101 CH6

We assume in the maximal flow problem that a. the flow out of a node is equal to the flow into the node. b. the source and sink nodes are at opposite ends of the network. c. the number of arcs entering a node is equal to the number of arcs exiting the node. d. None of the alternatives is correct.

A

The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means a. agent 3 can be assigned to 2 tasks. b. agent 2 can be assigned to 3 tasks. c. a mixture of agents 1, 2, 3, and 4 will be assigned to tasks. d. there is no feasible solution.

A

The assignment problem is a special case of the a. transportation problem. b. transshipment problem. c. maximal flow problem. d. shortest-route problem.

A

The number of units shipped from origin i to destination j is represented by a. xij. b. xji. c. cij. d. cji.

A

Consider a maximal flow problem in which vehicle traffic entering a city is routed among several routes before eventually leaving the city. When represented with a network, a. the nodes represent stoplights. b. the arcs represent one way streets. c. the nodes represent locations where speed limits change. d. None of the alternatives is correct.

B

Constraints in a transshipment problem a. correspond to arcs. b. include a variable for every arc. c. require the sum of the shipments out of an origin node to equal supply. d. All of the alternatives are correct.

B

If a transportation problem has four origins and five destinations, the LP formulation of the problem will have a. 5 constraints b. 9 constraints c. 18 constraints d. 20 constraints

B

The problem which deals with the distribution of goods from several sources to several destinations is the a. maximal flow problem b. transportation problem c. assignment problem d. shortest-route problem

B

The shortest-route problem finds the shortest-route a. from the source to the sink. b. from the source to any other node. c. from any node to any other node. d. from any node to the sink.

B

Which of the following is not true regarding an LP model of the assignment problem? a. Costs appear in the objective function only. b. All constraints are of the ≥ form. c. All constraint left-hand side coefficient values are 1. d. All decision variable values are either 0 or 1.

B

Arcs in a transshipment problem a. must connect every node to a transshipment node. b. represent the cost of shipments. c. indicate the direction of the flow. d. All of the alternatives are correct.

C

Consider a shortest route problem in which a bank courier must travel between branches and the main operations center. When represented with a network, a. the branches are the arcs and the operations center is the node. b. the branches are the nodes and the operations center is the source. c. the branches and the operations center are all nodes and the streets are the arcs. d. the branches are the network and the operations center is the node.

C

The difference between the transportation and assignment problems is that a. total supply must equal total demand in the transportation problem b. the number of origins must equal the number of destinations in the transportation problem c. each supply and demand value is 1 in the assignment problem d. there are many differences between the transportation and assignment problems

C

The parts of a network that represent the origins are a. the capacities b. the flows c. the nodes d. the arcs

C

Which of the following is not true regarding the linear programming formulation of a transportation problem? a. Costs appear only in the objective function. b. The number of variables is (number of origins) x (number of destinations). c. The number of constraints is (number of origins) x (number of destinations). d. The constraints' left-hand side coefficients are either 0 or 1.

C

In a transshipment problem, shipments a. cannot occur between two origin nodes. b. cannot occur between an origin node and a destination node. c. cannot occur between a transshipment node and a destination node. d. can occur between any two nodes.

D

In the general linear programming model of the assignment problem, a. one agent can do parts of several tasks. b. one task can be done by several agents. c. each agent is assigned to its own best task. d. one agent is assigned to one and only one task.

D

The network flows into and out of demand nodes are what makes the production and inventory application modeled in the textbook a a. shortest-route model. b. maximal flow model. c. transportation model d. transshipment model

D

The objective of the transportation problem is to a. identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost. b. minimize the number of origins used to satisfy total demand at the destinations. c. minimize the number of shipments necessary to satisfy total demand at the destinations. d. minimize the cost of shipping products from several origins to several destinations.

D

Which of the following is not a characteristic of assignment problems? a. costs appear in the objective function only b. the RHS of all constraints is 1 c. the value of all decision variables is either 0 or 1 d. the signs of constraints are always <

D

A dummy origin in a transportation problem is used when supply exceeds demand

False

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

False

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

False

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

False

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.

False

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

False

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.

False

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

True

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

True

Converting a transportation problem LP from cost minimization to profit maximization requires only changing the objective function; the conversion does not affect the constraints.

True

Flow in a transportation network is limited to one direction.

True

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

True

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

True

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

True

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

True

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

True

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

True

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

True

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

True

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

True

Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled.

True