Question 1

Transportation and assignment problems can be solved by the simplex method, though special purpose algorithms offer an easier solution procedure.

Accepted Answer

Transportation and assignment problems are special cases of linear programming problems that can indeed be solved using the simplex method. However, due to their specific structure, special purpose algorithms such as the transportation method for transportation problems and the Hungarian method for assignment problems are often used because they provide a more straightforward and computationally efficient solution procedure.

Question 2

The total supply must equal total demand in a transportation problem in order to solve it by the transportation algorithm.

Accepted Answer

In a transportation problem, if the total supply does not equal total demand, a dummy source (for excess demand) or a dummy destination (for excess supply) can be added to balance the problem, allowing it to be solved by the transportation algorithm.

Question 3

The total supply must be less than total demand in a transportation problem in order to solve it by the transportation algorithm.

Accepted Answer

In a transportation problem, the total supply can be equal to or less than the total demand. If the total supply is less than the total demand, the problem is considered unbalanced and can be balanced by adding a dummy source with the cost of transportation as zero to meet the excess demand.

Question 4

The total supply must be greater than total demand in a transportation problem in order to solve it by the transportation algorithm.

Accepted Answer

In a transportation problem, the total supply can be equal to or greater than the total demand. If the total supply exceeds total demand, a dummy destination with the excess supply amount is created to balance the problem, allowing it to be solved by the transportation algorithm.

Question 5

In a transportation problem, if the total supply is greater than total demand, all constraints in its formulation can be written as equality constraints.

Accepted Answer

In a transportation problem, if the total supply exceeds total demand, the problem is unbalanced, and to balance it, a dummy destination (with zero cost) is introduced to absorb the excess supply. Therefore, not all constraints can be written as equality constraints; the constraints for the original destinations remain as less than or equal to (≤) constraints to reflect the demand limits, while the supply constraints can be equalities.

Question 6

In a transportation problem, if the total supply is equal to total demand, all constraints in its formulation can be written as equality constraints.

Accepted Answer

In a transportation problem, when total supply equals total demand, each supply and demand constraint can be satisfied exactly, allowing all constraints to be written as equalities.

Question 7

The linear programming formulation of a transportation problem, in general, has demand constraints which are either $\geq$ or $=$ type.

Accepted Answer

Demand constraints in a transportation problem can be either greater than or equal to (≥) or equal to (=) type, depending on whether the demand at a destination is fixed or flexible.

Question 8

The linear programming formulation of a transportation problem, in general, has supply constraints which are either $\geq$ or $=$ type.

Accepted Answer

The linear programming formulation of a transportation problem typically has supply constraints of the $\leq$ or $=$ type, ensuring that the amount shipped from each supply point does not exceed its available supply.

Question 9

Scheduling production in different time periods of a planning horizon can be formulated as a transportation problem.

Accepted Answer

Scheduling production in different time periods can indeed be formulated as a transportation problem by treating different time periods as destinations and the production capacities as sources, thereby optimizing the allocation of production to meet demand over time.

Question 10

Transportation problem formulation can be used to help make location decisions when the total transportation cost is significant.

Accepted Answer

The transportation problem formulation is a type of linear programming problem that helps in determining the most cost-efficient way of distributing products from several suppliers to several consumers. It is particularly useful in making location decisions when the total transportation cost is a significant factor, as it aims to minimize these costs while meeting supply and demand constraints.

Question 11

Transportation problem formulation can be used to solve traffic congestion coming out of a ballpark at the end of a ball game.

Accepted Answer

The transportation problem formulation is primarily used for determining the most efficient way to distribute products from several suppliers to several consumers, optimizing for cost, time, or other factors. It does not directly address traffic congestion management, which involves complex dynamics like road capacity, traffic signal timing, and driver behavior.

Question 12

XYZ Inc. manufactures desks and chairs in all its four furniture manufacturing plants. It has 5 warehouses across the country. One transportation problem can be used to determine how to ship desks and chairs.

Accepted Answer

The transportation problem would need to be solved separately for desks and chairs unless they are considered as a single product type for shipping purposes, which is typically not the case due to their different sizes and handling requirements.

Question 13

In a linear programming formulation of the transshipment problem, if the total supply equals total demand, then all constraints could just be equality constraints.

Accepted Answer

In a transshipment problem where total supply equals total demand, each node's inflow must equal its outflow, allowing all constraints to be expressed as equalities.

Question 14

In a linear programming formulation of the transshipment problem, if the total supply is greater than the total demand, then all constraints could just be $\geq$ type constraints.

Accepted Answer

In a linear programming formulation of the transshipment problem, if the total supply exceeds total demand, the system must include both $\geq$ (or $\leq$) type constraints for supply or demand limitations and equality constraints to ensure the conservation of flow through the network. The $\geq$ type constraints alone cannot ensure that all supplied goods are properly accounted for in the network flow.

Question 15

A transshipment problem can be solved using the transportation formulation, as long as we are assured that no material stays in the intermediate points permanently.

Accepted Answer

The answer of A transshipment problem can be solved using...

Question 16

The transshipment problem formulation may be used in place of transportation formulation when there are two products that are being shipped, each having its own per unit cost of shipping.

Accepted Answer

The transshipment problem formulation is used to model scenarios where goods or commodities are transferred through intermediate nodes before reaching their final destinations, not specifically for handling two products with different shipping costs. The transportation problem focuses on shipping goods from sources to destinations at minimum cost, without the necessity of intermediate nodes.

Question 17

In a linear programming formulation of the assignment problem, the RHS of all constraints is greater than 1.

Accepted Answer

In the assignment problem, the right-hand side (RHS) of the constraints is typically equal to 1, ensuring that each task is assigned to exactly one agent (or vice versa) without exceeding the capacity of any agent or leaving any task unassigned.

Question 18

In a linear programming formulation of the assignment problem, the RHS of all constraints is equal to 1.

Accepted Answer

In the assignment problem, each task is to be assigned to one agent (or vice versa) in such a way that no task is unassigned and no task is assigned to more than one agent. This leads to constraints that ensure each task (or agent) is involved in exactly one assignment, hence the right-hand side (RHS) of these constraints is set to 1.

Question 19

The number of possible assignments in an assignment problem with 4 jobs and 4 workers to assign them to would be 16.

Accepted Answer

The number of possible assignments in an assignment problem with 4 jobs and 4 workers is calculated using the factorial of the number of jobs or workers, which is 4! (4 factorial), equal to 4 x 3 x 2 x 1 = 24, not 16.

Question 20

An assignment problem with 6 projects and 7 potential managers who can handle each of the projects, though with differing efficiency, cannot be solved since we would not know which manager to omit from assignment.

Accepted Answer

An assignment problem with a mismatch in the number of projects and potential managers can still be solved by adding dummy projects to equalize the number of projects and managers, ensuring a complete assignment is possible.

Quiz 6: Transportation, Assignment, and Transshipment Problems