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Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Shipping Costs ($ per skateboard) Maryland 50000 25.00 45.00 40.00 Factory/DCs Detroit Los Angeles 3 Austin Retailers/DCs Iowa Just Sports Sports 'N Stuff The Sports Dude 25.00 35.00 8 9 1 Iowa 40.00 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. 30.00 27.50 30.00 4 Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 6 42.50 Shipping Costs ($ per skateboard) 6 Idaho 35.00 Arkansas 40.00 40.00 32.50 42.50 32.50 7 Arkansas 27.50 25.00 42.50 7

Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Shipping Costs ($ per skateboard) Maryland 50000 25.00 45.00 40.00 Factory/DCs Detroit Los Angeles 3 Austin Retailers/DCs Iowa Just Sports Sports 'N Stuff The Sports Dude 25.00 35.00 8 9 1 Iowa 40.00 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. 30.00 27.50 30.00 4 Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 6 42.50 Shipping Costs ($ per skateboard) 6 Idaho 35.00 Arkansas 40.00 40.00 32.50 42.50 32.50 7 Arkansas 27.50 25.00 42.50 7

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section6.5: Set-covering And Location-assignment Models
Problem 34P
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Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Factory/DCs Detroit Los Angeles Austin 1 2 3 Retailers/DCs Just Sports Sports 'N Stuff Iowa The Sports Dude 25.00 35.00 40.00 8 9 4 1 Shipping Costs ($ per skateboard) Iowa 30.00 27.50 Maryland 30.00 25.00 4 45.00 40.00 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. 5 Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 42.50 6 Shipping Costs ($ per skateboard) 5 Idaho 35.00 Arkansas 40.00 32.50 40.00 42.50 6 32.50 Arkansas 27.50 25.00 42.50 7
Transcribed Image Text:Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Factory/DCs Detroit Los Angeles Austin 1 2 3 Retailers/DCs Just Sports Sports 'N Stuff Iowa The Sports Dude 25.00 35.00 40.00 8 9 4 1 Shipping Costs ($ per skateboard) Iowa 30.00 27.50 Maryland 30.00 25.00 4 45.00 40.00 Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers. 5 Maryland 20.00 Idaho 32.50 35.00 40.00 35.00 42.50 6 Shipping Costs ($ per skateboard) 5 Idaho 35.00 Arkansas 40.00 32.50 40.00 42.50 6 32.50 Arkansas 27.50 25.00 42.50 7
(b) Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form X;; where x¡; represents the number of units shipped from node i to node j.) Min s.t. Detroit Production -*14*15*16 Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand +x16 +x17≤350 + x1 xij≥0 for all i and j.
Transcribed Image Text:(b) Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. (Let Detroit be node 1, Los Angeles be node 2, Austin be node 3, Iowa be node 4, Maryland be node 5, Idaho be node 6, Arkansas be node 7, Just Sports be node 8, Sports Stuff be node 9, and Sports Dude be node 10. Express your answers in the form X;; where x¡; represents the number of units shipped from node i to node j.) Min s.t. Detroit Production -*14*15*16 Los Angeles Production Austin Production Iowa Shipments Maryland Shipments Idaho Shipments Arkansas Shipments Iowa Processing Maryland Processing Idaho Processing Arkansas Processing Just Sports Demand Sports Stuff Demand Sports Dude Demand +x16 +x17≤350 + x1 xij≥0 for all i and j.
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