Deck 19: Solution Procedures for Transportation and Assignment Problems

Question 1

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

Answer 1

C

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)(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 2

(the number of agents).

Question 3

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

Answer 3

True

Question 4

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 5

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

Question 6

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

Question 7

The transportation simplex method is limited to minimization problems.

Question 8

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 9

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 10

An example of a heuristic is the

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

Question 11

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 12

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

Question 13

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

Question 14

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 15

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 16

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

Question 17

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

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

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 21

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 22

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

Question 23

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