Question 1

Transportation problems always have integer solutions.

Accepted Answer

Transportation problems may have non-integer solutions, which would need to be rounded up or down to obtain an integer solution.

Question 2

The Hungarian Method is an algorithm used to solve transportation problems.

Accepted Answer

False

Question 3

A network representation is helpful because it shows the geographical layout of the sources and destinations of a problem.

Accepted Answer

False

Question 4

It is always necessary to add constraints to a transportation model in order to restrict variables to only integer values.

Accepted Answer

The answer of It is always necessary to add constraints...

Question 5

Transportation problems are concerned with distributing commodities from sources to destinations in such a way as to minimize the total distribution cost.

Accepted Answer

Transportation problems are indeed focused on minimizing the cost of distributing commodities from origins to destinations.

Question 6

It is not possible to solve a transportation problem that has $\le$ instead of = signs for the supply constraints.

Accepted Answer

While it is preferred to have = signs for the supply constraints in a transportation problem, it is still possible to solve a problem with ≤ or ≥ signs. The problem may require additional steps to convert the inequality constraints to equality constraints.

Question 7

Transportation problems always involve shipping goods from one location to another.

Accepted Answer

Transportation problems can involve optimizing various types of movements or flows, not just shipping goods. They can include scheduling, routing, and allocation of resources in various contexts, such as data transmission, energy distribution, and passenger transport.

Question 8

A network representation can be used to visualize a transportation problem.

Accepted Answer

A network diagram can be used to represent a transportation problem, where the nodes represent the origins and destinations of goods or passengers, and the edges represent the transportation routes between them. This helps in visualizing the optimal routes and costs associated with transporting goods or people.

Question 9

A network representation is an important tool for solving any size transportation problem.

Accepted Answer

The answer of A network representation is an important tool...

Question 10

Transportation problems can be solved by the simplex method.

Accepted Answer

The simplex method is a widely used algorithm for solving linear programming problems, including transportation problems. Therefore, transportation problems can be solved by the simplex method.

Question 11

Transportation problems are a special type of distribution-network problem.

Accepted Answer

Transportation problems involve the distribution of goods from multiple sources to multiple destinations, and therefore fall under the category of distribution-network problems.

Question 12

The supplies and demands provide all the data for a transportation problem.

Accepted Answer

The answer of The supplies and demands provide all the...

Question 13

The transportation model assumes that shipping costs are dependent on the distance that goods are shipped.

Accepted Answer

The answer of The transportation model assumes that shipping costs...

Question 14

The requirements assumption states that each source has a fixed supply of units,where the entire supply must be distributed to the destinations and that each destination has a fixed demand for units,where the entire demand must be received from the sources.

Accepted Answer

The requirements assumption is defined as each source having a fixed supply of units that must be distributed to all destinations and each destination having a fixed demand for units that must be received from all sources. Therefore, the statement is true.

Question 15

The linear programming model of a transportation problem is one of maximization of its objective function.

Accepted Answer

The objective function of a transportation problem is typically to minimize the total cost of transporting goods from sources to destinations. Therefore, the linear programming model of a transportation problem is one of minimization of the objective function.

Question 16

The transportation simplex method solves transportation problems much faster than the regular simplex method.

Accepted Answer

The transportation simplex method is a specialized algorithm designed specifically for solving transportation problems, and it takes advantage of the specific structure of these problems to solve them much faster than the regular simplex method.

Question 17

The feasible solutions property states that a pure transportation problem will have feasible solutions if and only if the sum of its supplies equals the sum of its demands.

Accepted Answer

This statement is true. The feasible solutions property is a fundamental property of pure transportation problems, and it states that if the sum of the supplies (total units available to be shipped from all sources) is equal to the sum of the demands (total units that need to be shipped to all destinations), then there will be feasible solutions to the transportation problem. This means that there will be ways to allocate shipments from sources to destinations such that all of the demands are met and all of the supplies are used up. However, if the sum of the supplies does not equal the sum of the demands, then there will be some sources or destinations that are over- or under-supplied, and the transportation problem will not have feasible solutions.

Question 18

As long as all its supplies and demands have integer values,any transportation problem with feasible solutions is guaranteed to have an optimal solution with integer values for all its decision variables.

Accepted Answer

This statement is true. It is known as the "Integer Solution Property" of transportation problems. However, if the supplies or demands have non-integer values, then the statement may not hold true.

Question 19

A transportation problem requires a unit cost for every source-destination combination.

Accepted Answer

In a transportation problem, unit cost is assigned to every source-destination combination. This cost represents the cost of shipping one unit of the product from a particular source to a particular destination.

Question 20

The transportation model assumes shipping cost per unit is the same regardless of the number of units shipped.

Accepted Answer

The transportation model assumes that the shipping cost per unit is constant and does not vary based on the quantity of units shipped.

Quiz 18: CD - Transportation and Assignment Problems