Question 1

Once one improvement is made to a transportation network using the stepping-stone method, the solution is optimal.

Accepted Answer

The stepping-stone method only guarantees a locally optimal solution, not a globally optimal solution. It is possible that further improvements can still be made to the transportation network.

Question 2

In a transportation problem, each destination must be supplied by one and only one source.

Accepted Answer

In a transportation problem, a destination can be supplied by multiple sources, as the goal is to minimize the total transportation cost while meeting the demand from all destinations and not exceeding the supply from any source.

Question 3

The maximal-flow technique would be helpful to city planners in determining how freeways should be expanded.

Accepted Answer

The maximal-flow technique is used to determine the maximum flow of a network, which could help city planners in determining how freeways should be expanded to optimize traffic flow.

Question 4

In the assignment problem, the costs for a dummy row will be equal to the lowest cost of the column for each respective cell in that row.

Accepted Answer

In the assignment problem, the costs for a dummy row or column are typically set to 0, not to the lowest cost of the column or row for each respective cell. This is because dummy rows or columns are added to balance the problem when the number of sources does not equal the number of destinations, and adding 0 cost ensures that the addition of these dummy assignments does not affect the total cost of the assignment.

Question 5

One of the advantages of the stepping-stone method is that if, at a particular iteration, we accidentally choose a route that is not the best, the only penalty is to perform additional iterations.

Accepted Answer

The statement is true. In the stepping-stone method, each iteration involves testing a set of candidate routes, and choosing the best one to improve the current solution. If we mistakenly choose a sub-optimal route, the algorithm will continue to search for an improved solution in the next iteration. There is no significant penalty for choosing a less optimal route in a single iteration, as long as we eventually converge to the best solution.

Question 6

Using the stepping-stone method to solve a maximization problem, we would choose the route with the largest positive improvement index.

Accepted Answer

The stepping-stone method involves testing different routes by adding or subtracting the transportation cost from each non-basic variable in turn. This creates an improvement index, also known as net change, for each route. The route with the largest positive improvement index is chosen since it would lead to the greatest increase in the objective function value if the corresponding basic variable were made non-basic.

Question 7

The objective of a transportation problem solution is to schedule shipments from sources to destinations while minimizing total transportation and production costs.

Accepted Answer

The objective of a transportation problem solution is indeed to schedule shipments from sources to destinations while minimizing total transportation and production costs.

Question 8

A closed route in the stepping-stone method that sums to zero means that an equivalent cost solution exists.

Accepted Answer

A closed route in the stepping-stone method that sums to zero indicates that the allocations are balanced, and hence, the current solution is optimal. This also means that there is no scope for improving the current solution by making further adjustments using the stepping-stone method. However, it does not necessarily mean that there exists an alternative solution with equivalent cost, but it indicates that the current solution is the best possible using the given set of constraints and cost coefficients.

Question 9

In finding the maximum quantity that can be shipped on the least costly route using the stepping-stone method, one examines the closed path of plus and minus signs drawn and selects the smallest number found in those squares containing minus signs.

Accepted Answer

This statement is true. In the stepping-stone method, one examines the closed path of plus and minus signs and selects the smallest number found in those squares containing minus signs, which represents the maximum quantity that can be shipped on the least costly route.

Question 10

In using the stepping-stone method, the path can turn at any box or cell that is unoccupied.

Accepted Answer

In the stepping-stone method, the path can turn at any occupied or unoccupied cell, not just unoccupied ones.

Question 11

A typical transportation problem may ask the question, "How many of X should be shipped to point E from source A?"

Accepted Answer

The question presented is a common example of a transportation problem, where the objective is to determine the optimal transportation plan or allocation of resources from sources to destinations.

Question 12

The maximal-flow technique would be a useful tool when we are maximizing the cost of shipping items from a series of supply depots to regional distribution centers.

Accepted Answer

The maximal-flow technique is used to maximize the flow of items through a network, such as finding the most efficient way to transport goods from a source to a destination. It is not directly related to the cost of shipping, which would require a different optimization technique.

Question 13

The transportation algorithm can be used to solve both minimization problems and maximization problems.

Accepted Answer

The transportation algorithm, also known as the transportation problem, is a linear programming technique that can be used to solve both minimization and maximization problems, depending on the objective function.

Question 14

The Hungarian method is designed to solve transportation problems efficiently.

Accepted Answer

The Hungarian method is specifically designed for solving assignment problems optimally, not transportation problems.

Question 15

Transportation models may be used when a firm is trying to decide where to locate a new facility.

Accepted Answer

Transportation models can help firms analyze different location options by considering factors such as shipping costs, distances to suppliers and customers, and transportation infrastructure.

Question 16

In a transportation problem, a single source may supply something to all destinations.

Accepted Answer

In a transportation problem, a single source (e.g. a factory, warehouse, etc.) can supply goods or products to multiple destinations (e.g. stores, customers, etc.).

Question 17

It is possible to find an optimal solution to a transportation problem that is degenerate.

Accepted Answer

Degeneracy can occur when one or more of the supply or demand constraints are not fully utilized, resulting in multiple basic feasible solutions. However, it is still possible to find an optimal solution using the methods of the transportation algorithm.

Question 18

Assignment problems involve determining the most efficient assignment of people to projects, salesmen to territories, contracts to bidders, and so on.

Accepted Answer

Assignment problems involve determining the optimal assignment of resources to different tasks or projects, based on certain criteria such as cost, time, or effectiveness. This is a common problem in operations research and management science, and it can be solved using algorithms such as the Hungarian method, the shortest path algorithm, or the network flow algorithm. By finding the best possible assignment, organizations can maximize their efficiency, productivity, and profitability, while minimizing their costs, risks, and errors.

Question 19

The objective of an assignment problem solution most often is to minimize the total costs or time of performing the assigned tasks.

Accepted Answer

The objective of an assignment problem solution is to minimize the total costs or time of performing the assigned tasks.

Question 20

Maximization assignment problems can easily be converted to minimization problems by subtracting each rating from the largest rating in the table.

Accepted Answer

By subtracting each element of the matrix from the largest element, a maximization problem is effectively converted into a minimization problem, as the goal becomes to minimize the complement of the original values, preserving the optimality of assignments.

Quiz 23: Transportation, Assignment, and Network Algorithms