# ch7 - Def A Transportation Problem is a special case of...

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Unformatted text preview: Def: A Transportation Problem is a special case of linear programming of the following form: min z = ∑ m i =1 ∑ n j =1 c ij x ij s . t . ∑ n j =1 x ij ≤ s i i = 1 , ..., m ∑ m i =1 x ij ≥ d j j = 1 , ..., n x ij ≥ Here, s i is the supply at source i , d j is the demand at destination j , and c ij is the cost of shipping 1 unit from source i to destination j . Def: A Balanced Transportation Problem (BTP) is a transportation problem in which total supply is equal to toal demand. min z = ∑ m i =1 ∑ n j =1 c ij x ij s . t . ∑ n j =1 x ij = s i i = 1 , ..., m ∑ m i =1 x ij = d j j = 1 , ..., n x ij ≥ Can describe a BTP easily with a cost and requirement table . 1 A trucking company ships canned peas by the truck load from 3 canneries to 4 warehouses. Warehouse 1 Warehouse 2 Warehouse 3 Warehouse 4 output Cannery 1 464 513 654 867 75 Cannery 2 352 416 690 791 125 Cannery 3 995 682 388 685 100 allocation 80 65 70 85 2 Example (similar to 7-1) A company wants to supply its customer with 3 widgits during each of the next 3 weeks. max production reg time max production overtime prod cost reg time (per unit) week 1 2 2 6,000 week 2 2 1 10,000 week 3 1 2 8,000 The overtime production cost per unit is 2,000 more than regular time production. Storage cost is 1,000 per unit per week. The starting inventory is 2 units.1,000 per unit per week....
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## This note was uploaded on 05/28/2011 for the course AMS 341 taught by Professor Arkin,e during the Spring '08 term at SUNY Stony Brook.

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ch7 - Def A Transportation Problem is a special case of...

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