Deck 19: Solution Procedures for Transportation and Assignment Problems

Question 1

A dummy origin in a transportation problem is used when supply exceeds demand.

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

A) (the number of agents) − 1.
B) (the number of agents).
C) (the number of agents) + 1.
D) (the number of agents) + (the number of tasks).

Answer 3

B

Question 4

An example of a heuristic is the

A) minimum-cost method.
B) stepping-stone method.
C) Hungarian method.
D) MODI method.

Question 5

The net evaluation index for occupied cells in the transportation simplex method is 0.

Question 6

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

A) net evaluation index.
B) degenerate value.
C) opportunity loss.
D) simplex multiplier.

Question 7

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

Question 8

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

Question 9

The difference between the transportation and assignment problems is that

A) total supply must equal total demand in the transportation problem
B) the number of origins must equal the number of destinations in the transportation problem
C) each supply and demand value is 1 in the assignment problem
D) there are many differences between the transportation and assignment problems

Question 10

The transportation simplex method is limited to minimization problems.

Question 11

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

A) an optimal solution.
B) an initial feasible solution.
C) a minimum-cost solution.
D) a degenerate solution.

Question 12

If a transportation problem has four origins and five destinations, one of the destinations will not be fully supplied.

Question 13

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

A) m + n − 2
B) m + n − 1
C) m + n
D) m + n + 1

Question 14

The transportation simplex method can be used to solve the assignment problem.

Question 15

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.

Question 16

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

Question 17

For an assignment problem with 3 agents and 4 tasks, the assignment matrix will have 3 rows and 4 columns.

Question 18

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

A) there is a shipment in every cell.
B) more than one stepping-stone path is available.
C) there is a tie for outgoing cell.
D) the net evaluation index for each unoccupied cell is ≥ 0.

Question 19

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

Question 20

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

A) minimum cost method.
B) MODI method.
C) stepping-stone method.
D) matrix reduction method.

Question 21

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.
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Question 22

​Develop the transportation tableau for this transportation problem.
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Question 23

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:
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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.

Question 24

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:
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Question 25

After some special presentations, the employees of the AV Center have to move overhead projectors back to classrooms. The table below indicates the buildings where the projectors are now (the origins), where they need to go (the destinations), and a measure of the distance between sites. Determine the transport arrangement that minimizes the total transport distance.

Question 26

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.
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Question 27

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.

Question 28

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

A) artificial variables.
B) one or more transshipment nodes.
C) a dummy origin or destination.
D) matrix reduction.

Question 29

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?
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Question 30

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.
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Question 31

​To use the transportation simplex method,

A) ​there can be no unacceptable routes.
B) ​the initial feasible solution cannot be degenerate.
C) ​a minimization objective function must be the case.
D) ​total supply must equal total demand.

Question 32

​A company ships products from four factories to four warehouses. The factory capacities, warehouse requirements, and per-unit shipping costs are shown below:
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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.)

Question 33

The MODI method is used to

A) identify an outgoing arc.
B) identify an incoming arc.
C) identify unoccupied cells.
D) identify an initial feasible solution.

Question 34

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.
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Question 35

Consider the transportation problem below.
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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.

Question 36

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: 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.

Question 37

​For an assignment problem where the number of agents does not equal the number of tasks, what adjustments must be made to allow the problem to be solved using the Hungarian method?

Question 38

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

Question 39

Solve the following assignment problem using the Hungarian method. No agent can be assigned to more than one task. Total cost is to be minimized.
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Question 40

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

A) converting all profits to opportunity losses.
B) a dummy agent or task.
C) matrix expansion.
D) finding the maximum number of lines to cover all the zeros in the reduced matrix.

Question 41

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

Question 42

​Explain how the transportation simplex method can be used to solve a transportation problem that has a maximization objective.

Question 43

​Explain how the Hungarian method can be used to solve an assignment problem that has a maximization objective.

Question 44

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