Question 1

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

Accepted Answer

The stepping-stone method is used in Phase II of the transportation simplex method to identify the outgoing arc. It involves finding a closed loop or "circuit" in the transportation table, and then adding or subtracting a variable along each arc in the circuit until a new basic feasible solution is obtained. The arc with the smallest or most negative reduced cost in the circuit is chosen as the outgoing arc.

Question 2

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

Accepted Answer

False

Question 3

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

Accepted Answer

False

Question 4

An example of a heuristic is the

Accepted Answer

Heuristics are problem-solving techniques that use practical rules or shortcuts to quickly solve complex problems. The minimum-cost method is an example of a heuristic used in transportation problems that employs a simple rule of selecting the lowest cost cell in a given row or column.

Question 5

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

Accepted Answer

The answer of If a transportation problem has four origins...

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

Accepted Answer

The net evaluation index is the per-unit change in the objective function when assigning flow to an unused arc in the transportation simplex method. The other options, degenerate value, opportunity loss, and simplex multiplier, are not relevant to this concept.

Question 7

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

Accepted Answer

Dummy agents or tasks are created in assignment problems to make the number of agents and tasks equal, and ensure that every agent is assigned a task.

Question 8

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

Accepted Answer

In the assignment problem, the optimal solution is found when the minimum number of lines needed to cover all the zeros in the cost matrix equals the number of agents (or tasks), according to the Hungarian algorithm.

Question 9

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

Accepted Answer

The transportation simplex method can be applied to solve the assignment problem, which is a special case of the transportation problem.

Question 10

The difference between the transportation and assignment problems is that

Accepted Answer

The answer of The difference between the transportation and assignment...

Question 11

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

Accepted Answer

The answer of To use the Hungarian method, a profit-maximization...

Question 12

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

Accepted Answer

The optimal solution in the transportation simplex method is reached when the net evaluation index (also known as the opportunity cost or reduced cost) for each unoccupied cell is greater than or equal to zero, indicating that no further cost reduction is possible.

Question 13

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

Accepted Answer

The answer of A dummy origin in a transportation problem...

Question 14

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

Accepted Answer

A degenerate solution occurs when there are fewer than m + n - 1 positive allocations in the transportation tableau, indicating that the solution does not use all the degrees of freedom available.

Question 15

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

Accepted Answer

The transportation simplex method is specifically designed for solving transportation problems with fewer variables and constraints, making it more efficient in solving large-sized transportation problems compared to general-purpose linear programming.

Question 16

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

Accepted Answer

The net evaluation index for occupied cells in the transportation simplex method is always greater than or equal to 0. It can only be 0 when the iteration is complete and an optimal solution is found. Therefore, the statement is true.

Question 17

The MODI method is used to

Accepted Answer

The answer of The MODI method is used to
...

Question 18

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

Accepted Answer

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 m + n - 1. This is because the method requires that there be at least m + n - 1 occupied cells in order to find a feasible solution.

Question 19

The transportation simplex method is limited to minimization problems.

Accepted Answer

The transportation simplex method can be used for both minimization (e.g., cost minimization) and maximization (e.g., profit maximization) problems by appropriately formulating the objective function.

Question 20

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

Accepted Answer

An unbalanced transportation problem requires the use of a dummy origin or destination to make it balanced before using the transportation simplex method. This is because the number of supply units does not equal the number of demand units in the problem. Adding a dummy origin or destination allows the problem to be balanced and solved using the transportation simplex method. The other options, such as using artificial variables or transshipment nodes, are not necessary for unbalanced transportation problems.

Quiz 19: Solution Procedures for Transportation and Assignment Problems