* Origin Atlanta Chicago 35 50 El Paso 25 Destination Dallas Denver New York 40 60 45 150 50 Demand 30 100 75 35 40 150 25 Supply 200 95 25 100 San Jose 90 150 300 150 c. Use the minimum cost method to find an initial feasible solution. The cost of processing each job at each work center is shown below. * Project Team A B Budgeting 32 38 Information 35 40 Cengage Learning Testing, Powered Cognero Volunteers 15 18 Forecasting 27 35 Page 8 Chapter 19 Solution Procedures for Transportation and Assignment Problems Atlanta 200 El Paso 50 30 35 95 40 300 Monthly Warehouse 75 100 25 150 150 Requirements (units) Determine how many workstations should be shipped per month from each plant to each warehouse to minimize monthly shipping costs, and compute the total shipping cost. Use the minimum cost method to find an initial feasible solution. Use the transportation simplex method to find an optimal solution. Optimal solution found using MODI and methods is below. Origin A B C Demand 1 .50 .80 .90 300 Destination 2 .90 1.00 .70 800 3 .50 .40 .80 400 Supply 100 500 900 a. What should the assignments be so that estimated total profit is maximized? Customer A B C D E ANSWER: 1 625 825 590 450 Customer A B C D E 2 575 650 650 750 Accountant 3 700 450 525 660 Accountant 5 3 1 4 2 Total Profit 4 550 750 690 390 5 800 775 750 550 Profit 700 700 825 690 750 37. Only one job can be assigned to each work center, and all jobs must be processed.

(Use the minimum cost method to find an initial feasible solution and the transportation simplex method to find an optimal solution.) ANSWER: Factory A to Warehouse 4 units Factory B to Warehouse 3 units Factory C to Warehouse 2 units Factory D to Warehouse 1 units Factory D to Warehouse 3 units Total Cost 41. has three fabrication departments with each producing a single unique product with equipment that is dedicated solely to its product.

To use the transportation simplex method, a transportation problem that is unbalanced requires the use of a. What will the monthly shipping cost be if the shipping plan is followed?

Requiremen t (units) 1 12 19 7 2 10 16 6 3 7 15 4 4 9 21 9 Monthly Factory Capacity (units) How many products should the company ship from each factory to each warehouse to minimize monthly shipping costs?

Determine which jobs should be assigned to which work center to minimize total processing cost. Work Center Job A B C E ANSWER: 1 25 65 55 Job A 2 40 60 65 Work Center 2 Cengage Learning Testing, Powered Cognero 3 35 55 75 4 20 65 85 Cost 45 Page 11 Chapter 19 Solution Procedures for Transportation and Assignment Problems and shipping costs are shown below: Warehouse Factory A Factory B Factory C Factory D Monthly Warehouse Min.

The transportation simplex method is limited to minimization problems.

For an assignment problem with 3 agents and 4 tasks, the assignment matrix will have 3 rows and 4 columns. To handle unacceptable routes in a transportation problem where cost is to be minimized, infeasible arcs must be assigned negative cost values. A solution to a transportation problem that has less than m n 1 cells with positive allocations in the transportation tableau is a. Task Agent 1 2 3 4 ANSWER: A 10 11 18 15 Agent 1 2 3 4 B 12 14 21 20 Task C B D A Total Cost C 15 19 23 26 D 25 32 29 28 Cost 15 14 29 15 73 32. Explain what adjustments are made to the transportation tableau when total supply and total demand are not equal. finding the maximum number of lines to cover all the zeros in the reduced matrix. All tasks must be assigned and no agent can be assigned to more than one task. Explain how the Hungarian method can be used to solve an assignment problem that has a maximization objective. To use the Hungarian method, a assignment problem requires a. The estimate of the time, in days, is given in the table below. The minimum cost method provided the solution shown below. Five customers needing their tax returns prepared must be assigned to five tax accountants. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. For an assignment problem where the number of agents does not equal the number of tasks, what adjustments must be made to allow the problem to be solved using the Hungarian method? Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a 0. Using the Hungarian method, the optimal solution to an assignment problem is found when the minimum number of lines required to cover the zero cells in the reduced matrix equals the number of agents. the net evaluation index for each unoccupied cell is 0. Identifying the outgoing arc in Phase II of the transportation simplex method is performed using the a. The optimal solution is found in an assignment matrix when the minimum number of straight lines needed to cover all the zeros equals Cengage Learning Testing, Powered Cognero Page 2 Chapter 19 Solution Procedures for Transportation and Assignment Problems d.

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