# sol7 - X X = ⇒ 5000 1000 4000 5000 1000 X 5000 X X = ⇒...

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AMS 341 Spring, 2011 Homework Set # 7 — Solution Notes Section 7.1, 1. Customer 1 Customer 2 Customer 3 Warehouse 1 15 35 25 40 Warehouse 2 10 50 40 30 unmet demand 90 80 110 20 30 30 30 #6, 7.1: Let y stand for the cost per check in different sites. We obtain the following cost and requirement table for the balanced transportation problem: Vendor Salary Personnel DUMMY Site 1 5 4 2 0 10000 Site 2 3 4 5 0 6000 5000 5000 5000 1000 #3. Let ( - ,y ) =(-,cost). The balanced formulation: Vendor Salary Personnel Dummy Site 1 (-,5) (-,4) (-,2) (-,0) 10000 Site 2 (-,3) (-,4) (-,5) (-,0) 6000 5000 5000 5000 1000 (a) Northwest cornor method: 5000 5000 6000 X 5000 5000 1000 = 5000 5000 0 6000 X X 5000 1000 = 5000 5000 0 X 6000 X X 5000 1000 = 5000 5000 0 X 5000 1000 X X X 1000 = 5000 5000 0 X 5000 1000 X X X X X (b) Min-cost method: 1000 9000 6000 5000 5000 5000 X = 5000 1000 4000 6000
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Unformatted text preview: X X = ⇒ 5000 1000 4000 5000 1000 X 5000 X X = ⇒ 4000 5000 1000 X 5000 1000 X 1000 X X = ⇒ 4000 5000 1000 X 5000 1000 X X X X X (c) Vogel’s method: 5000 5000 2 6000 3 5000 5000 X 1000 2 3 = ⇒ 5000 1000 4000 4 6000 3 5000 5000 X X 2-= ⇒ 5000 1000 4000 1 5000 1000 1 X 5000 X X 2--= ⇒ 4000 5000 1000 X 4 5000 1000 4 X 1000 X X---= ⇒ 4000 5000 1000 X-5000 1000 X 4 X X X X-4--#4. Transportation simplex method: (-,5) (4000,4) (5000,2) (1000,0) (5000,3) (1000,4) (-,5) (-,0) ( u 1 , u 2 , v 1 , v 2 , v 3 , v 4 , c 11 , c 23 , c 24 ) = (0 , , 3 , 4 , 2 , ,-2 ,-3 , 0), it is optimal....
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