AGEC 3413 Test 3 LSU

The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means: A) agent 3 can be assigned to 2 tasks. B) agent 3 can be assigned to no more than 2 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks. D) agents 1, 2, 3, and 4 can be assigned up to 2 tasks.

B) agent 3 can be assigned to no more than 2 tasks.

The assignment problem constraint x41 + x42 + x43 + x44 ≤ 3 means: A) agent 3 can be assigned to 4 tasks. B) agent 4 can be assigned to 3 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks 1, 2 or 3. D) There is no feasible solution.

B) agent 4 can be assigned to 3 tasks.

In the linear programming formulation of the shortest route problem, the constraint for each node represents: A) capacity on each path. B) conservation of flow. C) capacity on each branch. D) minimum flow.

B) conservation of flow.

For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type. A) up and down B) up C) down D) up or down

C) down

In a ________ integer model, some solution values for decision variables are integers and others can be non-integer. A) total B) 0-1 C) mixed D) all of the above

C) mixed

In a network modeling problem, the linear programming decision variables are given by: A) source node. B) sink node. C) network branches. D) network nodes.

C) network branches.

In the process of evaluating location alternatives, the transportation model method minimizes the: A) total demand. B) total supply. C) total shipping cost. D) number of destinations.

C) total shipping cost.

The problem that deals with the distribution of goods from several sources to several destinations is the: A) network problem. B) assignment problem. C) transportation problem . D) transshipment problem.

C) transportation problem .

In a transshipment problem, items may be transported: A) from destination to destination. B) from one transshipment point to another. C) directly from sources to destinations. D) all of the above

D) all of the above

Types of integer programming models are: A) total. B) 0-1. C) mixed. D) all of the above

D) all of the above

The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination. A) destination, source B) source, destination C) demand, source D) source, demand

D) source, demand

In an assignment problem all supply and demand values equal are: A) 0. B) 1. C) 2. D) greater than 1.

B) 1.

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

B) mutually exclusive

The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination

True

The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer.

True

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint.

conditional

The cost to send a unit of product from supply source A to demand location B would be represented in the ________ of the linear programming statements.

objective function

In an assignment problem, all demand and supply values are equal to ________.

one

The ________ model is an extension of the transportation model in which intermediate points are added between the sources and destinations.

transshipment

________ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

In a network flow model, a directed branch: A) is a branch with a positive distance value. B) is a branch in which flow is possible in only one direction. C) is a branch on which the flow capacity is exhausted. D) is a branch in which flow is not possible in either direction.

B) is a branch in which flow is possible in only one direction.

The minimal spanning tree allows the visitation of each node without backtracking.

False

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal spanning tree.

False

The shortest route network problem could help identify the best plan for running cables for televisions throughout a building.

False

In order to model a "prohibited route" in a transportation or transshipment problem, the cost assigned to the route should be ________.

high

A ________ network model could be used to represent the capacity of a series of dams for flood control

maximal flow

The goal of the ________ problem is to maximize the amount of flow of items from an origin to a destination

maximal flow

Determining where to build roads at the least cost within a park that reaches every popular sight represents a ________ network model.

minimal spanning tree

The ________ connects all nodes in a network so that the total branch lengths are minimized.

minimal spanning tree

A ________ integer model allows for the possibility that some decision variables are not integers.

mixed

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint.

mutually exclusive

In a 0-1 integer model, the solution values of the decision variables are 0 or 1.

True

The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized.

True

Determining where capacity needs to be added within a series of one-way roads within a park represents a ________ model

maximal flow

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

A) multiple choice

Which of the following is not an integer linear programming problem? A) pure integer B) mixed integer C) 0-1 integer D) continuous

D) continuous

A conditional constraint specifies the conditions under which variables are integers or real variables.

False

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected.

False

In a minimal spanning tree, the source and destination nodes must be connected along a single path.

False

In a mixed integer model, all decision variables have integer solution values.

False

In a mixed integer model, the solution values of the decision variables are 0 or 1.

False

In a transportation problem, items are allocated from sources to destinations at a maximum value.

False

In a transshipment model, the supply at each source and demand at each destination are limited to one unit.

False

In an unbalanced transportation model, all constraints are equalities

False

In an unbalanced transportation problem, if demand exceeds supply, the optimal solution will be infeasible.

False

In order to model a "prohibited route" in a transportation or transshipment problem, the route should be omitted from the linear program

False

The ________ method is based on the principle that the total set of feasible solutions can be partitioned into smaller subsets of solutions.

branch and bound

In a network flow problem, ________ connect nodes and show flow from one point to another

branches

In a network flow problem, the values assigned to ________ typically represent distance, time, or cost.

branches

In a typical network flow problem, the branches show flow from one node to the next. The nodes themselves are ________ points

junction (connecting)

In a ________ linear programming model, some of the solution values for the decision variables are required to assume integer values and others can be integer or noninteger.

mixed integer

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint.

multiple-choice

In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a ________ constraint.

multiple-choice

In a network flow problem, ________ represent junction points connecting branches.

nodes

A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area. Cost is proportional to distance traveled. The type of network model that best represent this situation is ________.

shortest route

Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a ________ network model.

shortest route

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the ________ solution technique

shortest route

In an unbalanced transportation problem, if supply exceeds demand, the shadow price for at least one of the supply constraints will be equal to ________.

zero

In a ________ linear programming model, the solution values of the decision variables are zero or one.

0-1 integer

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected. A) can also B) can sometimes C) can never D) must also

Answer: D

If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch? A) offices B) waiting areas C) heating and ventilation systems D) computer rooms

C) heating and ventilation systems

You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is : A) S1 + S3 + S7 ≥ 1. B) S1 + S3 + S7 ≤1. C) S1 + S3 + S7 = 2. D) S1 + S3 + S7 ≤ 2.

D) S1 + S3 + S7 ≤ 2.

A prohibited route in a transportation model should be assigned a value of zero.

False

Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

False

The branch and bound solution method cannot be applied to 0-1 integer programming problems.

False

The choice of the initial node in the minimal spanning tree technique must be the first node.

False

The first step of the minimal spanning tree solution to compute the distance of any path through the network.

False

The maximal flow algorithm may end with capacity remaining at the source

False

The source node is the input node in a maximal flow problem

True

The values assigned to branches typically represent distance, time, or cost.

True

A form of the transportation problem in which all supply and demand values equal 1 is the ________ problem.

assignment

In an integer program, if building one facility required the construction of another type of facility, this would be written as: ________.

x1 = x2

The objective of the maximal flow solution approach is to: A) maximize resource allocation . B) maximize the total amount of flow from an origin to a destination. C) determine the longest distance between an originating point and one or more destination points. D) determine the shortest distance between an originating point and one or more destination points.

B) maximize the total amount of flow from an origin to a destination.

The branch and bound method of solving linear integer programming problems is: A) an integer method. B) a relaxation method. C) a graphical solution. D) an enumeration method.

D) an enumeration method

For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model

True

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

True

In a transshipment problem, items may be transported directly from sources to destinations

True

In a transshipment problem, items may be transported from sources through transshipment points on to destinations.

True

Nodes represent junction points connecting branches

True

One type of constraint in an integer program is a multiple-choice constraint.

True

Regardless of the number of nodes in a network, the minimal spanning tree always contains the two nodes with the shortest distance between them

True

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem.

True

The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables.

True

The divisibility assumption is violated by integer programming.

True

The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination

True

The transshipment model includes intermediate points between the sources and destinations

True

A plant has four jobs to be assigned to four machines, and each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of four jobs to four machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________ model.

assignment

In a linear programming formulation of a transportation model, each of the possible combinations of supply and demand locations is a(n) ________.

decision variable

An appropriate choice of a model for analyzing the best shipping routes for a supply chain consisting of a manufacturer, warehouse, and retailer would be the ________ model. `

transshipment

An example of a ________ point is a distribution center or warehouse located between plants and stores.

transshipment

If the number of sources is greater than the number of destinations, then we have a(n) ________ assignment problem.

unbalanced

Binary variables are: A) 0 or 1 only. B) any integer value. C) any continuous value. D) any negative integer value

A) 0 or 1 only

In a balanced transportation model where supply equals demand: A) all constraints are equalities. B) none of the constraints are equalities. C) all constraints are inequalities. D) none of the constraints are inequalities.

A) all constraints are equalities.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem. A) always B) sometimes C) optimally D) never

A) always

The first step of the maximal flow solution method is to: A) arbitrarily select any path in the network from origin to destination. B) select the node with the shortest direct route from the origin. C) add the maximal flow along the path to the flow in the opposite direction at each node. D) select any starting node.

A) arbitrarily select any path in the network from origin to destination.

The first step of the minimal spanning tree solution method is to: A) select any starting node. B) select the node closest to the starting node to join the spanning tree. C) select the closest node not presently in the spanning tree. D) arbitrarily select any path in the network from origin to destination.

A) select any starting node.

The first step in the shortest route solution method is to: A) select the node with the shortest direct route from the origin. B) determine all nodes directly connected to the permanent set nodes. C) arbitrarily select any path in the network from origin to destination. D) make sure that all nodes have joined the permanent set.

A) select the node with the shortest direct route from the origin.

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the: A) shortest route solution technique. B) minimal spanning tree solution method. C) maximal flow solution method. D) minimal flow solution method.

A) shortest route solution technique.

In a ________ integer model, all decision variables have integer solution values. A) total B) 0-1 C) mixed D) all of the above

A) total

In a ________ integer model, the solution values of the decision variables are 0 or 1. A) total B) 0-1 C) mixed D) all of the above

B) 0-1

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is: A) 0. B) 1. C) 0 or 1. D) none of the above

B) 1.

Which of the following are assumptions or requirements of the transportation problem? A) There must be multiple sources. B) Goods are the same, regardless of source. C) There must be multiple destinations. D) There must be multiple routes between each source and each destination.

B) Goods are the same, regardless of source.

In a transportation problem, items are allocated from sources to destinations: A) at a maximum cost. B) at a minimum cost. C) at a minimum profit. D) at a minimum revenue.

B) at a minimum cost.

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected. A) must always B) can sometimes C) can never D) is already

B) can sometimes

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected. A) exactly 1, 2 B) exactly 2, 4 C) at least 2, 4 D) at most 1, 2

B) exactly 2, 4

The shortest route problem requires: A) each destination to be visited only once. B) finding the quickest route from the source to each node. C) that there be a branch from each destination to every other destination. D) that there be no two-way branches between nodes

B) finding the quickest route from the source to each node.

In an assignment problem: A) one agent can do parts of several tasks. B) one task can be done by only one agent. C) each agent is assigned to its own best task. D) several agents can do parts of one task.

B) one task can be done by only one agent.

If we wanted to represent water resources as a network flow problem, which of the following would be represented as nodes? A) canals B) pumping stations C) rivers D) pipelines

B) pumping stations

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: A) always optimal and feasible. B) sometimes optimal and feasible. C) always feasible. D) never optimal and feasible.

B) sometimes optimal and feasible

A branch where flow is permissible in either direction is a(n): A) directed branch. B) undirected branch . C) labeled branch. D) unlabeled branch.

B) undirected branch .

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

C) conditional

The difference between the assignment and the transportation problem is that: A) total supply must equal total demand in the assignment 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) both A and B

C) each supply and demand value is 1 in the assignment problem.

If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes? A) streets B) railway lines C) street intersections D) pedestrian right of ways

C) street intersections

The local Internet provider wants to develop a network that will connect its server at its satellite center in Valparaiso with the main city computer centers in Northwest Indiana to improve the Internet service and to minimize the amount of cable used to connect network nodes. If we represent this problem with a network: A) the cities are branches and cables are nodes. B) the cables are the branches and the cities are the nodes. C) the length of cables in miles are the branches, and the cities are the nodes. D) the cities are the branches and the length of cables in miles are the nodes.

C) the length of cables in miles are the branches, and the cities are the nodes.

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? A) x1 + x2 + x5 ≤ 1 B) x1 + x2 + x5 ≥ 1 C) x1 + x5 ≤ 1, x2 + x5 ≤ 1 D) x1 - x5 ≤ 1, x2 - x5 ≤ 1

C) x1 + x5 ≤ 1, x2 + x5 ≤ 1

Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs per unit are constant. B) There is one transportation route between each source and destination. C) There is one transportation mode between each source and destination. D) Actual total supply and actual total demand must be equal.

D) Actual total supply and actual total demand must be equal.

In the linear programming formulation of a transportation network: A) there is one variable for each arc. B) there is one constraint for each node. C) the sum of variables corresponding to arcs out of an source node is constrained by the supply at that node. D) all of the above

D) all of the above

The maximal flow algorithm: A) does not require flow on every branch for the final solution. B) may end with capacity remaining at the source. C) may end with capacity at those nodes leading immediately to the destination. D) all of the above

D) all of the above

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. A) multiple-choice B) mutually exclusive C) conditional D) corequisite

D) corequisite

The minimal spanning tree problem determines the: A) minimum amount that should be transported along any one path. B) maximum amount that can be transported along any one path. C) shortest distance between a source node and a destination node. D) minimum total branch lengths connecting all nodes in the network.

D) minimum total branch lengths connecting all nodes in the network.

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. A) always, optimal B) always, non-optimal C) never, non-optimal D) sometimes, optimal

D) sometimes, optimal

Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? A) x1 = 6, x2 = 4, Z = 54 B) x1 = 3, x2 = 6, Z = 51 C) x1 = 2, x2 = 6, Z = 46 D) x1 = 4, x2 = 6, Z = 56

D) x1 = 4, x2 = 6, Z = 56

Flows in a network can only be in one direction

False

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint.

False

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

False

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

False

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.

False

Regardless of the number of nodes in a network, the minimal spanning tree cannot contain the two nodes with the greatest distance between them.

False

The management scientist's fiance informed him that if they were to be married, he would also have to welcome her mother into their home. The management scientist should model this decision as a contingency constraint.

False

The shortest route problem requires that there be a branch from each destination to every other destination

False

A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.

True

A network is an arrangement of paths connected at various points through which items move.

True

A prohibited route in a transportation model should be assigned an arbitrarily high cost coefficient.

True

A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm

True

An assignment problem is a special form of transportation problem where all supply and demand values equal 1

True

Assignment linear programs always result in integer solutions

True

Branches connect nodes and show flow from one point to another

True

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.

True

In a balanced transportation model where supply equals demand, all constraints are equalities

True

In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

True

In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.

True

In a total integer model, all decision variables have integer solution values.

True

In a transportation problem, items are allocated from sources to destinations at a minimum cost.

True

In a transshipment problem, items may be transported from destination to destination and from source to source.

True

In a transshipment problem, items may be transported from one destination to another

True

In a transshipment problem, items may be transported from one source to another

True

In a transshipment problem, items may be transported from one transshipment point to another

True

Networks may be used to represent assignment problems

True

Once the shortest route to a particular node has been determined, that node becomes part of the permanent set.

True

The last step of the minimal spanning tree solution method is to make sure all nodes have joined the spanning tree.

True

The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria

True

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

True

The shortest route problem is to find the shortest distance between an origin and various destination points

True

The three types of integer programming models are total, 0-1, and mixed.

True

In a ________ transportation model where supply equals demand, all constraints are equalities.

balanced

In order to prevent the accumulation of inventory at transshipment points, they should be modeled as being ________ nodes

balanced

If one location for a warehouse can be selected only if a specific location for a manufacturing facility is also selected, this decision can be represented by a ________ constraint.

conditional

The shortest route problem formulation requires a statement that mandates that what goes in to a node must equal what comes out of that node. This is referred to as ________.

conservation of flow

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a ________ constraint."

contingency or mutually exclusive

A one-way street in a downtown area should be modeled as a(n) ________ branch in a maximal flow model

directed

Once a decision maker has determined the shortest route to any node in the network, that node becomes a member of the ________.

permanent set

A courier service located at the south edge of downtown dispatches three bicycle couriers with identical sets of architectural renderings that must go to three different downtown law offices as quickly as possible. This problem is a likely candidate for analysis using ________.

the shortest route solution/algorithm

In a ________ problem, items are allocated from sources to destinations at a minimum cost

transportation

In most real-world cases, the supply capacity and demanded amounts result in a(n) ________ transportation model.

unbalanced

In an integer program, if we were choosing between two locations to build a facility, this would be written as: ________.

x1 + x2 = 1