Journal of Industrial Engineering, University of Tehran, Special Issue, 2011, PP. 127-142 127
A Fuzzy Multi-Attribute Decision Making
Model for Selecting the Best Supply Chain Strategy: Lean, Agile or Leagile

Jafar Razmi *1, Maryam Seifoory1 and Mir Saman Pishvaee 1
Department of Industrial Engineering, University College of Engineering, University of Tehran, Tehran, Iran (Received 29 November 2010, Accepted 20 July 2011)

During recent years, determining appropriate strategy in the supply chain has become an important strategic issue. However, the nature of these decisions usually is complex and unstructured. To determine the best supply chain strategy, many quantitative and qualitative attributes such as cost, responsiveness and flexibility can be taken into account. In order to approximate the human subjective evaluation process, it would be desirable to apply a fuzzy MADM model. In this paper a fuzzy multi-attribute decision making (FMADM) model is developed to deal with strategy selection problem in a supply chain. A case study is used to validate the proposed model and the corresponding results show the power of the proposed model in handling subjective data in multi-attribute decision making process.

Keywords: Fuzzy multi-attribute decision making, Supply chain management, Strategy

1. Introduction
* Corresponding author: Tel: +98- 21- 88021067 Fax: +98- 21- 88013102 Email: [email protected]

A key feature of contemporary business is the competition among the supply chains instead of companies. In other words, delivering the right product, at the right time with a reasonable cost to consumers is not only the lynch pin to competitive success but also the key to survival [1]. The latter part of the 20th century saw the lean production paradigm positively impact many market sectors ranging from automotive industries to electronic industries. The focus of the lean approach has essentially been on the elimination of waste or muda. The upsurge of interest in lean manufacturing can be traced to the Toyota Production Systems. Lean is about doing more with less [2]. In particular there is much evidence to suggest that level scheduling combined with the elimination of muda as successfully delivered a wide range of products to those markets where cost is the primary order winning criteria. However, there are many other markets where the order winner is availability. This has led to the emergence of the agile paradigm typified by ‘quick response’ and similar initiatives [3]. Agility is a business wide capability that embraces organizational structures; information point in the material, systems, logistics processes and in particular, mindsets [4, 5]. Agility is being defined as the ability of an organization to respond rapidly to changes in demand, both in terms of volume and variety [3]. The emphasis is on adaptability to changes in the business environment and on addressing market and customer needs proactively [2]. A key characteristic of an agile organization is flexibility [6, 7, 8]. Indeed the origins of agility as a business concept lie in flexible manufacturing systems (FMS). Initially it was thought that the route to manufacturing flexibility was through automation to enable rapid change (e.g. reduced set-up times) and thus a greater responsiveness to changes in product mix or volume. Later this idea of manufacturing flexibility was extended into the wider business context [9] and the concept of agility as an organizational orientation was born [1]. Nevertheless, both paradigms lean and agile have their own advantages and imperfections and are not exclusive paradigms. So effectiveness of agility and leanness depends on business environment characteristics and customer needs. Even, they may be combined to advantage in a number of different ways. Hence, customer satisfaction and marketplace understanding are crucial elements for consideration when attempting to establish a new supply chain strategy. Combining agility and leanness in one supply chain via the strategic use of a decoupling point has been termed
‘‘leagility’’ [10]. The decoupling point is in the material flow streams to which the customer orders penetrates [11]. Therefore leagile is the combination of the lean and agile paradigms within a total supply chain strategy by positioning the decoupling point so as to best suit the need for responding to a volatile demand downstream yet providing level scheduling upstream from the market place [12].
The goal of this research is to investigate lean and agile concepts in the area of supply chain management and to represent a FMADM model to select the best supply chain strategy according to system characteristics. The rest of this paper is organized as follows. In the next section, some related works are reviewed. Section 3 illustrates the basic definitions and notations of the fuzzy numbers, linguistic variables and the fuzzy TOPSIS method. In Section 4, we present a hierarchical model for selecting the best supply chain strategy and decision making criteria. Section 5, describes numerical examples to demonstrate the applicability of proposed method. Finally, concluding remarks are summarized in
Section 6.

2. Literature review
Naylor et al. [10] compared the lean and agile manufacturing paradigms, highlighting the similarities and differences. They showed how the need for agility and leanness depends upon the total supply chain strategy, by considering market knowledge, information enrichment and the position of the decoupling point. The lean and agile paradigms, though distinctly different, can be combined within successfully designed and operated total supply chains [13, 10]. Cristopher and Towill [1] have sought to bring together the lean and agile philosophies to highlight the differences in their approach, but also to show the various ways in which these paradigms may be combined to enable highly competitive supply chains. They have focused on ‘market qualifiers’ and ‘market winners’. The lean supply paradigm has taught us the importance of reducing variation and enabling flow, so reducing the need for protective inventory and capacity. However, with the growth in product innovation and demand uncertainty, supply chains now need to strategically locate inventory and capacity. Investment in capacity to protect material flow rather than inventory is central to the agile supply paradigm and the use of separation principles provides a practical approach to exploring innovative approaches to mitigating the impact of the conflict. Stratton et al. [14] identify how TRIZ separation principles and TOC tools may be combined in the integrated development of responsive and efficient supply chains. Cagliano et al. [15] empirically explored the supply strategies of European manufacturing firms. Four clusters have been identified on the basis of the supplier selection criteria and the integration mechanisms adopted.
Vonderembse et al. [16] discuss supply chain strategy types including lean, agile and hybrid across three types of products: standard, innovative, and hybrid. They have developed a framework for categorizing the supply chain types according to product characteristics and stage of the product life cycle. Agarwal et al. [2] develop an analytic network process (ANP) model to identify the best supply chain strategy. They explore the relationship among lead-time, cost, quality, and service level and the leanness and agility of a supply chain.
Although there are many researches regarding conceptual approaches for selecting the supply chain strategy, most of the related literatures are devoted to some specific perspectives, such as supply chain type, product type and etc. It is clear that, selecting the supply chain strategy without considering all the relevant aspects does not lead to an effective result. This paper exploits the advantages of previous works to develop a comprehensive model for selecting the best supply chain strategy, which considerers all the relevant dimensions and using both quantitative and qualitative criteria. To overcome the issue of complexity and uncertainty in the considered problem, the fuzzy technique for order performance by similarity to ideal solution (Fuzzy-TOPSIS) is used to identify the most appropriate supply chain strategy.

3. Methodology
MADM deals with the problem of choosing an option from a set of alternatives which are characterized in terms of their attributes. It requires information on the preferences among the instances of an attribute, and the preferences across the existing attributes. An important advantage of most MADM techniques is that they are capable to analyze both quantitative and qualitative evaluation criteria together. The decision maker may express or define a ranking for the attributes as importance/weight. The aim of the MADM is to obtain the optimum alternative that has the highest degree of satisfaction for all of the relevant attributes. TOPSIS, outranking, and AHP are three of the most frequently used MADM techniques. TOPSIS and Fuzzy TOPSIS have been applied to solve a variety of problems [17, 18]. TOPSIS views a MADM problem with m alternatives as a geometric system with m points in the n dimensional space. The method is based on the concept that the chosen alternative should have the shortest distance from the positive-ideal solution and the longest distance from the negative-ideal solution. TOPSIS defines an index called similarity (or relative closeness) to the positive-ideal solution and the remoteness from the negative-ideal solution. Then the method chooses an alternative with the maximum similarity to the positive-ideal solution [19].
Despite the convenience of TOPSIS in handling both quantitative and qualitative criteria of multi-criteria decision making problems based on decision maker’s judgments, fuzziness and vagueness existing in many decision making problems may contribute to the imprecise judgments of decision makers in conventional TOPSIS approach. In other words, under many conditions, crisp data are inadequate to model real-life situations. Since human judgments including preferences are often vague and cannot be estimated with an exact numerical value, a more realistic approach may be to use linguistic assessments instead of numerical values.
Fuzzy TOPSIS refers to a method for multi-attribute decision making (MADM) under uncertainty, where a finite number of decision alternatives are evaluated under a finite number of performance criteria. The purpose of the analysis is to rank the alternatives in a subjective order of preference. The overall performance of these alternatives is herein assessed via proper assignment of numerical grades or scores measured through fuzzy theories to address the issue of vagueness of human preferential judgment [20]. A present study represents a FMADM model and explores the use of Fuzzy TOPSIS to select the best supply chain strategy according to system characteristics. Details of the proposed methodology are discussed sequentially in the following sections [21]. In summation, the algorithm of fuzzy TOPSIS method used in this paper is given as follows [20]:
Step 1: Form a committee of decisionmakers, and then identify the evaluation criteria.
Step 2: Choose the appropriate linguistic variables for the importance weight of the criteria and the linguistic ratings for alternatives.
Step3: convert the linguistic evaluations into triangular fuzzy numbers to construct the fuzzy-decision matrix and determine the fuzzy weight of each criterion.
Step 4: normalized fuzzy weight of each criterion and fuzzy-decision matrix.
Step 5: Construct weighted normalized fuzzy decision matrix.
Step 6: Determine FPIS and FNIS.
Step 7: Calculate the distance of each alternatives from FPIS and FNIS, respectively.
Step 8: Calculate the closeness coefficient of each alternatives.
Step 9: According to the closeness coefficient, we can understand the assessment status of each alternative and determine the ranking order of all alternatives.
Although we can determine the ranking order of all feasible strategies, a more realistic approach may be to use a linguistic variable to describe the current assessment status of each strategy in accordance with its closeness coefficient. In order to describe the assessment status of each strategy, we divide the interval [0, 1] into five sub-intervals. Five linguistic variables with respect to the sub-intervals are defined to divide the assessment status of strategies into five classes [20]. The decision rules of the five classes are shown in Table 1.

Table 1: Approval status
Closeness Coefficient (CCi) Assessment status
CCi є [0,0.2]
CCi є [0.2,0.35] CCi є [0.35,0.5] CCi є [0.5,0.85] CCi є [0.85,1] Do not recommend Recommend with high
Recommend with low
Approved and preferred

According to the table 1, it means that:
If CCi є [0, 0.2], then strategy Ai belongs to
Class I and the assessment status of strategy Ai is “not recommend”;
If CCi є [0.2, 0.35], then strategy Ai belongs to Class II and the assessment status of strategy Ai is “recommend with high risk”;
If CCi є [0.35, 0.5], then strategy Ai belongs to Class III and the assessment status of strategy Ai is “recommend with low risk”;
If CCi є [0.5, 0.85], then strategy Ai belongs to class IV and the assessment status of strategy Ai is “approved”;
If CCi є [0.85, 1], then strategy Ai belongs to
Class V and the assessment status of strategy Ai is “approved and preferred to recommend”.

3.1. Fuzzy numbers
In this section, some basic definitions of fuzzy sets, fuzzy numbers and linguistic variables are reviewed from Buckley [22], Kaufmann and Gupta [23], Negi [24] and Zadeh [25]. The basic definitions and notations below will be used throughout this paper until otherwise stated.

Definition 3.1. A fuzzy set A~ in a universe of discourse X is characterized by a membership functionA~(x) which associates with each element x in X a real number in the interval [0,1]. The function value A~(x) is termed the grade of membership of x in A~ [23].

Definition 3.2. A fuzzy set A~ in the universe of discourse X is convex if and only if:
A~(x1  (1)x2)  min(A~(x1),A~(x2))
For all x1, x2 in X and [0,1], where min denotes the minimum operator [26].

Definition 3.3. The height of a fuzzy set is the largest membership grade attained by any element in that set. A fuzzy set A~ in the universe of discourse X is called normalized when the height of A~ is equal to 1 [26].

Definition 3.4. A fuzzy number is a fuzzy subset in the universe of discourse X that is both convex and normal. Fig. 1 shows a fuzzy number n~ in the universe of discourse X that conforms to this definition [23].

Figure 1: Fuzzy number n~
Definition 3.5. A positive trapezoidal fuzzy number (PTFN) A~ can be defined as A~  (a1,a2,a3,a4) the membership function,
A~(x) is defined as: [23]

 x a

a2 a1
A( )x  a  x

a4 a3 
0 a2  x a3 a1  x a2

a3  x a4 x  a x a1,  4

For a trapezoidal fuzzy number,
A~  (a1,a2,a3,a4) ifa2  a3, then A~ is called a triangular fuzzy number and is showed as A~  (a1,a2,a3)(figure.2).










Figure 2: Triangular fuzzy number

In other word a a a1, 2, 3 are the lowest possible value, the most possible value, and the largest possible value respectively.

Definition 3.6. A linguistic variable is a variable whose values are expressed in linguistic terms [27]. The concept of a linguistic variable is very useful in dealing with situations, which are too complex or not well defined to be reasonably described in conventional quantitative expressions.
It is not possible to make mathematical operations directly on linguistic values. This is why; the linguistic scale must be converted into a fuzzy scale. In the literature about fuzzy methods, one can find a variety of different fuzzy scales. (See, for example [28, 29, 30]. The triangular fuzzy conversion scale given in figure 3 is used in the evaluation model of this paper (adapted from [31]).

4. A hierarchical model for selecting the best supply chain strategy
The first step is devoted to construct a model to identify the system alternatives and criteria to evaluate the supply chain strategies. Due to the complexity of the decision making process in selecting the supply chain strategy, a hierarchical model is used in this paper. Figure 4 shows the hierarchical model for selecting the best supply chain strategy. The key parameters for this model can be categorized into four levels. The first level of the model deals with the essence of the difference between leanness and agility in terms of the total value provided to the customer, which included responsiveness, (service level) that is the critical factor calling for agility, and cost, that is clearly linked to leanness [1]. In order to specify the effects of cost and responsiveness on decision making alternatives, these two criteria are broken into relevant sub criteria which lie in level 2. Sub criterions of cost are inventory cost, process cost, supply cost, transportation cost and shortage cost. Sub criteria of responsiveness are flexibility, lead time and innovation. The third level of model consists of flexibility’s sub criteria which are product type flexibility (machine flexibility), volume flexibility (production capacity flexibility), supply flexibility, manpower flexibility and transportation flexibility. The fourth level of model deals with the decision making alternatives which are lean, agile and leagile strategies. The overall objective is to select the best strategy for improving performance of the case supply chain. In order to select the most appropriate supply chain strategy, decision makers should determine the important weight of each criterion and performance rating of alternatives with respect to each criterion and by using linguistic variables. Then the linguistic variables should be converted to fuzzy triangular numbers and finally, the ranking order of alternatives can be determined using fuzzy TOPSIS approach. In the next section, the decision making criteria will be explained in detail.

4.1. Responsiveness
Responsiveness is related to the ability of a manufacturing system to utilize its existing resources to make a rapid and balanced response to predictable and unpredictable changes [32]. It is the ability to identify changes and respond fast to them, reactively or proactively, and recover from them [33]. Three sub criteria under the umbrella of responsiveness are considered in the hierarchy to evaluate the importance of responsiveness over the alternatives.

Flexibility is the ability to process different products and achieve different objectives with the same facilities. A key characteristic of an agile organization is flexibility [6, 8]. Initially it is thought that the route to manufacturing flexibility is through automation to enable rapid changeovers (i.e. reduced set-up times) and thus enable a greater responsiveness to changes in product mix or volume. Later this idea of manufacturing flexibility is extended into the wider business context that embraces organizational structures, information systems, logistics processes and in particular, mindsets. The supply chain may be broken down into three basic segments: sourcing,

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