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Chapter 19 Solution Procedures for Transportation and Assignment Problems True False 1. The transportation simplex method can be used to solve the assignment problem. The variable costs and capacity for each department is shown below.
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.
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?
If a transportation problem has four origins and five destinations, one of the destinations will not be fully supplied.
When an assignment problem involves an unacceptable assignment, a dummy agent or task must be introduced.
In the case of transportation problems, the algorithm is essentially a disguised form of the dual simplex algorithm of 4§2.
Assignment problems, which are special cases of transportation problems, pose difficulties for the transportation algorithm and require the development of an algorithm which takes advantage of the simpler nature of these problems.