Question 1

In a capacitated transshipment problem, some or all of the transfer points are subject to capacity restrictions.

Accepted Answer

The answer of In a capacitated transshipment problem, some or...

Question 2

In the general assignment problem, one agent can be assigned to several tasks.

Accepted Answer

Yes, this is one of the characteristics of the general assignment problem, where there can be multiple assignments of tasks to a single agent.

Question 3

A transportation problem with 3 sources and 4 destinations will have 7 variables in the objective function.

Accepted Answer

A transportation problem with 3 sources and 4 destinations will have 12 variables in the objective function, not 7. The objective function will have one variable for each possible route between sources and destinations.

Question 4

The assignment problem is a special case of the transportation problem in which all supply and demand values equal one.

Accepted Answer

The answer of The assignment problem is a special case...

Question 5

A transshipment constraint must contain a variable for every arc entering or leaving the node.

Accepted Answer

A transshipment constraint is a linear equation that represents the conservation of flow for a node in a transportation network. It must include a variable for every incoming and outgoing arc to the node, as the total incoming flow must equal the total outgoing flow at the node.

Question 6

A transportation problem with 3 sources and 4 destinations will have 7 decision variables.

Accepted Answer

A transportation problem with 3 sources and 4 destinations will have 12 decision variables (3 x 4 = 12).

Question 7

A transshipment problem is a generalization of the transportation problem in which certain nodes are neither supply nodes nor destination nodes.

Accepted Answer

This statement is true, as a transshipment problem involves intermediate nodes through which goods are transshipped to their final destinations.

Question 8

The maximal flow problem can be formulated as a capacitated transshipment problem.

Accepted Answer

The maximal flow problem involves finding the maximum amount of flow that can be sent through a network of nodes and edges, while respecting capacity constraints. This is equivalent to a capacitated transshipment problem, where goods are transshipped from node to node such that capacity constraints are not violated. Therefore, the statement is true.

Question 9

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 10

Flow in a transportation network is limited to one direction.

Accepted Answer

The answer of Flow in a transportation network is limited...

Question 11

In the LP formulation of a maximal flow problem, a conservation-of-flow constraint ensures that an arc's flow capacity is not exceeded.

Accepted Answer

The conservation of flow constraint ensures that the amount of flow into a node equals the amount of flow out of that node, not that an arc's flow capacity is not exceeded. The constraint that ensures an arc's flow capacity is not exceeded is called the capacity constraint.

Question 12

The capacitated transportation problem includes constraints which reflect limited capacity on a route.

Accepted Answer

In capacitated transportation problem, capacity constraints are included which limit the amount of flow that can be transported along a route.

Question 13

Write the LP formulation for this transportation problem.

Accepted Answer

The answer of Write the LP formulation for this transportation...

Question 14

In a transportation problem with total supply equal to total demand, if there are four origins and seven destinations, and there is a unique optimal solution, the optimal solution will utilize 11 shipping routes.

Accepted Answer

If there are four origins and seven destinations, there are a total of 28 possible shipping routes. However, even if there is a unique optimal solution, it does not necessarily mean that all 28 routes will be utilized. The optimal solution could use fewer or more than 11 routes.

Question 15

Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.

Accepted Answer

Transshipment problem involves intermediate nodes where shipments can both enter and leave, while transportation problem only involves supply nodes and demand nodes with shipments moving in one direction only.

Question 16

The direction of flow in the shortest-route problem is always out of the origin node and into the destination node.

Accepted Answer

In the shortest-route problem, the objective is to find the shortest path from an origin node to a destination node, which inherently means the flow is directed out of the origin and into the destination.

Question 17

When a route in a transportation problem is unacceptable, the corresponding variable can be removed from the LP formulation.

Accepted Answer

This is true. If a route is unacceptable, it means that the corresponding variable (representing that route) should be set to zero in the LP formulation, effectively eliminating it from consideration in the solution.

Question 18

If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.

Accepted Answer

A transportation problem with four origins and five destinations will have 4+5=9 variables in the LP formulation and therefore 9 constraints (one for each origin and one for each destination).

Question 19

The shortest-route problem is a special case of the transshipment problem.

Accepted Answer

The shortest-route problem involves finding the shortest path between two nodes in a graph or network, while the transshipment problem involves determining how to transport goods from sources to destinations through intermediate nodes, maximizing profit or minimizing cost. The shortest-route problem can be considered a subset of the larger transshipment problem, as it involves determining the optimal flow of goods along a specific path within a larger network.

Question 20

When the number of agents exceeds the number of tasks in an assignment problem, one or more dummy tasks must be introduced in the LP formulation or else the LP will not have a feasible solution.

Accepted Answer

In an assignment problem, if the number of agents exceeds the number of tasks, introducing dummy tasks (with zero cost) ensures that the problem remains balanced and every agent is assigned to a task, but not having dummy tasks does not mean the LP will not have a feasible solution; it just means some agents will not be assigned tasks.

Quiz 6: Distribution and Network Models