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chap11_2011_2

chap11_2011_2 - 11.5 Traveling Salesman and Routing Models...

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11.5 Traveling Salesman and Routing Models
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Example 11.8 NCB Circuit Board TSP Figure 11.4 shows the tiny example that we will investigate for fictional board manufacturer NCB. We seek an optimal route through the 10 hole locations indicated. Table 11.7 reports straight-line distances di,j between hole locations i and j. Lines in Figure 11.4 show a fair quality solution with total length 92.8 inches. The best route is 11 inches shorter (see Section 12.6). 1 2 3 4 5 6 7 8 9 10 1 3.6 5.1 10.0 15.3 20.0 16.0 14.2 23.0 26.4 2 3.6 3.6 6.4 12.1 18.1 13.2 10.6 19.7 23.0 3 5.1 3.6 7.1 10.6 15.0 15.8 10.8 18.4 21.9 4 10.0 6.4 7.1 7.0 15.7 10.0 4.2 13.9 17.0 5 15.3 12.1 10.6 7.0 9.9 15.3 5.0 7.8 11.3 6 20.0 18.1 15.0 15.7 9.9 25.0 14.9 12.0 15.0 7 16.0 13.2 15.8 10.0 15.3 25.0 10.3 19.2 21.0 8 14.2 10.6 10.8 4.2 5.0 14.9 10.3 10.2 13.0 9 23.0 19.7 18.4 13.9 7.8 12.0 19.2 10.2 3.6 1 2 3 4 5 6 7 8 9 10
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Formulating the Symmetric TSP (11.15) (11.16)
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Subtours (11.17) 1 2 3 4 5 6 7 8 9 10
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ILP Model of the Symmetric TSP [11.25]
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ILP Model of the Asymmetric TSP [11.26]
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Quadratic Assignment Formulation of the TSP [11.27] s.t. Let
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Example 11.9 KI Truck Routing Kraft Incorporated confronts such multiple-route design problems in planning truck delivery of its food products to over 100,000 commercial, industrial, and military customers in North America. Known customer requirements must be grouped into truckloads and then routes planned. Our tiny fictitious version of the KI case has 20 stops to be serviced from a single depot. Stop, i fi Stop, i fi 1 0.25 11 0.21 2 0.33 12 0.68 3 0.39 13 0.16 4 0.40 14 0.19 5 0.27 15 0.22 6 0.70 16 0.38 7 0.28 17 0.26 8 0.43 18 0.29 9 0.50 19 0.17 10 0.22 20 0.31 1 2 3 4 5 6 7 8 9 12 19 18 16 13 11 10 15 14 17 20
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Example 11.9 KI Truck Routing 1 2 3 4 5 6 7 8 9 12 19 18 16 13 11 10 15 14 17 20
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KI Truck Routing Example Model s.t. Let (11.18)
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KI Truck Routing Example Model
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Fixed charges can be modeled with new binary variables and switching constraints. Facility Location and Network Design are common cases of fixed charges. Facility Location Models Facility/plant/warehouse location models choose which of a proposed list of facilities to open in order to service specified customer demands at minimum total cost. [11.29] 11.6 Facility Location and Network Design Models
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Example 11.10 Tmark Facilities Location AT&T has confronted many facility location problems in recommending sites for the toll-free call-in centers of its telemarketing customers. Such centers handle telephone reservations and orders arising in many geographic zones. Since telephone rates vary dramatically depending on the zone of call origin and the location of the receiving center, site selection is extremely important. A well-designed system should minimize the total of call charges and center setup costs. Our version of this scenario will involve fictional firm Tmark. Figure 11.7 shows the 8 sites under consideration for Tmark’s catalog order centers embedded in a map of the 14 calling zones. Table 11.9 shows corresponding unit calling charges, ri,j, from each zone j to various centers i, and the zone’s anticipated call load, dj.
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