Exam 19: Solution Procedures for Transportation and Assignment Problems

Four employees must be assigned to four projects. Only one employee can be assigned to each project, and all projects must be completed. The cost of each employee completing each project is shown below. Determine which employee should be assigned to which project to minimize total project completion cost. Compute the total project completion cost. Project Employee 1 2 3 4 Al \ 300 \ 325 \ 500 \ 350 Ben 400 525 575 600 Cal 350 400 600 500 Dan 400 350 450 450

To use the Hungarian method, a profit-maximization assignment problem requires

Al Bergman, staff traffic analyst at the corporate headquarters of Computer Products Corporation (CPC), is developing a monthly shipping plan for the El Paso and Atlanta manufacturing plants to follow next year. These plants manufacture specialized computer workstations that are shipped to five regional warehouses. Al has developed these estimated requirements and costs: Warehouse Plant Chicago Dallas Denver New York San Jose Monthly Plant Production (units) Atlanta \ 35 \ 40 \ 60 \ 45 \ 90 200 El Paso 50 30 35 95 40 300 Monthly Warehouse Requirements (units) 75 100 25 150 150 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. a.Use the minimum cost method to find an initial feasible solution. b.Use the transportation simplex method to find an optimal solution. c.Compute the optimal total shipping cost.

The following table shows the unit shipping cost between cities, the supply at each origin city, and the demand at each destination city. Solve this minimization problem using the transportation simplex method and compute the optimal total cost. Destination Origin Terre Haute Indianapolis Ft. Wayne South Bend Supply St. Louis 8 6 12 9 100 Evansville 5 5 10 8 100 Bloomington 3 2 9 10 100 Demand 150 60 45 45

A solution to a transportation problem that has less than m + n - 1 cells with positive allocations in the transportation tableau is

The transportation simplex method is limited to minimization problems.

Explain what adjustments are made to the transportation tableau when total supply and total demand are not equal.

The per-unit change in the objective function associated with assigning flow to an unused arc in the transportation simplex method is called the

Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a 0.

Five customers needing their tax returns prepared must be assigned to five tax accountants. The estimated profits for all possible assignments are shown below. Only one accountant can be assigned to a customer, and all customers' tax returns must be prepared. What should the customer-accountant assignments be so that estimated total profit is maximized? What is the resulting total profit? Accountant Customer 1 2 3 4 5 A \ 500 \ 525 \ 550 \ 600 \ 700 B 625 575 700 550 800 C 825 650 450 750 775 D 590 650 525 690 750 E 450 750 660 390 550

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.

Identifying the outgoing arc in Phase II of the transportation simplex method is performed using the

Develop the transportation tableau for this transportation problem.

Consider the transportation problem below. Destination Origin 1 2 3 Supply A \ .50 \ .90 \ .50 100 B .80 1.00 .40 500 C .90 .70 .80 900 Demand 300 800 400 a.Use the minimum cost method to find an initial feasible solution. b.Can the initial solution be improved? c.Compute the optimal total shipping cost.

Solve the following transportation problem using the transportation simplex method. State the minimum total shipping cost. Origin Supply Destination Demand A 500 300 400 300 300 Shipping costs are: Destination Source 2 3 5 9 12 10

When an assignment problem involves an unacceptable assignment, a dummy agent or task must be introduced.

Explain what adjustments are made to the transportation tableau when there are unacceptable routes.

The MODI method is used to

Using the transportation simplex method, the optimal solution to the transportation problem has been found when

To handle unacceptable routes in a transportation problem where cost is to be minimized, infeasible arcs must be assigned negative cost values.