire information of evaluation attribute, xp; alik the adjusting factor, as defined in Eq. (3); dp(li) the binary attribute selection variable that if the quantitative evaluation attribute xp belongs to the subordinate attributes set of yli, i.e. xp is used to measure the belief acceptability of yli then dp(li) ¼ 1; otherwise, dp(li) ¼ 0; d(aj)(li) the binary attribute selection variable that if the qualitative evaluation attribute yaj belongs to the subordinate attributes set of yli, i.e. yaj is used to measure the belief acceptability of yli, then d(aj)(li) ¼ 1; otherwise, d(aj)(li) ¼ 0; e very small number; Zlik the value of the basic acceptability, Kaj; xaj is the belief acceptability of the subordinate evaluation attribute, yaj; and xli is the belief acceptability of the master evaluation attribute, yli. Eq. (5) is the objective function of the 0–1 nonlinear programming model to optimize the total belief acceptabilities of the CCH. The first part of Eq. (5) represents the belief acceptabilities of the quantitative attributes and the second part of Eq. (5) represents the aggregate belief acceptabilities of the other qualitative attributes in CCH. If all attributes in Klik are used to measure the belief acceptability yli, then Q Q d ¼ 1; otherwise, d yaj 2Klik dðajÞðliÞ yaj 2Klik dðajÞðliÞ ¼ 0. Eq. (6) is an alternative notation to represent the value of the belief acceptability of Klik. Eq. (7) represents the alternative condition to calculate the belief acceptability for attribute in the different layer of the CCH. Eq. (8) is the same as Eq. (3) in that alik is the adjusting factor to equally normalize the contribution of the belief acceptabilities from the corresponding subordinate attributes set, Klik. Eq. (9) constrains the total consumed resource of acquiring information to be less than P the available P amount of the resource. Let d ¼ l;i dpðliÞ = l;i dpðliÞ þ e while dp ffi 1 then quantitative attribute xp is selected from the CCH; otherwise, dp ¼ 0. Eq. (10) is a restriction that an attribute can not be used to measure the belief acceptabilities of its master attributes if its own belief acceptability is zero. Lastly,

4. Fuzzy decision-making on supply chain partnering The fuzzy decision-making procedures for selecting the most favourable strategic SC alliance comprises four steps: (1) developing the FRH that bounds the evaluation attributes with a set of fuzzy rules to evaluate the attributes’ performances judged by the decision-maker, (2) calculating the fuzzy favorabilities of all candidate SCs, and (3) ranking the aggregate fuzzy favorabilities and selecting the most favourable SC to partner with. The detailed procedures are depicted as follows: Step 1. Develop the FRH that bounds the evaluation attributes with a set of fuzzy rules to evaluate the attributes’ performances judged by the decisionmaker: Since a set of resultant evaluation attributes with the maximum total belief acceptability are identified in the OCH, the task immediately following is to develop a ‘‘binding function’’ to describe the relationships among the master attribute and its subordinate attributes set. This paper develops a relationship intensity function, F, that is defined by a set of fuzzy performance evaluation rules. One of the advantages for applying the fuzzy rule based approach to connect evaluation attributes is to relax the following two strict assumptions in the weight-based approach, which has been widely used by past researchers [11]: (1) the evaluation attributes are independent and (2) the trade-off rate between two attributes is a constant [16]. The fuzzy hierarchical relationship structure plus the fuzzy rule based relationship intensity function developed in this paper can improve the handling of the interdependency among evaluation attributes. The relationship intensity function, Fli, defines the relationship between the master evaluation attribute, yli, and all of its subordinate attributes, yaj 2 Zli, and Zli ¼ {yaj|yaj 2 Klik, a ¼ l þ 1, 8k}. In the following equations, a fuzzy if-then rule set that specifies the relationship between yli and yaj can be expressed as the relationship intensity function, Fli, as in Eq. (12). The

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corresponding aggregate fuzzy performance value, ~vbyli of yli is calculated in Eq. (13): Fli : if ~vbyli

~ aj;s Þ ^ li ðyaj is A yaj 2Z

~ ¼ Sbyli Fli

~ li;t Þ then ðyli is B

(12)

Step 2-1. Calculate the fuzzy performances of attributes in the (l ¼ L l)th layer of the FRH based on the following Eq. (14): b

(13)

~ aj;s is the Sth linguistic term for yaj and s ¼ 1, where A ~ li;t the tth linguistic term for yli and t ¼ 1, 2, 2, . . ., B ~ . . ., SAb is candidate supply chain b; Sbli the set of subordinate fuzzy performance n values of the o master ~ attribute, yli, of SAb, and Sbli ¼ ~vbyaj jyaj 2 Zli ; ~vbyaj the fuzzy performance value of the subordinate attribute, yaj, of SAb; and ~vbyli is the fuzzy performance value of the master attribute, yli, of SAb Based on the OCH illustrated in Fig. 3, Eqs. (12) and (13), the FRH of the evaluation attributes is constructed to calculate the SC favourability, ~vb00 for candidate SC b, SAb as shown in Fig. 4. In FRH, ~ Sbli ¼ ð~vbyaj jyaj 2 Zli Þ stands for the set of fuzzy performances of SAb on the evaluation attributes belonging to Zli. Step 2. 8b, calculate the fuzzy favor abilities, ~vb00 , of all candidate SCs, SAb:

~vbyðL 1Þi ¼ ~SðL 1Þi  FðL 1Þi

(14)

where ~vbyðL 1Þi is the fuzzy performance value of the ~ master attribute, y(L 1)i, of SAb; SbðL 1Þi the set of subordinate fuzzy performance values of the master attribute, y(L 1)i, of candidate SC b, SAb, and ~ SbðL 1Þi ¼ ð~vbxp jyaj 2 ZðL 1Þi Þ; ~vbxp the fuzzy performance value of the quantitative attribute, xp, of SAb; F(L 1)i is the relationship intensity function containing a set of fuzzy rules to define the relationship between y(L 1)i and its subordinate attributes, xp 2 Z(L 1)i; 8 is the sup-t composition Step 2-2. Calculate the fuzzy performances of attributes in the (l ¼ l l)th layer of the FRH based on Eq. (13). Step 2-3. Repeat Step2 until obtaining the final aggregate fuzzy performance, i.e. the fuzzy favourability, ~vby00 , of SAb on the ultimate evaluation attribute,

Fig. 4. The fuzzy relationship hierarchy (FRH).

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From previous steps, the fuzzy utility scores of all candidate SC alliances are obtained. The decisionmaker then can employ any preferred fuzzy ranking method to rank the candidate SC alliances according to their final fuzzy utility scores. Step 3. Select the most favourable SC to partner with based on the ranks of the fuzzy favorabilities of the candidate SCs: Since the value of the fuzzy favourability of the candidate SC is a fuzzy number, in this paper a fuzzy ranking technique developed by Lee and Li [21] is adopted, which ranks fuzzy numbers based on their fuzzy means and standard deviations. The basic assumption is that the decision-maker intuitively prefers the fuzzy favourability with high fuzzy mean and low fuzzy standard deviation. The derivation of the fuzzy mean and standard deviation is based on the uniform distribution of fuzzy events. Let xð~vby00 Þ and sð~vby00 Þ denote the fuzzy mean and standard deviation of the fuzzy favourability of SC b, SAb, respectively. The ranking policies for two fuzzy favorabilities, ~vby00 and ~vay00 of SAb and SAa are as follows: if xð~vby00 Þ > xð~vay00 Þ then

ð~vby00 Þð~vay00 Þ

if xð~vby00 Þ > xð~vay00 Þ and

sð~vby00 Þ < sð~vay00 Þ then ~vby00 > ~vay00

(15)

(16)

if not Eq. (15) and not Eq. (16), then ~vby00 < ~vay00

(17)

171

The fuzzy strategic alliance selection framework proposed in this paper can be also deployed as a whatif decision support tool. For example, if the decisionmaker feels that the final favourability of the SC is not ‘‘high’’ enough, he/she can always increase the evaluation budget and run through the SC evaluation framework from Section 3 to Section 4 again. More evaluation attributes will then be considered and the ‘‘total belief acceptability’’ of the evaluation attributes thus will be increased.

5. An illustrative supply chain example in the personal computer industry 5.1. Background information The objective of this section is to demonstrate, step by step, the applicability of the proposed fuzzy framework for selecting the optimal SC to partner with under limited evaluation resources. Assuming that Company T owns several factories in both the Asian-Pacific and the Latin America areas with the core industrial capability in PC manufacturing and assembly. Company T plans to join one of the three strategic supply chain alliances in order to expand the company’s global market. The characteristics of the candidate SC are depicted as follows: (1) Candidate supply chain #1: As shown in Fig. 5, SC #1 contains several strongly affiliated companies. Its manufacturing factories are located in Taiwan, Philippines, and Mainland

Fig. 5. The logistics network of supply chain #1.

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Fig. 6. The logistics network of supply chain#2.

China. These factories are responsible for producing PC components including computer motherboards, memories, power suppliers, and monitors. SC #1 purchases key computer components including CPUs, chipsets, and hard disks from factories in Taiwan, Malaysia, Singapore, and Mainland China. To quickly respond to the customer demand changes, assembly factories and distribution centres are located near the consumer markets in the Northern America, Brazil, Europe, China, Mexico, and Taiwan. (2) Candidate supply chain #2: SC #2 includes a dominant company that focuses on PC assembly

and marketing, as well as several original equipment manufacturers (OEMs). As shown in Fig. 6, the assembly factories and distribution centres are located in Northern America, Singapore, England, Canada, and Brazil to meet the demands in each local area. The OEM members in Taiwan and China are responsible for manufacturing semi-finished PCs. In addition, the dominant company has the power to directly trade with key component suppliers, and it purchases the components for the OEM partners. These components are then shipped directly to the OEMs from key component suppliers in Japan, Taiwan, Korea, and Singapore.

Fig. 7. The logistics network of supply chain #3.

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Table 4 The customized configuration hierarchy (CCH) of the evaluation attributes Attribute

AMC/relative measuring reliability

Performance attributes/variables

Cost (US$)

y00: Supply chain competitive advantage

K01 ¼ {y11, y12, y13}/0.75, K02 ¼ {y11, y13}/0.25

y11: Customer demand change

–

y12: Production and logistics management y13: Relation ship building x1: Variation in demand quantity

– – 140

x2: Variation in types of products or services x3: Changes in demand locations x4: Variation in price y21: Supply network performance

124 190 209 –

y22: Manufacturing network performance y23: Distributing network performance

– –

x27: Cost to integration [4]

213

x28: Likelihood of long-term relationship [6] x5: Consistency in meeting specifications and delivery deadlines [6]

171

x6: Production reliability [6] x7: Flexibility in meeting customer demands [8] x8:Price/cost [18] x9: After-sale support [6] xl0: Production capability [9] x11: Time from order to delivery [8] x12: Cost reduction capability [6]

186 211

y11: Customer demand change

y12: Production and logistics management

y13: Relationship building

y21: Supply network performance

y22: Manufacturing network performance

y23:Distributing network performance

K111 ¼ {x1}/0.2, K112 ¼ {x1,x2}/0.3, K113 ¼ {x1,x2,x3,x4}/0.5

K121 ¼ {y21}/0.1, K122 ¼ {y22}/0.1, K123 ¼ {y23}/0.1, K124 ¼ {y21,y22,y23}/0.7

K131 ¼ {x30}/0.35, K132 ¼ {x30,x31}/0.5, K133 ¼ {x31}/0.25, K124 ¼ {y21,y22,y23}/0.7

K211 ¼ {x5,x8}/0.2, K212 ¼ {x5,x8,x11}/0.3, K213 ¼ {x6,x7,x8,x9,x10}/0.5

K221 ¼ {x12,x13,x14,x15}/0.25, K222 ¼ {x13,x15,x17,x18}/0.3, K223 ¼ {x12,x14,x16}/0.2, K224 ¼ {x12,x14,x16,x17}/0.25

K231 ¼ {x19,x20,x22,x23}/0.4, K232 ¼ {x19,x21,x24,x25}/0.3, K233 ¼ {x22,x23}/0.1, K234 ¼ {x22,x23,x26}/0.2

x13: Ability to change production volumes rapidly [6] x14: Average defect rate x15: order fulfilled rate x16: order lead time of manufacturing x17: Average inventory level in the producers x18: Average WIP level x19: Service level

75

61 210 186 82 135

182 148 186 78 80 204 195

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Table 4 (Continued ) Attribute

AMC/relative measuring reliability

Performance attributes/variables

Cost (US$)

x20: Delivery reliability [8] x21: Delivery reliability [8] x22: On time delivery [17,18] reliability [8] x23: Transportation cost x24: Average Inventory level in the distributors x25: Response to create a service element [8] x26: After-sale service [8]

39 174 76 76 190 206 183

Fig. 8. Optimized configuration hierarchy for the illustrative example.

Table 5 Total belief acceptability of the CCH under different available budgets Available budget

US$ 500

US$ 1000

US$ 1500

US$ 2000

US$ 2500

US$ 3000

US$ 3500

US$ 4000

US$ 4500

Total belief acceptability

0

0.54

0.64

0.68a

0.75

0.81

0.94

0.98

1

a

Optimal total belief acceptability.

(3) Candidate supply chain #3: SC #3 is a vertically integrated mega-company, as shown in Fig. 7. It has a manufacturing factory in Japan supplying TFT-LCDs and several factories producing hard disks in Thailand and Singapore. These key components are then transported by air to

regional distribution centres in the global market. The overall products, except the key components, are outsourced to other companies in Taiwan and Chain. Quasi-products are transported to assembly factories in each market once they are finished in the outsourcing

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companies. The global logistics headquarter of SC #3 dynamically controls the key component flow between distribution centres and assembly factories to meet the customers’ varying demands. 5.2. Illustrative procedures Based on both the business characteristics and the contemporary global logistics situations, the decisionmaker of Company T invites experts from the related areas to assist in the decision-making process. The detailed illustrative procedures for the fuzzy strategic alliance selection framework for the SC partnering problem are provided as follows:

butes, is shown in Fig. 8. The optimal total belief acceptability is 68%. Table 5 also provides a what-if analysis about the resultant total belief acceptabilities under different budgetary constraints. For example, if the decision-maker of Company T can spend up to US$ 4500 in gathering the evaluation attributes’ information, then all evaluation attributes Table 6 Illustrative fuzzy rules for the supply network performance (y21) and its subordinate attributes Antecedent of the if-then rule (subordinate attributes of y21) x8

x11

y21

Bad

Cheap

Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow Fast Normal Slow

Bad Bad Bad Bad Bad Bad Bad Bad Bad Bad Bad Bad Excellent Normal Acceptable Normal Acceptable Acceptable Normal Bad Bad Normal Bad Bad Excellent Excellent Bad Normal Acceptable Bad Acceptable Acceptable Bad Acceptable Acceptable

Moderate-cheap

Moderate-expensive

Expensive

Acceptable

Cheap

Moderate-cheap

Acceptable

Step 2. Determine the OCH of the evaluation attributes with maximum total belief acceptability under Company T’s budgetary constraints.

Moderate-expensive

Expensive

Excellent

Because gathering the information about the evaluation attributes requires monetary expenditures, the decision-maker of Company T then selects the attributes with the most believable information under the budgetary constraint. The problem of maximizing the total belief acceptability of the evaluation attributes under US$ 2000 budget limit is formulated as a 0–1 non-linear programming model as Eqs. (5)–(11). The mathematical software package Lingo 8.0 is used to solve the optimization problem. The resultant OCH, which contains fifteen quantitative attributes and seven qualitative attri-

Consequent

x5

Step 1. Generate the CCH of the evaluation attributes specifically for the PC industry: According to the GCH developed in this paper (please refer to Table 3) which compiles 183 generic evaluation attributes for supply chain selection, a CCH containing seven qualitative attributes and 26 quantitative attributes is extracted by the decision-maker as in Table 4. In addition to constructing the mastersubordinate relationships among these evaluation attributes, due to the practical limitations in acquiring complete information of the attributes, the belief acceptability as well the estimated information acquisition cost of the evaluation attributes are also determined by the decision-maker as in Table 4.

175

Cheap

Moderate-cheap

Moderate-expensive

Expensive

y21: Supply network performance; x8: price/cost; x5: consistency in meeting specifications and delivery deadlines; x11: time from order to delivery.

176

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Fig. 9. Fuzzy relationship hierarchy (FRH) for the illustrate example.

as included in the CCH can be considered and have 100% belief acceptability. Step 3. Construct the FRH with a set of fuzzy rules to measure the fuzzy performances of the evaluation attributes:

Once the optimal evaluation attributes are determined, a set of fuzzy rules are developed by the expert in Company T to describe the relationship among the master attribute and its subordinate attributes. Table 6 demonstrates thirty six fuzzy rules that are developed to infer the performance of the master evaluation

Table 7 Fuzzy performance of the evaluation attributes for the candidate supply chains Universe of the discourse for the evaluation attributes

x1: Variation in demand quantity, (0,1) unit x2: Variation m types of product or service, (0,12) month x5: Consistency in meeting specifications and delivery deadlines, (0,1) rating score x8: Price/Cost, (0,100) $ x11: Time from order to delivery, (0,12) day x12: Cost reduction capability, (0,1) rating score x14: Average defect rate, (0,1) rating score x16: Order lead time of manufacturing, (0,12) day x17: Average inventory level in the producers, (20,60) day x19: Service level, (0, 1) rating score x20: Delivery capacity, (50,200) thousand units per month x22: Ontime delivery, (-3,3) x23: Transportation cost, (0,100) US$ 10,000 x27: Cost to integration, (0,100) US$ 10,000 x28: Likelihood of long-term relationship, (0,100) rating score

Fuzzy performances of the evaluation attributes Supply chain #1

Supply chain #2

Supply chain #3

g(0.15,0.55) g(0.50,5.50) g(0.125,0.875)

g(0.20,0.65) g(0.50,4.00) g(0.125,0.375)

g(0.15,0.70) g(0.50,3.00) g(0.10, 0.25)

t(30, 40, 50) t(2.5, 3, 7) g(0.05,0.80) g(0.05,0.10) g(1, 8) t(25, 30, 35) t(0.8,0.9,1) g(5,80) g(0.5,1) g(5,20) t(50, 70, 90) t(30, 40, 50)

t(60, 70, 80) t(2, 3, 5, 6) g(0.05,0.70) g(0.05,0.25) g(2, 4) t(45, 50, 55) t(0.7, 0.95, 1) g(5,150) g(0,1, 2) g(10,50) t(40, 55, 67) t(65, 70, 80)

t(40, 50, 60) t(1, 1.50, 3.50 g(0.1,0.95) g(0.1,0.05) g(1.50, 3) t(55, 60, 65) t(0.85, 0.9, 1) g(3,180) g(0.1,0) g(7,25) t(0,5,10) t(85, 90, 95)

g(s, m): Gaussian membership function with parameters s and m; t(a, b, c): Triangular membership function with parameter a, b, c.

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Fig. 10. Fuzzy performance values of the candidate supply chains.

177

178

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attributes, ‘‘y21: Supply network performance’’. For example:

If

‘‘x5: Consistency in meeting specifications and delivery deadlines’’ is ‘‘Bad’’ and ‘‘x8: Price/cost’’ is ‘‘Cheap’’ and ‘‘x11: Time from order to delivery’’ is ‘‘Fast’’ Then ‘‘y21: Supply network performance’’ is ‘‘Bad’’

selected as the most favourable strategic alliance for Company T. Certainly, if the final favourability of SC #1 is either not high enough or acceptable by the decision-maker, he/she can raise the budget for acquiring more evaluation attributes with more precise information and run through the fuzzy SC selection framework again.

6. Conclusions After the fuzzy rule base has been developed, a FRH, as shown in Fig. 9, is constructed to represent the complete relationship among the attributes bound by the corresponding relationship intensity functions. The SC experts of Company T then gather the information on all the quantitative evaluation attributes and calculate the fuzzy performances (Eqs. (12)–(14)) for the three candidate SCs, respectively (please refer to Table 7). Step 4. Calculate the final SC fuzzy favor abilities, i.e. the aggregate fuzzy performances, of the candidate supply chains, respectively. Apply the fuzzy ranking procedure to rank the fuzzy favorabilities and select the most favourable SC as the strategic SC alliance to partner with: Once the fuzzy performances of all quantitative subordinate attributes are obtained, based on the same procedures in Eqs. (12)–(14), the fuzzy performance values of all qualitative master attributes: (1) y11: customer demand change (2) y12: production and logistics management (3) y13: relationship building (4) y21: supply network performance (5) y22: manufacturing network performance, and (6) y23: distributing network performance, are provided in Figs. 6(g)-10(b), respectively. The calculations are done by Matlab version 6.1. The three candidates’ final SC fuzzy favorabilities, ~v00 , i.e. the fuzzy performance of y00: supply chain competitive advantage, are shown in Fig. 10a. The fuzzy means and standard deviations of the SC favorabilities for the three candidate SCs are; (0.498, 0.088), (0.443, 0.078), and (0.343, 0.064), respectively. Based on the fuzzy ranking procedures defined in Eqs. (15)– (17), the rankings of the SC favorabilities are: SC #1 > SC #2 > SC #3. Therefore, supply chain #1 is

Joining an existing global SC in order to boost business growth is a common practice for industries. However, how to select the best SC to partner with is a critical decision because there are numerous decision attributes that need to be evaluated. This paper systematically compiles over 180 attributes, including both quantitative/qualitative and subjective/objective attributes. Furthermore, this paper develops a fuzzy decision-making framework to assist a company in selecting the most favourable SC to be allied with. Firstly, it applies a hierarchical decision-making structure to provide a flexible configuration mechanism to build up the relationships among evaluation attributes, based on the particular characteristics of the industry. Secondly, the fuzzy framework transforms the decision-making problem as a 0–1 non-linear programming model which extracts the most acceptable evaluation attributes under the constraint on evaluation cost. Thirdly, the fuzzy framework develops a relationship intensity function to bind the fuzzy performances of the evaluation attributes with a set of inference fuzzy rules. The final aggregate fuzzy performance from all subordinate attributes then becomes as the resultant evaluation index, i.e. the fuzzy favourability, which is used to measure the overall performance of the candidate SCs. The decision-maker then can select the top-ranked SC as the most favourable strategic alliance to partner. Finally, an illustrative example successfully demonstrates how a PC company can select the most favourable strategic SC alliance of three candidate SCs based on the proposed fuzzy decision-making framework. The future stage of this research is focused on the adjustment of the optimal production-distribution policy of the most favourable resultant SC after the joining of the new partner.

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[16] J. Efstathiou, V. Rajkovic, Multiattribute decision making using a fuzzy heuristic approach, IEEE Transactions on Systems, Man, and Cybernetics SMC-9 (6) (1979) 326–333. [17] S.T. Cavusgil, P.-L. Yeoh, M. Mitri, Selecting foreign distributors, Industrial Marketing Management 24 (4) (1995) 297–304. [18] V. Mummalaneni, K.M. Dubas, C. Chiang-nan, Chinese purchasing managers’ preferences and trade-offs in supplier selection and performance evaluation, Industrial Marketing Management 25 (2) (1996) 115–124. [19] M. Beynon, B. Curry, P. Morgan, The Dempster–Shafer theory of evidence: an alternative approach to multicriteria decision modelling, Omega 28 (1) (2000) 37–50. [20] J.W. Guan, D.A. Bell, Evidence Theory and its Applications, vol. 1. Amsterdam, North Holland, 1991. [21] E.S. Lee, R.L. Li, Comparison of fuzzy numbers based on the probability measure of fuzzy events, Computer and Mathematics with Applications 15 (1988) 887–896. [22] Z. Babic, N. Plazibat, Ranking of enterprises based on multicriteria analysis, International Journal of Production Economics 56–57 (1998) 29–35. Chun-Wei R. Lin is Chairman and Associate Professor in the Department of Industrial Engineering and Management, National Yunlin University of Science & Technology (NYUST), Taiwan, ROC. Dr. Lin has a PhD in Industrial Engineering from The Pennsylvania State University. He was also the founder for the Innovation and Incubation Center and Commercial Automation Center in NYUST. His current research interests are in dynamic supply chain management, enterprise resource planning, and global logistics. Hong-Yi S. Chen is a Ph.D. Candidate in the Department of Industrial Engineering and Management, National Yunlin University of Science & Technology, Taiwan, ROC. He is currently a distinguished visiting scholar in the Department of Industrial Engineering, Purdue University, sponsored by the National Science Council, Taiwan, ROC. His research interest is focused in supply chain and logistics system design.