Deck 19: Solution Procedures for Transportation and Assignment Problems

Question 1

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

Answer 1

True

Question 2

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

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

Answer 2

B

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

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

Question 7

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 8

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 9

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 10

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

Question 11

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

Question 12

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.

Question 13

The transportation simplex method can be applied only to a balanced problem; if a problem is not balanced,a dummy origin or dummy destination must be added.

Question 14

The transportation simplex method is limited to minimization problems.

Question 15

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

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

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 18

An example of a heuristic is the

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

Question 19

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.

Question 20

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

Question 21

In order to identify the arc that will cause the largest reduction per unit in the total cost of the current solution,we use the MODI method.The MODI method is used to identify

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

Question 22

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 23

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.​

Question 24

A large screen printer is faced with six jobs due on Tuesday.The plan is to do the jobs on Monday so they will be ready on time.The shop has six worker-machine pairs that can work on any of the six jobs.Because of differing experience levels and machine capabilities,processing times differ.The processing times presented in the table below are in minutes.What is the optimal assignment of jobs to worker-machine pairs that minimizes total processing time?
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Question 25

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 the outgoing cell.
D)the net evaluation index for each unoccupied cell is ≥ 0.

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

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 28

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 29

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 30

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 31

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

Question 32

​Develop the transportation tableau for this transportation problem.​ ​
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Question 33

The Hungarian method involves

A)matrix reduction.
B)subtracting and adding appropriate values to yield an optimal solution.
C)continuing iteratively until the value of one of the solutions is zero.
D)All of these are correct.

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.​

Question 35

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 36

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.​

Question 37

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:
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Question 38

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.​

Question 39

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.