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Dotol, Fant, Melon, & Zhou The.Case.Study To illustrate the network design optimization procedure, we consider a case study inspired by an example proposed in Luo et al. (2001). The target product is a typi-cal desktop computer system consisting of a computer, hard-disk driver, monitor, keyboard, and mouse. The SC is composed of N =6 stages: suppliers, manufactur-ers, distributors, retailers, consumers, and recyclers. In the following, we apply and discuss the different steps of the proposed design procedure for this case study. Candidate.Selection The first module of the DSS structure in Figure 1 has to perform the candidate selec-tion for each stage of the IESC case study. As an example, we focus on the partner selection for the second stage, that is, the manufacturers. Obviously, the methodol-ogy proposed for manufacturer selection is applicable to each stage of the IESC. Table 1. Performance matrix of manufacturers with scores for each criterion n1c n2c n3c E 80 70 20 RM 30 15 60 F 10 90 85 FL 40 10 30 T 65 30 80 Q 85 80 60 n4c n5c n6c n7c n8c n9c 10 90 35 35 60 30 80 70 40 90 30 75 55 30 60 40 15 20 55 75 80 15 90 45 30 80 10 45 45 20 50 65 50 60 15 10 c c c c c c 10 11 12 13 14 15 30 30 65 70 40 80 10 60 20 30 85 40 10 35 45 25 40 20 40 20 40 20 30 20 30 90 35 40 15 35 40 15 60 45 60 30 Table 2. Thresholds and weights for the Electre method Indifference threshold Preference threshold Veto threshold Weights E RM F FL T Q 10 25 20 5 10 20 20 45 30 10 20 30 35 85 60 30 60 60 1.0 0.6 0.8 0.6 0.6 0.6 Table 3. Manufacturers’ rankings according to the Electre method for the case study Position 1 2 3 5 6 7 8 9 10 12 13 Manufacturer n5c n1c n3c, n12c n8c n6c n2c c c 13 15 n7c,n11c n10c n4c, n9c, c 14 Copyright © 2007, Idea Group Inc. Copying or distributing in print or electronic forms without written permis-sion of Idea Group Inc. is prohibited. Service Computing for Design and Reconfiguration of Integrated E-Supply Chains 343 Figure 4. The stages of the IESC network for the case study Stage P1 18,e18 Stage P2 n1 17, 17 n2 m25 m15 n m35 5 m45 57 4 m4,10,e4,10 Stage P3 Stage P4 Stage P5 n6 m68 n8 m8,10,e8,10 m5,10 m78,e78 7,10 7,10 m9,10,e9,10 n7 m79,e79 n9 m59 m11,5 Stage P6 m10,11 n11 m10,12 n12 m10,13 n13 10,14 n14 m14,3 Supplier Manufacturer Distributor Retailer Consumer Recycler The first step of the procedure determines the candidate set of the second stage, for example, P c={n c,n c …,n c}, where we assume that 15 candidates are competing to join the second stage of the IESC. In the second step of the procedure, the decision makers define the most relevant criteria for the selection: F, RM, E, FL, T, and Q. Obviously, such a choice can only be based on experience and expert knowledge of the IESC processes, products, and actors. Then, in the third step, a data-analysis system assigns the scores to each candidate. Table 1 reports the performance matrix assigned to each alternative manufacturer. Subsequently, since the Electre method is employed, the decision makers assign the thresholds and weights for the case study as shown in Table 2. Using the thresholds of Table 2, the Electre method seeks for an outranking relation. Table 3 shows the final ranking of the candidates, obtained with a Matlab implementation of the method that employs the intrinsic characteristic of the Matlab programming environment to operate with matrices (MathWorks Inc., 2002). The reader is referred to Mousseau et al. (2000) for a discussion on the definition of the decision parameters required by the Electre method, and to a previous work by the authors (Dotoli et al., 2005) for further insights on the provided example. According to the results in Table 3, the decision maker selects P ={n c} if one manufacturer only is to be included in the network. On the contrary, if several manufacturers have to be incorporated in the IESC, a corresponding number of candidates are selected from Table 3 starting from the one with the highest posi- Figure 5. The digraph associated with the IESC of the case study n1 n2 n3 n4 x x4 x3 x2 x8 x5 n5 x6 10 x7 11 n6 12 x9 n7 15 x22 13 n8 16 18 n10 19 14 n9 17 x21 x20 x23 n11 n12 n13 n14 Copyright © 2007, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. Dotol, Fant, Melon, & Zhou tion. For instance, if two manufacturers are to be included in the IESC, the decision maker selects P ={n c,n c}. Note that the former choice is made in the following so that one manufacturer only is selected. The IESC network obtained after the iteration of the candidate-selection technique for each stage is depicted in Figure 4, while its digraph is shown in Figure 5, com-posed as follows: four suppliers, one manufacturer, two distributors, two retailers, one consumer, and four recyclers, for a total of N=14 partners. The data for the IESC are reported in Table 4 (Luo et al., 2001), showing the value of each performance index Mq with q=1, …, 4 associated with the links of the considered IESC. More precisely, the adopted performance indices are total cost (M ), energy (M ), CO2 emission (M3), and cycle time (M4). We indicate generically by cycle time Table 4. Data sheet for the network links in the case study Links Edges Variables Cost (M1) in $ Energy (M2) in MJ CO emission Cycle time (M3) in KgCE (M4) in hours m18, e18 y18 x1 m17, e1,7 y17 x2 m15 y15 x3 m25 y25 x4 m35 y35 x5 m45 y45 x6 m4,10, e4,10 y4,10 x7 m56 y56 x8 m5,10 y5,10 x9 m57 y57 x10 m59 y59 x11 m68 y68 x12 m78, e78 y78 x13 m7,10, e7,10 y7,10 x14 m79, e79 y79 x15 m8,10, e8,10 y8,10 x16 m9,10, e9,10 y9,10 x17 m10,11 y10,11 x18 m10,12 y10,12 x19 m10,13 y10,13 x20 m10,14 y10,14 x21 m11,5 y11,5 x22 m14,3 y14,3 x23 41.80 359.00 0.87 19.30 46.70 332.00 0.74 16.80 319.00 1479.00 2.21 12.50 308.00 1776.00 2.19 12.80 238.00 1540.00 3.10 16.20 246.00 1409.00 1.47 10.20 53.90 369.00 30.20 5.30 448.00 3618.00 8.74 19.20 379.00 3542.00 296.00 4.20 358.00 2885.00 6.26 16.20 358.00 3259.00 223.00 3.90 20.89 13.40 0.87 121.70 25.20 16.40 1.10 123.00 22.90 35.10 2.58 65.80 20.70 9.18 0.59 61.30 64.00 90.40 0.56 120.30 58.10 4.68 0.13 100.00 0.42 4.80 0.37 0.80 0.42 4.80 0.37 0.80 0.42 4.80 0.37 0.80 0.42 4.80 0.37 0.80 -18.00 -11.00 0.74 4.80 -28.00 -6.60 1.10 6.50 Copyright © 2007, Idea Group Inc. Copying or distributing in print or electronic forms without written permis-sion of Idea Group Inc. is prohibited. Service Computing for Design and Reconfiguration of Integrated E-Supply Chains 345 associated with an m-link the related time required by the transportation and/or the production process. The considered performance index values are reported in Table 4 and depend on the type of link (m- and e-link, or m-link only), the distance between the connected SC partners, the transportation mode (truck, car, airplane, etc.), and the type of material to be transported. In particular, the cost and energy performance indices reported in the last two rows of Table 4, respectively associ-ated with links m and m , are negative. In fact, in the recycler stage P , partner n is a demanufacturer with an output link m connecting to manufacturer n , and partner n is a material recoverer with an output link m connecting to supplier n (see Figure 4). Hence, the total cost and energy associated with links m and m are negative; that is, they correspond to recycling materials and parts. According to the data in Table 4, the IESC in Figure 4 exhibits the m- and e-links while the remaining, links are m-links. Moreover, 0the ,associated ,digraph D=(N,E) depicted in Figure 5 has N=14 nodes and E=23 edges. Obviously, edges y , y , y , y , y , y , y , and y are associated both with m- and e-links, and the remaining edges of the digraphs are associated with m-links only. Moreover, each edge in E is labeled by its corresponding variable x with h=1, …, E used in the optimization procedure and defined in the previous section. Optimization.Model Various computational experiments are performed to minimize cost, energy con-sumption, CO emission, and total lead time (TLT). In particular, the TLTis defined as the total time elapsed from the instant at which the raw material begins its travel until the instant the finished product is delivered to consumers. Furthermore, a multiobjective function for Problem 2 is chosen. The solutions are obtained via the well-known two-phase simplex method in the Matlab framework (MathWorks Inc., 2002; Venkataraman, 2001). The first step of the optimization is to define the model constraints. Then Problem 1 or Problem 2 is solved. BOM constraints. The component supplier constraints are obtained assuming that the BOM of the second stage in Figure 4, representing the manufacturer, is the fol-lowing: computer (C), hard-disk driver (H), monitor (M), and keyboard and mouse (K). We suppose that C is produced by n and n ; H is produced by n , n , and n ; M is produced by n , n , and n ; and K is produced by n and n (Luo et al., 2001). Hence, with reference to Figure 5, the constraints imposed on the variables labeling the edges are as follows: Copyright © 2007, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. Dotol, Fant, Melon, & Zhou x3 + x4 ≥1 x3 + x4 + x5 ≥1. (18) x4 + x5 + x6 ≥1 x5+x6 ≥1 Path constraints. The case study includes only one manufacturer and only one consumer (node n of stage P and n of P , respectively, in Figure 4). Hence, a path between nodes n and n is needed. Consequently, we build the N×E incidence matrix I associated with digraph D. Moreover, we define the 23-vector b =[b b … b ] with b =-1 b =1 and b =0 for p≠5, 10 and p=1, …, 23. The constraint that imposes the presence of a path starting from node n and ending in node n is written as follows: IM x≥b5,10. (19) Mutual-exclusion constraints. It is assumed that one and only one partner is to be included in the IESC recycler stage (stage P in Figure 4). Furthermore, only one type of commerce has to be present between the second and third stages, and one and only one m and e-link has to be present among the first stage and the others. Hence, with reference to Figure 5, the mutual-exclusion constraints are the following: x 8 + x 9 + x20 + x21 ≤1 x 3 + x 4 + x 5 ≤1 . (20) x + x2 + x7 =1 Table 5. The values of objective functions f1, f2, f3, and f4 for Problem 1 f1 ($) min f1 946.02 min f2 1030.92 min f3 1037.50 min f4 997.90 f2 (MJ) 6566.30 6112.66 6415.86 6799.00 f3 (KgCE) 16.34 12.51 11.38 329.88 f4 (hours) 98.20 190.00 190.30 16.70 Figure 6. Solution digraph of min(f1) n1 n2 n3 x4 n5 14 n10 x21 x5 10 n7 n14 x23 Copyright © 2007, Idea Group Inc. Copying or distributing in print or electronic forms without written permis-sion of Idea Group Inc. is prohibited. ... - tailieumienphi.vn
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