* In assignment problems, dummy agents or tasks are created when the number of agents and tasks is not equal. *

* In assignment problems, dummy agents or tasks are created when the number of agents and tasks is not equal. *

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.

All projects must be assigned and no team can be assigned to more than one project. Total cost : Origin Atlanta Chicago 35 75 Dallas 40 50 El Paso 30 100 Demand Destination Denver New York 60 45 125 75 35 25 100 Supply 200 95 25 25 San Jose 90 40 150 150 300 150 b. Only one accountant can be assigned to a customer, and all tax returns must be prepared.

Use the Hungarian method to determine which team works with which project. Initial feasible solution found using the minimum cost method is below. Cengage Learning Testing, Powered Cognero Page 10 Chapter 19 Solution Procedures for Transportation and Assignment Problems Origin 1 .50 A 100 B 100 C 100 Destination 2 .90 1.00 .40 400 .90 b. Supply .50 100 .80 Demand 3 500 .70 .80 800 300 900 800 400 The solution cannot be improved. The estimated profits for all possible assignments are shown below.

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.

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.

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