Exam 19: Solution Procedures for Transportation and Assignment Problems

The transportation simplex method is a two-phase method that first finds an initial feasible solution and then makes iterative improvements in the solution until an optimal solution is reached.

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? ​

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

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.​

​Develop the transportation tableau for this transportation problem.​ ​ ​

Finding an initial feasible solution can be done by using a heuristic procedure.

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

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.​ ​

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

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.​

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

Canning Transport is to move goods from three factories (origins)to three distribution centers (destinations).Information about the move is given below.Solve the problem using the transportation simplex method and compute the total shipping cost. ​ Shipping costs are as follows: ​ ​

In the transportation simplex method,when total supply is greater than total demand,we introduce a dummy destination with demand less than the excess of supply over demand.

The transportation simplex method is limited to minimization problems.

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

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. ​

To use the transportation simplex method,

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

To use the transportation simplex method,a transportation problem that is unbalanced requires the use of