This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 71) 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....
View
Full
Document
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.
 Spring '08
 Arkin,E
 Linear Programming

Click to edit the document details