Exam 19: Solution Procedures for Transportation and Assignment Problems

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

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. Be sure to compute the total project completion cost. ​​

​A company ships products from four factories to four warehouses. The factory capacities, warehouse requirements, and per-unit shipping costs are shown below: ​ ​ How many products should the company ship from each factory to each warehouse to minimize monthly shipping costs? What will the monthly shipping cost be if the shipping plan is followed? (Use the minimum cost method to find an initial feasible solution and the transportation simplex method to find an optimal solution.)

The stepping-stone method requires that one or more artificially occupied cells with a flow of zero be created in the transportation tableau when the number of occupied cells is fewer than

The transportation simplex method is limited to minimization problems.

The transportation simplex method is more efficient than general-purpose linear programming for solving large-sized transportation problems.

A manufacturer of electrical consumer products, with its headquarters in Burlington, Iowa, produces electric irons at Manufacturing Plants 1, 2, and 3. The irons are shipped to Warehouses A, B, C, and D. The shipping cost per iron, the monthly warehouse requirements, and the monthly plant production levels are: ​​ ​ How many electric irons should be shipped per month from each plant to each warehouse to minimize monthly shipping costs? 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 per month.

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

Use the Hungarian method to obtain the optimal solution to the following assignment problem in which total cost is to be minimized. All tasks must be assigned and no agent can be assigned to more than one task. ​​

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? ​​

Four jobs must be assigned to four work centers. Only one job can be assigned to each work center, and all jobs must be processed. The cost of processing each job at each work center is shown below. Determine which jobs should be assigned to which work center to minimize total processing cost. Compute the total processing cost. ​ ​

The MODI method is used to

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

The difference between the transportation and assignment problems is that

A professor has been contacted by four not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. 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. The professor's estimate of the time, in days, is given in the table below. Use the Hungarian method to determine which team works with which project. All projects must be assigned and no team can be assigned to more than one project. ​​

Solve the following transportation problem using the transportation simplex method. State the minimum total shipping cost. Shipping costs are:

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

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.

The optimal solution is found in an assignment matrix when the minimum number of straight lines needed to cover all the zeros equals

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