Semiconductor Fuzzy Multiple Objectives Programming To DEAM - Online Article
Introduction
With the increasing use of total quality management (TQM) and just-in-time (JIT) concepts within a wide range of firms, the question of supplier selection has become extremely important (Verma and Pullman 1998). Bankar and Khoska (1995) classified the supplier selection process as an important operational management (OM) decision . They suggested that OM research should attempt to identify the supply chain management practices that provide the most competitive advantage. There are also many articles that highlight tradeoffs among the items of quality, cost, and delivery performance in the supplier selection process (Ben-Akiva and Lerman 1991; Louviere 1988). For example, these conceptual articles emphasized that managers should not select suppliers only by low cost, but should consider quality, delivery performance, as well as other attributes (Verma and Pullman 1998). However, the empirical results show the relative importance of different supplier attributes in actual choices of suppliers is not the same as the perceived importance of the attributes. For example, it appears that management perceives quality to be the most important attribute, however, they assign greater weight to delivery performance and/or cost when choosing a supplier. This paradox often occurs in companies, thus, how to quantify the tradeoff issues to reveal upper management considerations in supplier selection is an important research topic.
In a semiconductor factory, hundreds of types of raw materials are used for manufacturing, according to the evaluation of suppliers. A supplier’s performance would strongly impact manufacturing costs, yields, and industrial fluency (Park, et al. 2001; Verma and Pullman 1998), therefore, a method to select the proper suppliers is a critical issue. The Sony Fukushima Corporation reported that it has basic purchasing guidelines using quality, cost, delivery, service, and environmental (QCDSE) factors (Sony Fukushima Corporation 2003). In practice, the same evaluating items are also used in a semiconductor manufacturing company. Our real example is from a semiconductor manufacturing company in China, called company X for anonymity purposes. In company X, each quarter normally places responsibility on the members of the Incoming Quality Control (IQC) Department to evaluate and rank a supplier’s performance for the Procurement Department’s reference regarding order allocation. The members of IQC assign weights in QCDSE, respectively, and then they tally the scores, thus ranking the suppliers. The better the ranking of a supplier, the more purchases are allocated to this supplier in the next order. The inherit weakness of this ranking procedure is its subjective nature, because weights can be assigned according to individual preferences or prejudices, some supplier could obtain a higher ranking resulting in benefiting less-deserving suppliers, and thereby weaken the trustworthiness of supplier management. To allow a supply chain to work smoothly, cooperation between suppliers and the semiconductor company is required. Running an open, upright honest system with no bribes is highly required in company X. Thus, the development of an objective method for reviewing QCDSE factors is grounded in empirical work. Therefore, the input/output concept of DEA is used to reflect these trade-offs and solve the supplier selection issue.
Charnes et al. (1978) developed data envelopment analysis (DEA) to evaluate the relative efficiencies of each decision making unit (DMU), containing multiple input/output variables (Ben-Akiva and Lerman 1991). DEA is an assessment approach in management science, which has been extensively adopted to assess the efficiency of multiple-input and multiple-output systems. There are many successful cases of application in non-profit businesses, such as schools, libraries, and public hospitals, in addition to for profit businesses, such as banks and hotels, as presented in (Liu, et al. 2003; Schaffnit, et al. 1997; Brockett, et al. 1997). However, it has not been widely used for semiconductor manufacturing applications, such as a buyer’s supplier ratings in IQC.
However, two reasons make the conventional DEA unable to directly rank the DMU. One is unrealistic weight; and the other is the insufficient DMU numbers (Chiang and Tzeng 2000; Chiang and Tzeng 2003 ). The concept of a common set of weights, as is shown in (Roll, et al. 1991; Roll and Golany 1993), is offered as an alternative for dealing with the issue of unrealistic weight. Consequently, the FMOP approach was proposed to improve the discrimination power of the classic DEA method (Chiang and Tzeng 2000; Chiang and Tzeng 2003). Common weights for all DMU could be simultaneously derived with an acceptably large number of efficient DMU. There are two advantages to using this method: (1) improving the discriminating power of DEA omitting relative viewpoint evaluation of DMU weights, therefore, all generated efficiencies of all DMU with a common base can be directly ranked; (2) solution to the multiple objective programming problems, without the restriction of limiting the number of DMU. Because supplier ranking is related to purchase allocation, this method is adopted to simultaneously evaluate and rank the suppliers.
DEA and Fuzzy Multiple Objective Programming for DEA
Before introducing DEA models for assessment in efficiency, common notations, as used in the follow-up, are summarized below.
Indices:
k – DMU, k = 1, …, n;
i – inputs, i = 1, …, r;
j – outputs, j = 1, … , s;
Data:
xik - the value of ith input for the kth DMU;
yjk- the value of jth output for the kth DMU;
ε - a small positive number called the non-Archimedean quantity;
Variables:
vi, uj - virtual multipliers for input i, output j respectively ; - unitary weight for all DMU in the fuzzy multiple objective programming to DEA;
hk - the efficiency for the kth DMU by the conventional DEA;
zk - the efficiency for the kth DMU by FMOP to DEA.
CCR Model of DEA
This model was originally proposed by Charnes et al. (Charnes, et al. 1978). According to their model, for each DMUk, the following model must be solved one time. If there are n DMU, the following model must be performed n times to generate the efficiency hk for DMUk for k = 1, 2,…, n.
The objective here is to find the largest sum of the weighted outputs of the DMUk, while keeping the sum of its weighted inputs at unit value 1, and forcing the ratio of the sum of weighted outputs to the sum of weighted inputs for any DMU to be less than or equal to 1. The efficiency ratio of each DMU is calculated by its own best multipliers, not by common multipliers for all DMU. Thus, this model often results in several efficient DMU in order to construct an efficient frontier, which would not meet the supplier’s performance evaluation. The efficiency results for all DMU cannot be directly ranked. Thus, FMOP to DEA (Chiang and Tzeng 2000; Chiang and Tzeng 2003 ) is adopted to rate the suppliers.
FMOP to DEA
FMOP to DEA provides a unitary weight for all DMU, which are evaluated by an equal standard (Chiang and Tzeng 2000; Chiang amd Tzeng 2003 ). By this approach, we can obtain the efficiency rating of each DMU more fairly. Moreover, all DMU can be treated simultaneously, which makes it effective in handling large numbers of DMU.
Model 1
- By considering the efficiencies of all DMU, it can establish a multiple objective linear programming (MOLP) model, as shown in Model 1, which can be solved by the fuzzy multiple objective linear programming (FMOLP) approach, as proposed by Zimmermann (Zimmermann 1978). FMOP to DEA adopts this approach to obtain common weights, which can maximize all DMU’s efficiencies.
The concept of FMOLP utilizes membership function transfers of multiple objective functions into one objective function. The membership function is as follows: - Where and are the negative ideal solution and the positive ideal solution, respectively, for the value of the objective function , such that the degree of membership function is [0, 1].
The degree of membership function of in refers to the achievement level of the efficiency ratio for DMUk .The problem of obtaining the maximum decision is to choose . - Then, let the achievement level of the objective functions for Model 1 to be at a larger level
- Eq. (4), via variable transformation, has transformed where zj is a convex combination of and ; Eq. (3) can be rewritten as Eq. (5). According to the concept of multiple objective linear programming, we can determine a weight that satisfies all DMU restrictions. The weight , is the common weight of all DMU, which are evaluated on a consistent standard of ranking.
- By rewriting Model 1, Model 2 can be obtained. Model 2 is nonlinear programming, which can be solved by the bisection method, as proposed by Sakawa and Yumine (1983). By employing Model 2, a common weight can be determined for all DMU, which directly rank all DMU.
Introduction
With the increasing use of total quality management (TQM) and just-in-time (JIT) concepts within a wide range of firms, the question of supplier selection has become extremely important (Verma and Pullman 1998). Bankar and Khoska (1995) classified the supplier selection process as an important operational management (OM) decision . They suggested that OM research should attempt to identify the supply chain management practices that provide the most competitive advantage. There are also many articles that highlight tradeoffs among the items of quality, cost, and delivery performance in the supplier selection process (Ben-Akiva and Lerman 1991; Louviere 1988). For example, these conceptual articles emphasized that managers should not select suppliers only by low cost, but should consider quality, delivery performance, as well as other attributes (Verma and Pullman 1998). However, the empirical results show the relative importance of different supplier attributes in actual choices of suppliers is not the same as the perceived importance of the attributes. For example, it appears that management perceives quality to be the most important attribute, however, they assign greater weight to delivery performance and/or cost when choosing a supplier. This paradox often occurs in companies, thus, how to quantify the tradeoff issues to reveal upper management considerations in supplier selection is an important research topic.
In a semiconductor factory, hundreds of types of raw materials are used for manufacturing, according to the evaluation of suppliers. A supplier’s performance would strongly impact manufacturing costs, yields, and industrial fluency (Park, et al. 2001; Verma and Pullman 1998), therefore, a method to select the proper suppliers is a critical issue. The Sony Fukushima Corporation reported that it has basic purchasing guidelines using quality, cost, delivery, service, and environmental (QCDSE) factors (Sony Fukushima Corporation 2003). In practice, the same evaluating items are also used in a semiconductor manufacturing company. Our real example is from a semiconductor manufacturing company in China, called company X for anonymity purposes. In company X, each quarter normally places responsibility on the members of the Incoming Quality Control (IQC) Department to evaluate and rank a supplier’s performance for the Procurement Department’s reference regarding order allocation. The members of IQC assign weights in QCDSE, respectively, and then they tally the scores, thus ranking the suppliers. The better the ranking of a supplier, the more purchases are allocated to this supplier in the next order. The inherit weakness of this ranking procedure is its subjective nature, because weights can be assigned according to individual preferences or prejudices, some supplier could obtain a higher ranking resulting in benefiting less-deserving suppliers, and thereby weaken the trustworthiness of supplier management. To allow a supply chain to work smoothly, cooperation between suppliers and the semiconductor company is required. Running an open, upright honest system with no bribes is highly required in company X. Thus, the development of an objective method for reviewing QCDSE factors is grounded in empirical work. Therefore, the input/output concept of DEA is used to reflect these trade-offs and solve the supplier selection issue.
Charnes et al. (1978) developed data envelopment analysis (DEA) to evaluate the relative efficiencies of each decision making unit (DMU), containing multiple input/output variables (Ben-Akiva and Lerman 1991). DEA is an assessment approach in management science, which has been extensively adopted to assess the efficiency of multiple-input and multiple-output systems. There are many successful cases of application in non-profit businesses, such as schools, libraries, and public hospitals, in addition to for profit businesses, such as banks and hotels, as presented in (Liu, et al. 2003; Schaffnit, et al. 1997; Brockett, et al. 1997). However, it has not been widely used for semiconductor manufacturing applications, such as a buyer’s supplier ratings in IQC.
However, two reasons make the conventional DEA unable to directly rank the DMU. One is unrealistic weight; and the other is the insufficient DMU numbers (Chiang and Tzeng 2000; Chiang and Tzeng 2003 ). The concept of a common set of weights, as is shown in (Roll, et al. 1991; Roll and Golany 1993), is offered as an alternative for dealing with the issue of unrealistic weight. Consequently, the FMOP approach was proposed to improve the discrimination power of the classic DEA method (Chiang and Tzeng 2000; Chiang and Tzeng 2003). Common weights for all DMU could be simultaneously derived with an acceptably large number of efficient DMU. There are two advantages to using this method: (1) improving the discriminating power of DEA omitting relative viewpoint evaluation of DMU weights, therefore, all generated efficiencies of all DMU with a common base can be directly ranked; (2) solution to the multiple objective programming problems, without the restriction of limiting the number of DMU. Because supplier ranking is related to purchase allocation, this method is adopted to simultaneously evaluate and rank the suppliers.
DEA and Fuzzy Multiple Objective Programming for DEA
Before introducing DEA models for assessment in efficiency, common notations, as used in the follow-up, are summarized below.
Indices:
k – DMU, k = 1, …, n;
i – inputs, i = 1, …, r;
j – outputs, j = 1, … , s;
Data:
xik - the value of ith input for the kth DMU;
yjk- the value of jth output for the kth DMU;
ε - a small positive number called the non-Archimedean quantity;
Variables:
vi, uj - virtual multipliers for input i, output j respectively ; - unitary weight for all DMU in the fuzzy multiple objective programming to DEA;
hk - the efficiency for the kth DMU by the conventional DEA;
zk - the efficiency for the kth DMU by FMOP to DEA.
CCR Model of DEA
This model was originally proposed by Charnes et al. (Charnes, et al. 1978). According to their model, for each DMUk, the following model must be solved one time. If there are n DMU, the following model must be performed n times to generate the efficiency hk for DMUk for k = 1, 2,…, n.
The objective here is to find the largest sum of the weighted outputs of the DMUk, while keeping the sum of its weighted inputs at unit value 1, and forcing the ratio of the sum of weighted outputs to the sum of weighted inputs for any DMU to be less than or equal to 1. The efficiency ratio of each DMU is calculated by its own best multipliers, not by common multipliers for all DMU. Thus, this model often results in several efficient DMU in order to construct an efficient frontier, which would not meet the supplier’s performance evaluation. The efficiency results for all DMU cannot be directly ranked. Thus, FMOP to DEA (Chiang and Tzeng 2000; Chiang and Tzeng 2003 ) is adopted to rate the suppliers.
FMOP to DEA
FMOP to DEA provides a unitary weight for all DMU, which are evaluated by an equal standard (Chiang and Tzeng 2000; Chiang amd Tzeng 2003 ). By this approach, we can obtain the efficiency rating of each DMU more fairly. Moreover, all DMU can be treated simultaneously, which makes it effective in handling large numbers of DMU.
Model 1
- By considering the efficiencies of all DMU, it can establish a multiple objective linear programming (MOLP) model, as shown in Model 1, which can be solved by the fuzzy multiple objective linear programming (FMOLP) approach, as proposed by Zimmermann (Zimmermann 1978). FMOP to DEA adopts this approach to obtain common weights, which can maximize all DMU’s efficiencies.
The concept of FMOLP utilizes membership function transfers of multiple objective functions into one objective function. The membership function is as follows: - Where and are the negative ideal solution and the positive ideal solution, respectively, for the value of the objective function , such that the degree of membership function is [0, 1].
The degree of membership function of in refers to the achievement level of the efficiency ratio for DMUk .The problem of obtaining the maximum decision is to choose . - Then, let the achievement level of the objective functions for Model 1 to be at a larger level
- Eq. (4), via variable transformation, has transformed where zj is a convex combination of and ; Eq. (3) can be rewritten as Eq. (5). According to the concept of multiple objective linear programming, we can determine a weight that satisfies all DMU restrictions. The weight , is the common weight of all DMU, which are evaluated on a consistent standard of ranking.
- By rewriting Model 1, Model 2 can be obtained. Model 2 is nonlinear programming, which can be solved by the bisection method, as proposed by Sakawa and Yumine (1983). By employing Model 2, a common weight can be determined for all DMU, which directly rank all DMU.
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