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Unformatted text preview: Chapter 7 Transportation, Assignment, and Transshipment Problems Learning Objectives 1. Be able to identify the special features of the transportation problem. 2. Become familiar with the types of problems that can be solved by applying a transportation model. 3. Be able to develop network and linear programming models of the transportation problem. 4. Know how to handle the cases of (1) unequal supply and demand, (2) unacceptable routes, and (3) maximization objective for a transportation problem. 5. Be able to identify the special features of the assignment problem. 6. Become familiar with the types of problems that can be solved by applying an assignment model. 7. Be able to develop network and linear programming models of the assignment problem. 8. Be familiar with the special features of the transshipment problem. 9. Become familiar with the types of problems that can be solved by applying a transshipment model. 10 Be able to develop network and linear programming models of the transshipment problem. 11. Be able to utilize the minimumcost method to find an initial feasible solution to a transportation problem. 12. Be able to utilize the transportation simplex method to find the optimal solution to a transportation problem. 13. Be able to utilize the Hungarian algorithm to solve an assignment problem. 14. Understand the following terms. transportation problem modified distribution (MODI) method origin assignment problem destination Hungarian method network flow problem opportunity loss transportation tableau transshipment problem minimum cost method capacitated transshipment problem steppingstone path Solutions: 7  1 Chapter 7 1. The network model is shown. Phila. New Orleans Boston Columbus Dallas Atlanta 5000 3000 7 5 2 1 2 6 6 2 1400 2000 3200 1400 2. a. Let x 11 : Amount shipped from Jefferson City to Des Moines x 12 : Amount shipped from Jefferson City to Kansas City x 23 : Amount shipped from Omaha to St. Louis Min 14 x 11 + 9 x 12 + 7 x 13 + 8 x 21 + 10 x 22 + 5 x 23 s.t. x 11 + x 12 + x 13 30 x 21 + x 22 + x 23 20 x 11 + x 21 = 25 x 12 + x 22 = 15 x 13 + x 23 = 10 x 11 , x 12 , x 13 , x 21 , x 22 , x 23 , b. Optimal Solution: Amount Cost Jefferson City  Des Moines 5 70 Jefferson City  Kansas City 15 135 Jefferson City  St. Louis 10 70 Omaha  Des Moines 20 160 Total 435 3. a. & b. The linear programming formulation and optimal solution as printed by The Management Scientist are shown below. The first two letters in the variable names identify the from 7  2 Transportation, Assignment, and Transshipment Problems node for the shipping route and the last two identify the to node. Also, The Management Scientist prints < for . LINEAR PROGRAMMING PROBLEM MIN 2PHAT + 6PHDA + 6PHCO + 2PHBO + 1NOAT + 2NODA + 5NOCO + 7NOBO S.T....
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 Spring '09
 shakroh
 Math

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