Question 1

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

Accepted Answer

A heuristic procedure is an algorithmic approach that finds solutions by making educated guesses and assumptions. This type of procedure can be used to find an initial feasible solution in optimization problems, which can be refined later. Therefore, it is true that finding an initial feasible solution can be done by using a heuristic procedure.

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

Accepted Answer

The optimal solution in an assignment matrix is found when the minimum number of straight lines needed to cover all the zeros equals the number of agents. This is known as the "minimum number of lines covering method" and is used in the Hungarian algorithm for solving the assignment problem. In general, the number of lines needed to cover all the zeros is at most the number of agents, so the choice B is the best option.

Question 3

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

Accepted Answer

False

Question 4

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 5

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

Accepted Answer

When the number of agents and tasks is not equal, dummy agents or tasks are created to balance the problem and make it solvable.

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)

Accepted Answer

A transportation problem is considered degenerate if there are fewer than m + n - 1 cells with positive allocations in the transportation tableau. In this case, the solution obtained may not be unique, and cycling may occur in the simplex method, leading to difficulty in finding the optimal solution. Therefore, the solution obtained is called a 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

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 8

The difference between the transportation and assignment problems is that

Accepted Answer

In the assignment problem, each supply and demand value is typically 1, as it involves assigning tasks to agents one-to-one, whereas the transportation problem deals with varying supply and demand values.

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

Accepted Answer

The stepping-stone method requires that the number of occupied cells be equal to the number of rows plus the number of columns minus one (m+n-1). This is because each row and column must have exactly one basic variable. Therefore, in order to create artificial cells with zero flow, we need to have at least one unoccupied cell. So the minimum number of occupied cells required is m+n-1. Therefore, the answer is B, m+n-1.

Question 10

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

Accepted Answer

The transportation simplex method can be used to solve linear programming problems, which includes the assignment problem as a special case. Therefore, it is true that 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.

Accepted Answer

The transportation simplex method is specifically designed for transportation problems and takes advantage of the problem's special structure to solve it more efficiently. General-purpose linear programming algorithms may be less efficient for transportation problems as they do not take advantage of this structure. Therefore, the transportation simplex method is generally more efficient for 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.

Accepted Answer

The transportation simplex method indeed begins with finding an initial feasible solution and then iteratively improves it until an optimal solution is obtained.

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.

Accepted Answer

The statement is true. The transportation simplex method requires that the number of sources (origins) is equal to the number of destinations, which means the problem is "balanced." If the problem is unbalanced, a dummy origin or dummy destination needs to be added to balance the problem before applying the transportation simplex method.

Question 14

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 15

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

Accepted Answer

Yes, the Hungarian method involves finding the optimal assignments by selecting cells in the reduced matrix that contain a 0. This is done using a series of steps that involve determining the minimum number of lines needed to cover all the zeros in the matrix, identifying the optimal assignments, and adjusting the matrix as needed to find the final solution.

Question 16

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

Accepted Answer

Infeasible arcs in a transportation problem are assigned a very high cost (not negative) to ensure they are not selected in the solution. Negative costs would encourage their selection, which is contrary to the goal of avoiding these routes.

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.

Accepted Answer

This statement is true. The Hungarian method involves finding a minimum cost assignment by identifying a set of independent zero cells in a reduced cost matrix. The number of lines required to cover all these cells should be equal to the number of agents in the problem for the solution to be optimal.

Question 18

An example of a heuristic is the

Accepted Answer

A heuristic is a method or approach that uses practical, intuitive, and experience-based strategies to solve problems. The minimum cost method is a heuristic used in transportation problems to find an initial solution by selecting the lowest cost cells first, without considering the optimality of the solution. The other options (stepping-stone method, Hungarian method, and MODI method) are all algorithms used for finding optimal solutions to transportation problems, rather than heuristics.

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.

Accepted Answer

When total supply is greater than total demand, we introduce a dummy destination with demand equal to the excess of supply over demand to balance the problem.

Question 20

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...

Quiz 19: Solution Procedures for Transportation and Assignment Problems