Management and Production Engineering Review Volume 10 • Number 1 • March 2019 • pp. 69–82 DOI: 10.24425/mper.2019.129570 A HYBRID FSIR-TOPSIS APPROACH FOR SELECTING OF MANUFACTURING LEVERS Mehdi Ajalli1 , Mohammad Mahdi Mozaffari2 , Ali Asgharisarem3 1 2 3 Faculty of Management, University of Tehran, Iran Faculty of Social Science, Imam Khomeini International University (IKIU), Iran Faculty of Management and Accounting, Bu-Ali Sina University, Iran Corresponding author: Mehdi Ajalli Faculty of Management University of Tehran Tehran, Iran phone: 0098-9126410243 e-mail: ajalli@ut.ac.ir Received: 6 December 2017 Accepted: 18 February 2019 Abstract One of the strategic decisions of any organization is decision making about manufacturing strategy. Manufacturing strategy is a perspective distinguishing a company from other present companies in that industry and creates a kind of stability in decisions and gives a special direction to organizational activities. SIR (SUPERIORITY& INFERIORITY Ranking) method and their applications have attracted much attention from academics and practitioners. FSIR proves to be a very useful method for multiple criteria decision making in fuzzy environments, which has found substantial applications in recent years. This paper proposes a FSIR approach based methodology for TOPSIS, which using MILTENBURG Strategy Worksheet in order to analyzing of the status of strategy of the Gas Company. Then formulates the priorities of a fuzzy pair-wise comparison matrix as a linear programming and derives crisp priorities from fuzzy pair-wise comparison matrices Manufacturing levers (Alternatives) are examined and analyzed as the main elements of manufacturing strategy. Also, manufacturing outputs (Criteria are identified that are competitive priorities of production of any organization. Next, using a hybrid approach of FSIR and TOPSIS, alternatives (manufacturing levers) are ranked. So dealing with the selected manufacturing levers and promoting them, an organization makes customers satisfied with the least cost and time. Keywords strategy, Miltenburg’s worksheet, Fuzzy Superiority & Inferiority Ranking (FSIR), TOPSIS, manufacturing levers, manufacturing outputs. Introduction strategy forming the context for the business strategy which in turn forms the context for each functional strategy including manufacturing. Skinner also has described the importance of a strategic alignment of the manufacturing function; manufacturing strategy has become one of the most discussed issues in the field of operations management. [2] provides a tool for the assessment of manufacturing’s strategic role, and introduce product/process matrix. [3] proposed a framework for generic manufacturing strategies which is derived from [4, 5] approach of generic strategies and Hayes and Wheelwright’s productprocess matrix. [6] and [7] have made empirical ob- There is many studies on manufacturing strategy (MS). For the first time Skinner (1969) [1] introduced manufacturing strategy to exploit certain properties of the manufacturing function to achieve competitive advantages. Manufacturing strategy is defined as a pattern of decisions, both structural and infrastructural, which determine the capability of a manufacturing system in order to meet a set of manufacturing objectives that fit with the overall business objectives. Skinner’s approach have led to a predominant hierarchical process model starting from corporate 69 Management and Production Engineering Review servation of the strategy formulation and implementation process, and find that the process is essentially hierarchical, which is consistent with Skinner’s approach. In a preliminary study of the ?rst HPM data set (High-Performance Manufacturing Project), Anderson & Schroeder (1999) [8] evaluated the process of manufacturing strategy empirically with a sample of 53 respondents. The paper focuses on the link between business strategy and manufacturing strategy and provides first insights how these strategy levels affect each other. The literature in the area of management strategy contains an excellent set of conceptualizations. In business and academic journals there exist plenty of articles telling industry what to do. The manufacturing industry, for instance, is told to integrate its financial, marketing and production strategies, develop an operational focus, and match its processing system to its product design and mix, and a host of other things. According to the Hill’s point of view [9], manufacturing strategy should be supportive to the achievement of a company’s competitive priorities. Hill also proposes a five-step procedure to link manufacturing strategy to order winners in order to achieve the congruence between them. Miltenburg [10] proposed an overall framework with three steps for performing an analysis of a company’s manufacturing strategy in terms of congruence with the production system, its products, and its capabilities. In a study, Bates et al. [11] analyze the relationship between manufacturing strategy and organizational culture in 41 US plants and stress the link between the business strategy and the manufacturing strategy as well. At present, most research focuses on strategy content. However, research on manufacturing strategy development is relatively limited. Safsten et al. [12] investigate the usability of Miltenburg’s framework in small and medium sized manufacturing companies, and further suggest some changes of the model. Lee et al. [13] propose a framework for a decision-support system to support the formulation of a manufacturing strategy which consists of manufacturing system modeling and analyzing performance measures. The proposed decisionsupport system enables the formulation of manufacturing strategy using what-if analysis against dynamic manufacturing environments. Quezada et al. [14] developed a methodology for the development of a manufacturing strategy by means of exploiting the concepts of the analytic hierarchy process. In terms of this methodology, a manufacturing strategy can be formulated by creating a five level hierarchy: focus, company objectives, strategic business units, critical success factors and manufacturing decision areas. This methodology also allows a strategic diagnosis 70 of the current manufacturing system and the generation and evaluation of action plans to improve the company competitiveness. Slack et al. [15] give some indications on how to assess the support from the operations function. According to Slack view, manufacturing strategy is part of a manufacturing company’s total strategy. It contains the pattern of strategic decisions and actions which set the role, objectives and activities of the manufacturing in a manufacturing company. Just as with any type of strategy, we can consider its content and process separately. The content of manufacturing strategy comprises the specific decisions and actions which set the manufacturing role, objectives and activities. Platts et al. [16] proposed a three stage procedure of developing manufacturing strategy. The procedure uses profiles of market requirements and achieved performance to show up the gaps which the manufacturing strategy must address. The literature Operation Management (OM) describe six indicators for plant competitive performance such as unit cost of manufacturing, standard product quality, on-time delivery, fast delivery, flexibility in changing the product mix and flexibility in changing volume, etc. [17]. Karacapilidis et al. [18] develop a computerized knowledge management system for the collaborative development of manufacturing strategy. The system is used to capture the strategists’ rationale and stimulates knowledge elicitation, and it can support the social and knowledge processes of collaborative strategy development by integrating a domain specific modeling formalism. Many publications offer conceptual frameworks, give empirical evidence, etc. concerning the use of a manufacturing strategy. While extensive literature on manufacturing strategy has been written since the 1960s, still some research questions remain unanswered. Today, manufacturing companies are forced to stand up to competitors in the light of a highly competitive environment. This can be achieved by a specific alignment of the manufacturing function. Through the formulation of a manufacturing strategy, the strategic potential of the manufacturing function can be realized, leading to superior competitiveness. Despite the fact that manufacturing strategy is commonly accepted as an important approach, there is still a lack of empirical work, especially regarding the use of manufacturing strategies in a broad international context [19]. Arafa et al. [20] has discussed the manufacturing strategy and enterprise dynamic capability. The typical strategic planning process for industrial enterprises starts by defining the business strategy that the firm will utilize. According to the selected type of strategy, firms have to generate a portfolio of capabilVolume 10 • Number 1 • March 2019 Management and Production Engineering Review ities that will determine the contribution of the manufacturing function to overall business performance. By analyzing different scenarios using a system dynamic simulation approach and considering market competitive dynamics, this study explores the volume flexibility measure considering both the operating environment and the simultaneous strategic behavior of the competing firms. Jia et al. [21] proposed an approach for manufacturing strategy development based on fuzzy-QFD. The study starts by analyzing the process of manufacturing strategy development and the features of QFD. In this research, the proposed methodology for developing manufacturing strategy uses QFD as a transforming device to link competitive factors with manufacturing decision categories such as structural decision categories and infrastructural categories, and uses HOQ as a main tool in different stages of manufacturing strategy development process. Zahirul and Maybelle [22], discovered how the strategic change following a corporate takeover impacted the nature and extent of use of the firm’s management control systems (MCS), in particular its performance measurement system (PMS). They used Michael Porter’s theory of competitive advantage and Robert Simons’ levers of control framework to illustrate and interpret changes in the PMS within an Australian multinational subsidiary following its takeover by an overseas corporation. To provide empirical evidence on this issue, face-to-face interviews and archival data are used. Pradip et al. [23] investigated the employment of manufacturing strategy in packaging industry of Indian company by three constructs manufacturing as competitive force, functional integration of manufacturing, strategic planning and communication. The final purpose of this paper is proposing a framework for linking and exploring the pattern of manufacturing strategy implementation, differences in manufacturing decisions/levers, manufacturing outputs and business performance of a firm. This is applied by grouping the equipment in four class based on the increasing level of manufacturing strategy implementation using cluster analysis. Fantino Giorgio [24] in a doctoral dissertation focused on workers skills as a competitive asset in world. In this context, the new actors have to understand and measure the advantage of investing in distinguished skills of their workers and translate this investment into competitive advantage. Luqman et al. [25] used AHP approach for selecting of manufacturing process of Composite Bicycle’s Crank Arm. The master purpose of this paper Volume 10 • Number 1 • March 2019 is investigating the potential type of manufacturing process to fabricate composite bicycle crank arm in order to help manufacturing in identification the best process to be applied in manufacturing of composite bicycle crank arm to decrease the manufacturing cost. Undoubtedly, formulating the manufacturing strategy and the way of achieving it is one of the most important factors of business planning process of an organization, but in many cases, no attention is paid to it and there is not enough knowledge about it. To respond to this lack, a research is conducted in an industrial unit that is one of the great component makers of the country. The main purposes of this research are as follows; • ranking manufacturing strategies; • ranking manufacturing levers and assigning them optimally to support from manufacturing strategy. For achieving these objectives, this paper proposes Miltenburg’s strategy worksheet, and a Fuzzy Superiority & Inferiority Ranking (FSIR), based TOPSIS methodology which formulates the priorities of a fuzzy pair-wise comparison matrix as a linear programming and derives crisp priorities from fuzzy pair-wise comparison matrices. The Superiority & Inferiority Ranking (FSIR) method is one of the new and relative complex Multi Criteria Decision Making methods. There are preference functions in this method such as PROMETHEE, which after calculating the preference of each alternative to the criteria, and finding the paired preference functions of alternatives due to the criteria, superiority and inferiority matrix must be formed. At the next step weighted flow matrix is formed such as SAW and TOPSIS techniques, and alternatives can be ranked by calculating the flows. The fuzzy set theory approaches could resemble human reasoning in use of approximate information and uncertainty to generate decisions. Furthermore, fuzzy logic has been integrated with MCDM to deal with vagueness and imprecision of human judgment. This paper outlines the theoretical basis of manufacturing strategy and Miltenburg’s worksheet. Fuzzy logic that is the basis for this research analysis has been thoroughly explored and then the research methodology is discussed. Superiority and Inferiority ranking (SIR) techniques and subsequently expression of this technique in the fuzzy space are shaping the next phase of this article. Using fuzzy SIR techniques in strategy analysis – that is one of the innovations of this study – and its implementation in a typical sample and then expression of conclusions from findings form the final stages of this research. 71 Management and Production Engineering Review Fuzzy SIR uses fuzzy set theory to express the uncertain comparison judgments as a fuzzy numbers. The reminder of this paper is organized as follows: Sec. 2, Introduces the research area (Abzarsazi Industries of Iran); Sec. 3, describes manufacturing strategy (Manufacturing outputs as Criteria’s and Manufacturing levers as Alternatives); Sec. 4, reviews the literature of TOPSIS, Fuzzy TOPSIS and Fuzzy TOPSIS stepwise procedure; Sec. 5, gives a brief review of Fuzzy SIR; in Sec. 6, case study of this research is presented; and finally in Sec. 7, is the conclusion of this paper. Research area (Abzarsazi industries of Iran) Abzarsazi Industries produces metal components that tries to improve its quality, safety and occupational hygiene performance constantly by establishing quality management systems, safety and occupational hygiene based on ISO 9001:2008 and OHSAS 18001:2007 for achieving its strategic aims. At present, having efficient human resource and equipped and advanced shop floors and also various processes of production such as machining, thermal operations, forging, founding, die making, etc. this industry is one of pioneer component maker companies in the country. Production managers always want to offer a better and more diversified and cheaper product. On the other hand, Demands of customers increases and competitors offer more products, but what do producers offer to customers? According to Miltenburg’s strategy worksheet there are six important outputs including in time delivery, cost, quality, performance, flexibility and innovation [26]. Applying a competitive strategy requires using a suitable production system and applying a production system also needs supplying an acceptable level of manufacturing levers. Manufacturing levers or manufacturing factors are human resources, organizational structures & controls, production planning & control, sourcing, process technology and facilities. Also existing limitations for organization is budget and time (Management and Employment). Certainly, supplying the above manufacturing levers makes the organization reach ideal conditions, but do the existing limitations allow realizing this vision? According to the existing limitations, investing for improving which manufacturing lever(s) can be better effective in implementing suitable production systems and achieving the competitive advantages of the organization? It is better for producing companies to follow policies to meet expectations of cus72 tomers in long term, to prevent from making sketchy decision and temporal improvements. Then the main question of the research is as follows: According to limitation of resources in Abzarsazi Industries such as budget and time(Employments and Managers), and considering the Criteria’s (Delivery, Cost, Quality, Performance, Flexibility, Innovativeness), improvement of which Manufacturing levers including human resources, organizational structure, substructures, production planning, process technology or supply resources can cover criteria of evaluating customers of Abzarsazi Industries? The power of organizations in response to rapid changes of the environment and accountability to demands of customers in current competition conditions are the most important advantages. Doing the present research and finding suitable manufacturing levers according to demands of customers are necessary to achieve this aim. The results of solving this problem are: ranking manufacturing strategies, choosing a suitable production system, choosing manufacturing levers and allocating resources optimally to support from manufacturing levers. Implementing procedures of the research increases customers’ satisfactions, production share relative to competitors and develops the organization more. Manufacturing strategy Organizations compete with each other to survive and achieve success and use a strategy to be better to survive and guarantee their success in long term. The nature of strategy is selection of different implementation of activities compared to competitors, so that it brings a unique value situation. According to Porter, a stable strategic situation is the result of a system of activities that any of them enhances the other. In strategy planning, three levels are defined for strategy: Corporate strategy, of Business strategy and functional strategy. The level of corporate strategy includes macro decisions of the company. The business strategy notes the way of competition at any business. According to the general direction of corporate strategy, business managers make decisions about competitive advantage of any business. Finally, functional strategies are designed for supporting function sectors of the company from corporate strategy and business strategy. [27] define the manufacturing strategy as a consistent model of decisions in production that is related to business strategy. According to this definition, manufacturing strategy is a body whose contents are decisions relatVolume 10 • Number 1 • March 2019 Management and Production Engineering Review ed to production and its two features are consistency of decisions with each other and their relations with business strategy [27]. Hill thinks the manufacturing strategy is the way of coordination for achieving consistency among production capabilities and success requirements [28]. Strategies show the way achieving the goals, so selecting correct and effective ways is critical. One of the suitable analytical models in manufacturing strategy and production system is Miltenburg strategy worksheet. Combining models and tools presented by other researchers, Miltenburg has presented a general framework for analyzing the manufacturing strategy of a company due to its convergence with production system and its capabilities [26]. Manufacturing outputs (Criteria’s) Production competitive priorities are one of the contextual elements of manufacturing strategy. In this element, the importance of any competitive priorities in production system is identified. The study of previous researches (to 1990s) about manufacturing strategy shows that there is a general agreement on four priorities of cost, quality, delivery and flexibility. Almost most theoreticians believe that in manufacturing strategy, the importance and priority of any of these four factors must be determined. Skinner believes that the emphasis of any of these priorities is a guideline for designing and planning a production system. For example, if in a production system, reduction of cost is chosen as the first priority, it shows that in production planning, cost reduction plans must be paid more attention. There are two views about competitive priorities: • the view of exchanging competitive priorities, • the view of high class global companies. Advocates of the first view believe that producing companies are not able to simultaneously achieve all competitive priorities and as a result, there is a king of exchange between selection of competitive priorities and more attention to one of competitive priorities leads to less attention to other priorities. However, advocates of the second view believe that producing companies established today and famous as high class global producers retract this rule and apply competitive priorities including cost, quality, flexibility and quick delivery simultaneously on their production system. Managers always try to offer a better and more diversified product more quickly. An organization being a pioneer in one or more of such cases can guarantee its victory against competitors. Industry offers six manufacturing outputs to the customers (Table 1). These six outputs are the result of Miltenburg’s clasVolume 10 • Number 1 • March 2019 sification and match of eleven variables estimated in the study of Miltenburg [26]. Table 1 Manufacturing outputs [26]. Delivery Time between taking orders and delivery to customers. How does a delay occur in most orders? How are delays? Cost Costs of materials, work force, overload and other resources used for producing a product Quality The extent of matching between materials and operations and demands and expectations of customers Performance The features of products and the extent in which features and design allow a product to do what other products can’t do Flexibility The extent in which the volume of the existing products can increase or decrease to respond to demands of customers quickly Innovativeness The ability of introducing new products quickly by changing the design of the existing products Manufacturing levers (alternatives) Most big organizations have three levels of strategy as corporate strategy, Business strategy and Functional strategy. Main factors at business level are production, marketing, financial affairs and human relations. Each of these factors must perform inside certain limitations and these limitations will effect on strategies. At the third level of strategic planning orders (functional level), each of functional areas as marketing, production, financial affairs, etc. provide strategies for supporting from certain goals of the organization. Manufacturing strategy is composed of eight main components: production technology, capacity, facilities and deployment, process technology, human resources, operational decisions, integration of suppliers and quality (Fig. 1). Fig. 1. Hierarchy of strategic planning in an organization. Many authors have expanded lists of strategic decision aspects or production subsystems. In one of famous lists, six subsystems are slated for pro73 Management and Production Engineering Review duction. These subsystems are called Manufacturing levers (factors) and are: human resources, organizational structures & controls, production planning & control, sourcing, process technology and facilities (Table 2). Table 2 Manufacturing levers. Human resources The level of skill, wage, educational policies and promotion, employment security and etc for all groups of staff Organizational Formal communications between groups structures (queues) in production systems. The way & controls of decision making, what is the dominant culture? Which system is used for evaluating performance and motivation? Production planning & control Rules and policies planning and controlling the following: flow of materials, activities of queued staff, operation of supporting from production and introducing new products Sourcing The amount of vertical integration, how does the production system manage that part of production and distribution system not owned? How are the relations with suppliers Process technology The type of equipment, the extent of automation, connection between production process parts Facilities The location, size and focus of individual shop floors, the type and time of variations in these shop floors Any variation at the level of functional strategies of the organizations creates adjustments in manufacturing levers. Small variations in manufacturing levers improve the current production system and extensive modulations of manufacturing levers can result in variation of the production system. In other words, the combination of the six factors determines perfectly that whether the production system is job shop or batch flow, OPL1 , EPL2 , FMS3 , JIT4 or continuous flow. When the existing production system changes to other system, wide modulations are required for all six factors. Research methodology The fuzzy TOPSIS Decision-making is the procedure to find the best alternative among a set of feasible alternatives. Sometimes, decision-making problems considering several criteria are called multi-criteria decision-making (MCDM) problems [30, 31] and of- ten require the decision makers to provide qualitative/quantitative assessments for determining the performance of each alternative with respect to each criterion, and the relative importance of evaluation criteria with respect to the overall objective of the problems. So, Multi-criteria decision making (MCDM) refers to screening, prioritizing, ranking, or selecting a set of alternatives (also referred to as “candidates” or “actions”) under usually independent, incommensurate or conflicting criteria [32]. These problems will usually result in uncertain, imprecise, indefinite and subjective data being present, which makes the decision-making process complex and challenging. In other words, decision-making often occurs in a fuzzy environment where the information available is imprecise/ uncertain. Therefore, the application of fuzzy set theory to multi-criteria evaluation methods under the framework of utility theory has proven to be an effective approach [33]. The overall utility of the alternatives with respect to all criteria is often represented by a fuzzy number, which is named the fuzzy utility and is often referred to by fuzzy multi-criteria evaluation methods. The ranking of the alternatives is based on the comparison of their corresponding fuzzy utilities [34]. The TOPSIS is extended for group decisionmaking in a fuzzy environment [30] and incorporation the fuzzy set theory and the basic concepts of positive and negative ideal to expand multi-criteria decision-making in a fuzzy environment [31] and fuzzy pair-wise comparison and the basic concepts of positive ideal and negative ideal points to expand multi-criteria decision-making in a fuzzy environment [35]. A fuzzy multi-criteria decision-making method based on concepts of positive ideal and negative ideal points to evaluate bus companies’ performance is also proposed [36]. Many ranking methods based on the fuzzy concepts have been proposed to solve the multiple criteria decision-making(MCDM) problems, e.g. [35, 37– 48] etc. However, to efficiently resolve the ambiguity frequently arising in available information and do more justice to the essential fuzziness in human judgment and preference, the fuzzy set theory [49], has been used to establish a fuzzy TOPSIS problem [30, 37–39, 43, 47, 49–51]. Fuzzy TOPSIS uses fuzzy set theory to express the uncertain comparison judgments as a fuzzy numbers. The main steps of fuzzy TOPSIS are as follows: Step 1: Construct the decision matrix as below: 1 Operator – Paced Line Flow – Paced Line Flow 3 Flexible Manufacturing System 4 Just in Time 2 Equipment 74 Volume 10 • Number 1 • March 2019 Management and Production Engineering Review C1 A1 A2 .. . Am Wj C2 e11 X e12 X e21 X e22 X em1 X em2 X f1 W f2 W ... ... ... .. . ... Cn e1n X emn X fn W ... For Cj− (j ∈ Cost) =⇒ Min xlij = ∅ =⇒ xN ij =   ∅ ∅ ∅ xu , xm , xl ij  2 a∗ = (Vijm − Ij+m ) − (Vijl − Ij+l ) , 2  b∗ = (Vijm − Ij+m ) − (Viju − Ij+u ) e2n X eij = (xl , xm xu ) , W fj = (wl , wm wu ). That: X ij ij ij j j j If there is multi decision maker, we should calculate the simple mean for all of decision makers. Step 2: Normalize the DM as below: For Cj+ (j ∈ Benefit) =⇒ Max xuij = p =⇒ xN ij =   xlij xm xu ij ij P , P , P ij where v uX o 2 u n n m − Vij − Ij−m + c∗ + d∗ di = t j=1 where 2  c∗ = (Vijm − Ij−m ) − (Vijl − Ij−l )  2 d∗ = (Vijm − Ij−m ) − (Viju − Ij−u ) Step 6: Ranking with relation below: CC i = ij u e =⇒ Normalize x e Step 3: Constructing weighted Normalized DM as below: Ve = u e⊗w e C1 A1 A2 .. . Am Ve11 Ve21 Vem1 C2 Ve12 Ve22 Vem2 ... ... ... .. . ... Cn Ve1n Ve2n Vemn m u u = (ulij × wjl , um ij × wj uij × w j ) Step 4: Determining the Fuzzy Positive & Negative Ideal Solution as below:   I + = Ie1+ , Ie2+ , . . . , Ien+   = MaxVei1 , MaxVei2 , . . . , MaxVein I− = So that the alternative with less CC i is the better alternative. SIR Method l m u Veij = u eij ⊗w ej = (wij , wij wij )  d− i d+ + d− i i Ie1− , Ie2− , . . . , Ien−    = MinVei1 , MinVei2 , . . . , MinVein Step 5: Calculating Distance between each Alternative & Fuzzy Positive & Negative Ideal Solution as below: v uX o u n n m  +m 2 ∗ + b∗ t d+ = − I + a V i ij j j=1 Volume 10 • Number 1 • March 2019 This method (Similarity & Inferiority Ranking: SIR) is one of the new and relative complex Multi Criteria Decision Making methods. There are preference functions in this method such as PROMETHEE, which after calculating the preference of each alternative to the criteria, and finding the paired preference functions of alternatives due to the criteria, superiority and inferiority matrix must be formed. At the next step weighted flow matrix is formed such as SAW and TOPSIS techniques, and alternatives can be ranked by calculating the flows. In SIR method we use such scores that these scores are obtained by comparing values of criteria. Assume that we have two alternatives A and A′ . To calculate the scores for these ordinal data with respect to criterion g (to be maximized), we use the preference structure {P, I} as follows: AP A′ (A is preferred to A′ ) iff g(A) > g(A′ ), AIA′ (A is indifferent to A′ ) iff g(A) = g(A′ ), where g(A) and g(A′ ) are the criteria values for A and A′ on criterion g. First we must form a decision matrix. In any multi-criteria decision making method, the decision maker determines a number of criteria. Let A1 , A2 , ..., Am be m alternative and (g1 , g2 , ..., gn ) be n cardinal criteria. gj (Ai ) is the performance of the i-th alternative Ai with respect to the j-th criteriong j . gj (.) Is a real-valued function (i = 1, 2, ..., m; j = 1, 2, ..., n) 75 Management and Production Engineering Review    D  g1 (A1 ) g1 (A2 ) .. . g2 (A1 ) g2 (A2 ) . g2 (Am ) g1 (Am ) g3 (A1 ) ··· .. . gn (A1 ) gn (A2 ) .. . ··· gn (Am )  Ij (A)i = P (Ak , Ai ) = k=1   .  P (A, A′ ) = f (d) = f (g(A) − g(A′ )), (1) P (A, A′ ) is the preference of A over A′ . m X fj (gj (Ak ) − gj (Ai )). k=1 (3) The superiority and inferiority indexes are used to form superiority matrix (S-matrix) and inferiority matrix (I-matrix). S-matrix provides information about the intensity of superiority of each alternative on each criterion, whereas, I-matrix provides information about the intensity of inferiority: The superiority matrix (S-matrix)   S1 (A1 ) S2 (A1 ) S3 (A1 ) Sn (A1 )  S1 (A2 ) S2 (A2 ) ··· Sn (A2 )    S . .. .. ..   . . . Then we weight each criterion. In this step we can use some method like AHP or Shannon entropy. Now we can compare the criteria value on each criterion [52]. The generalized criterion is calculated using the elements of the decision matrix. The differences between criteria values are used to estimate the intensity of the preference of A over A′ as per equation (1): ··· S1 (Am ) S2 (Am ) Brans [53] proposed six generalized criterion types which can be used to capture the characteristics of functions that represent the specified criteria. According to the attitude towards the preference structure and intensity of preference, the decision maker selects the generalized criteria (along with its associated parameter). Table 3 lists the types of generalized criteria. It should be noted that the intensity of preference for Types 3, 5, and 6 changes gradually from 0 to 1. In this research, Criterion with linear preference and indifference area has been used. For each alternative Ai , the superiority index Sj (Ai ) and inferiority index Ij (Ai ) with respect to the j-th criterion are calculated as follows: m m X X Sj (A)i = P (Ai , Ak ) = fj (gj (Ai ) − gj (Ak )), k=1 m X Sn (Am ) The inferiority matrix (I-matrix)  I1 (A1 ) I2 (A1 ) I3 (A1 ) In (A1 )  I1 (A2 ) I2 (A2 ) ··· In (A2 )  I .. .. . ..  . . I1 (Am ) I2 (Am ) ··· In (Am )    .  The superiority and inferiority indexes (arranged in S- and I-matrix, respectively) are aggregated into two types of global preference indexes: superiority flow (S-flow) ϕ≻ (.) and inferiority flow (I-flow) ϕ≺ (.). The S- and I-flows are basically the intensity of each alternative. The former flow measures how an alternative is globally superior to (or outranks) all the others, whereas, the latter flow measures how an alternative is globally inferior to (or outranked by) all the others. k=1 (2) Table 3 Generalized criteria. Criterion Type 1: True Criterion with linear preference ( f (d) = 1 0 if d ≥ 0 if d < 0 Type 4: Level Criterion 8 > < f (d) = > : 76 1 1 2 0 if d ≥ p if q < d ≤ p if d ≤ q Criterion Type 2: Quasi criterion ( f (d) = 1 0 if d ≥ q if d < q Type 5: Criterion with linear preference and indifference area 1 if d ≥ p d−q f (d) = if q < d ≤ p p−q 8 > < > : 0 if d ≤ q Criterion Type 3: Criterion with linear preference 1 if d ≥ p d if 0 < d ≤ p f (d) = p 8 > < > : 0 if d ≤ 0 Type 6: Gaussian criterion 8 < f (d) = :  1−e 0 −d2 σ2  if d ≥ 0 if d < 0 Volume 10 • Number 1 • March 2019 Management and Production Engineering Review There are two aggregation procedures which are used to obtain S- and I-flows. These are SAW and TOPSIS procedures. The SAW is considered the simplest and clearest procedure. It is usually used as a benchmark to compare the results obtained from other procedures. The TOPSIS is considered very logical way of approaching the discrete MCDM problems. However, it is computationally more complex than SAW [54]. The following sub-sections describe the structures of SAW and TOPSIS procedures. SAW procedure; S- and I-flows are calculated based on the weight of criteria (wj ) as follows: n X Wj Sj (Ai ), (4) ϕ≻ (Ai ) = j=1 ϕ≺ (Ai ) = n X Wj Ij (Ai ), (5) Ii− (Ai ) =  n X  Wj j=1 (0 ≤ λ ≤ ∞),   A+ I = min I1 (Ai ) , ..., min In (Ai ) i i = (I1+ , ..., In+ ),   A− I = max I1 (Ai ) , ..., max In (Ai ) i i = (I1− , ..., In− ). n X ϕn (Ai ) = ϕ≻ (Ai ) − ϕ≺ (Ai ) , ϕr (Ai ) = Wj = 1 (Wj ≥ 0). i=1 TOPSIS procedure; S-flow is calculated based on ideal solution AS+ and negative-ideal solution AS− for the superiority matrix (S-matrix) as follows: Si− (Ai ) , Si− (Ai ) − Si+ (Ai ) 1/λ  n X
λ Wj Sj (Ai ) − Sj+ Si+ (Ai ) =   ϕ≻ (Ai ) = j=1 (0 ≤ λ ≤ ∞), 1/λ  n X
λ Wj Sj (Ai ) − Sj− Si− (Ai ) =   j=1  (6) (7) (8) (0 ≤ λ ≤ ∞),  A+ S = max S1 (Ai ), ..., max Sn (Ai ) i i = (S1+ , ..., Sn+ ),   A− S = min S1 (Ai ), ..., min Sn (Ai ) i i = (S1− , ..., Sn− ). (9) (10) I-flow is calculated based on ideal solution IS+ and negative-ideal solution IS− for the inferiority matrix (I-matrix) as follows: Ii+ (Ai ) ϕ≺ (Ai ) = − , Ii (Ai ) − Ii+ (Ai ) 1/λ  n  X
λ Wj Ij (Ai ) − Ij+ Ii+ (Ai ) =   j=1 (0 ≤ λ ≤ ∞), Volume 10 • Number 1 • March 2019 (11) (12) (13) (14) (15) Net and relative flows; Net flow (n-flow) and relative flows (r-flow) are calculated utilizing S- and I-flows as per equations (8) and (9): j=1 where 1/λ
λ Ij (Ai ) − Ij−  (ϕ≻ ϕ≻ (Ai ) . (Ai ) − ϕ≺ (Ai )) (16) (17) Four complete ranking are obtained from S-, I-, n- and r-flows. These are S-ranking (ℜ> ), I-ranking (ℜ< ), n-ranking (ℜn ), and r-ranking (ℜr ). The Sranking ℜ> = {P> , I> }, is obtained based on the descending order of ϕ≻ (Ai ) as follows: Ai P > Ak iff ϕ≻ (Ai ) > ϕ≻ (Ak ) , (18) Ai I > Ak iff ϕ≻ (Ai ) > ϕ≺ (Ak ) . (19) The I-ranking ℜ< = {P< , I< }, obtained based on the ascending order of ϕ≺ (Ai ) as follows: Ai P < Ak iff ϕ≺ (Ai ) > ϕ≺ (Ak ) , (20) Ai I < Ak iff ϕ≺ (Ai ) = ϕ≺ (Ak ) . (21) The n-ranking and r-ranking are obtained based on the descending order of n- and r-flows, respectively. Partial ranking (ℜ) is obtained by combining Sranking ℜ> , and I-ranking ℜ< , in a partial ranking structure as follows: ℜ = {P, I, R} = ℜ> ∩ ℜ< . (22) The intersection principle, proposed by Brans et al. (1986) and Roy et al. (1992), is adopted to compare any two alternatives as follows: Preference relation P : APA′ iff (AP > A′ and AP < A′ ) or (AP < A′ and AI > A′ ) or (AI > A′ and AP < A′ ). (23) Indifference relation I: AIA′ iff AI > A′ and AI < A′ . (24) 77 Management and Production Engineering Review Incomparability relation R: x́upq ARA′ iff (AP > A′ and A′ P < A) (25) or (A′ P < A and AP > A′ ). Fuzzy SIR stepwise procedure Step 1: Construct the Decision Matrix as below: e e X A1 X11 e e X A2 . .. . .. Am Wj 21 e f W ... X12 ... X1n 22 . .. ... . .. . .. Xm2 ... e f W Xm1 1 e e X C2 2 Cn A1 A2 . .. Am 2n e f W Xmn ... Wj n I eij = (xl , xm xu ) , W fj = (wl , wm wu ) That: X ij ij ij j j j If there is multi decision maker, we should calculate the simple mean or weighted mean for all of decision makers. Step 2: Construct the Pair-wise Matrix as below: C1 A1 A2 .. . Am A1 ´ X11 ´ X21 .. . ´ Xm1 A2 ´ X12 ´ X22 .. . ´ Xm2 e e e e e e e´ij = (x́l x́m x́u ) That: X ij ij ij x́lpq = ( xlpj − xliq ; 0; ... ... ... .. . ... Am ´ X1m ´ X2m .. . ´ Xmm e e = A1 e P es C1 S11 = x́m pq = m xm pj − xiq ; 0; > iq otherwise C2 1 1j e P es f f W C P Ie C Ie = 1 ... 2 ... ... e P Ie A2 .. . Am Iij = f Wj f W1 W2 + n 1j k j k k 1j k ij 2 1 i1 P se P weϕeP se Cn S1n = ... W1 11 e ... Sij = f C P Ie P weϕeP se Ie = Wn + n n in 1n k k j k 1j k ij ... f Wn Step 4: Combining the TOPSIS approach with FSIR in step3 and ranking by TOPSIS as below: S e wj A+ A− I u xlpj +xm pj +xpj 3 u xl +xm iq +xiq 3 wj > iq otherwise A+ A− (26) ( u xl +xm iq +xiq 3 u xlpj +xm pj +xpj 3 xupj − xuiq ; 0; (28) Step 3: Construct a Superiority & Inferiority Matrix as below: S C1 ( u xlpj +xm pj +xpj 3 u xl +xm iq +xiq 3 I+ I− , > iq otherwise (27) ϕ− = I− I+ + I− (29) Step 5: Ranking by FSIR as below: 5.1. 1 ϕ+ ⊕ϕ− ϕ+ ⊕ ϕ− A1 A2 . .. Am 78 ea i u = (ali ,am i ai ) eb = (b ,b i l i m bu ) i i Ratio Flow (Doubis & Prade) ϕ+ ϕ+ ⊕ϕ− ec = (c ,c i l i Doubis & Prade Method m cu ) i i Volume 10 • Number 1 • March 2019 Management and Production Engineering Review 5.2. A1 A2 .. . Am ϕ+ ϕ e+ 1 ϕ e+ 2 .. . ϕ e+ m That for example the number (−15.24152) in column ϕ+ is calculated as below: ϕ− ϕ e− 1 ϕ e− 2 .. . ϕ e− m Net-Flow ϕ en1 = ϕe+ e− 1 ⊖ϕ 1 + n ϕ e2 = ϕe2 ⊖ ϕe− 2 .. . ϕ enm = ϕe+ e− m⊖ϕ m bm i −15.24152 = (−0.40594 ∗ 0.9375) Yager Method +(−0.625 ∗ 4.375). 1 = m, ai bli = au − am 1 − i m2 i , m ai ai bui = l 1 am i − ai − , am am2 i i (30) +m m cm .bi , i = ϕi +m m l m + (ϕ+m − ϕ+l cli = cm i − [(bi − bi ).ϕi i i ).bi ], +m m u + (ϕ+u − ϕ+m ).bm cui = cm i ]. i − [(bi − bi ).ϕi i i (31) Case study (Evaluation and Selecting of Manufacturing Levers) Step 1: Now we use Fuzzy SIR to evaluate the Manufacturing Levers. We will use a numerical illustration to show our method. In first, set up the fuzzy decision making matrix of Manufacturing Levers evaluation according to opinions of five experts in Abzarsazi Industries of Iran with fuzzy linguistic variables. On the other hand, in this step, a questionnaire prepared and five experts in Abzarsazi Industries completed it with linguistic variables. To convert the fuzzy linguistic variables to fuzzy number can use the Table 4. Table 4 Linguistic variables for paired comparison criteria. VL (Very low) 0 0.5 2 L (Low) 1 2 3 ML (Medium Low) 2 3.5 4 M (Medium) 4 5 6 MH (Medium High) 5 6.5 8 H (High) 7 8 9 VH (Very High) 8 9.5 10 So, the fuzzy decision making matrix of Manufacturing Levers evaluation according to opinions of five experts in Abzarsazi Industries of Iran with fuzzy number will extracted, and finally, the Integrated Fuzzy Decision Matrix will be as Fig. 2. Step 2: Construct the Pair-Wise Matrices according to all of criteria’s. Step 3: Construct a Superiority & Inferiority Matrix as Figs 3 and 4. Volume 10 • Number 1 • March 2019 +(0 ∗ 6.0625) + (0.29631 ∗ 5.875) +(−0.76563 ∗ 4.9375) + (−1.1875 ∗ 5.5625) That for example the numbers (−0.13312, 0.062514, 0.649049) in table above are calculated as below:   −0.40594 ∗ 0.9375, −0.13312 = − e∗   0.09375 0.062514 = − ∗ 1.90625, e∗   0.59375 0.649049 = ∗ 3.125 e∗ where e∗ = max (0.59375, 2.85875, 1.96825, 1.030938, 0, 2.187). And the number (0.339273) in column ϕ+ is calculated as 16.17266 . 0.339273 = 31.49575 + 16.17253 That A+, A− are maximum and minimum of column numbers. Step 4: Combining the TOPSIS approach with FSIR in Step 3 and ranking by TOPSIS as Fig. 5. Step 5: Ranking by FSIR as Fig. 6. Conclusion In this paper, Manufacturing levers (Alternatives) are examined and analyzed as the main elements of manufacturing strategy. Also, manufacturing outputs (Criteria’s) are identified that are competitive priorities of production of any organization. Next, using a hybrid approach of FSIR and TOPSIS, alternatives (manufacturing levers) are ranked. Generally, evaluation and selecting of Manufacturing Levers and its problems as well as subjective judgment of appraiser are vague and uncertain, and so fuzzy set theory helps to convert DM preferences and judgments into meaningful results by applying linguistic values to measure each criterion with respect to every levers. In this paper, a multi-criteria group decision making model has been developed based on fuzzy set theory to efficiently deal with the ambiguity of the decision making problems in practical cases to evaluate the levers and comparing them. Fuzzy SIR is a helpful tool in multi-criteria decision making, in this method two superiority and inferiority flows 79 Management and Production Engineering Review show that an alternative how can be preferred to another alternatives. Other flows (n-flow and r-flow) in this method show that which of superiority or inferiority flow is more powerful than another. It makes decision making process more reliable. So dealing with the selected manufacturing levers and promoting them, an organization makes customers satisfied with the least cost and time. Attachments: Fig. 2. The Integrated Fuzzy Decision Matrix. Fig. 3. The Superiority Matrix. Fig. 4. The Inferiority Matrix. Fig. 5. Combining the TOPSIS approach with FSIR in step3 and ranking by TOPSIS. Fig. 6. Final ranking using FSIR. 80 Volume 10 • Number 1 • March 2019 Management and Production Engineering Review References [1] Skinner W., Manufacturing-missing link in corporate strategy, Harvard Business Review, 136–145, 1969. [2] Hayes R.H., Wheelwright S.C., Restoring our Competitive Edge, Free Press, New York, 1984. [3] Kotha S., Orne D., Generic manufacturing strategies: A conceptual synthesis, Strategic Management Journal 10, 211–231, 1989. 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