Decision Models Exam 2

Which of the following is an appropriate application for a maximum flow model?

-Maximizing the data capacity of a computer network -Maximizing the number of people who pass through an exhibit

Binary integer programming problems can answer which types of questions?

-Should a project be undertaken? -Should an investment be made? -Should a plant be locayed at a particular location?

Which of the following is an example of a transshipment node?

-Storage Facilities -Processing Facilities -Short Term Investment -Warehouses

which of the following statements about minimum-cost flow problems is false?

-Supply nodes have negative net flow -Transshipment nodes have positive net flow

In a project selection problem, which of the following constraints can be modelled using binary variables?

-Whether or not to select a project -The minimum number of projects to select, -The maximum number of projects to select -Selecting one project is only possible if some other project is also selected

the crew scheduling problem can be formulated as

-a set covering problem -a binary integer problem

which of the following about crew scheduling problems are true?

-all functional constraints are set covering constraints -the objective is to minimize total cost

which of the following is a way to investigate the effect of simultaneous changes to objective function coefficients?

-apply the 100% rule -use a two way parameter analysis report -try the changes on a spreadsheet

if a minimum-cost flow problem has more supply (total capacity at all supply nodes) than demand (total demand at demand nodes)

-convert supply constraints to <= constraints -add a dummy demand node to the network

which of the following is a potential application for a minimum cost flow model?

-developing a plan to ship a product from several factories to a number of warehouses -determining the maximum amount of a product that can be shipped through a distribution network -assigning consultants to projects around the world

What are assumptions of robust optimization with independent parameters?

-each parameter's value is not influenced by the values of other parameters -each parameter has a range of uncertainty -all functional constraints are either <= or >=

when a model uses binary integer decision variables

-shadow prices cant be calculated -solvers sensitivity report is unavailable

Which of the following statements about shortest path problems are true?

-the objective is to find the path that minimizes the distance travelled -travel through the network starts at the origin

in a product mix problem, it is often difficult to estimate

-the profitability of new products -the cost of new raw materials

Binary integer values are useful to model what types of decisions? 1. Yes-or-No decisions 2. The quantity of a product to produce 3. The amount of money to invest in a certain project

1 Only

a minimum-cost flow model has three sources and four destinations. How many constraints will be needed to ensure that the quantity shipped does not exceed capacity?

3

In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If project A can be undertaken only if project B is also undertaken then the following constraint needs to be added to the formulation:

A ≤ B

Which of the following will have negative net flow in a minimum cost flow problem?

Demand nodes

Changing the objective function coefficients may or may not change the optimal solution, but it will always change the value of the objective function

False

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

False

If activities A and B are mutually exclusive, the constraint xA ≤ xB will enforce this relationship in a linear program.

False

The constraint x1 ≤ x2 in a BIP problem means that alternative 2 cannot be selected unless alternative 1 is also selected.

False

The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity.

False

Variables whose only possible values are 0 and 1 are called integer variables.

False

Which of the following statements about integer programming is TRUE?

In a pure Binary Integer Program all variables must be either 0 or 1.

What is the objective of a maximum flow problem?

Maximize the amoubnt flowing through a network.

in a transportation problem, the demand nodes have a fixed requirement. In a __________ problem, the demand node has no limit on requirements.

Maximum flow

Which of the following is not an assumption of a maximum flow problem?

That flow can move toward the sink and away from the sink.

Which of the following is not an assumption of a shortes path problem?

The lines connecting certain pairs of nodes always travel in either direction.

For a minimum cost flow problem to have a feasible solution, which of the following must be true?

There is an equal amount of supply and demand

Which of the following is not an assumption of a minimum cost flow problem?

There is an equal number of supply and demand nodes.

A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.

True

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

True

If the change to a right-hand side is within the allowable range, the value of the shadow price remains valid

True

In a maximum flow problem, the cost of shipping across each arc is irrelevant

True

Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem.

True

T/F Setup cost is only associated if there is a number of units above zero produced

True

Variables whose only possible values are 0 and 1 are called binary variables.

True

When binary variables are used in a linear program, the Solver Sensitivity Report is not available.

True

When certain parameters of a model represent managerial policy decisions, what-if analysis provides information about what the impact would be of altering these policy decisions

True

what if analysis refers to the process of addressing questions that occur when?

after the basic model has been solved to optimality

a firm is attempting to find the most efficient means of allocating consulting jobs amongst its 5 consultants. What model would be most appropriate?

assignment problem

option A is a contingent decision if option A _______ be accepted if option B is accepted first

can only

the maximum amount that can flow through any arc is known as the

capacity

if it is acceptable to have a constraint which has a probability of being violated, an analyst can add

chance constraints to the model

the parameters of the model are entered into the

data cells

Number of demand constraints is equal to the number of

demand nodes

a set covering constraint requires the sum of a set of binary decision variables to be ______ than or equal to one

greater

In robust optimization, a constraint that cannot be violated is known as a

hard constraint

objective function value

is the quantity of Product_2 times the change in objective function coefficient

If a path in a network allows travel in either direction, it is referred to as a

link

to identify a robust solution with independent parameters, assign the ____________ value for each coefficient on the left of a <= sign of a constraint

maximum

when a firm can choose at most one of a set of options, the options are

mutually exclusive

quantity shipped restraint is equal to

number of sources

mixed BIP model

only a portion of the decision variables are binary

the allowable range for an objective function coefficient shows the range of objective function coefficients that will not result in a change in the

optimal solution

In the shortest path problem, the starting problem is known as the

origin

which is not a type of minimum-cost flow problem?

product mix problems

a Bip model which attempts to minimize costs while satisfying only set covering constraints is called

set covering problem

Which of the following represents the marginal gain in the objective value that would occur if one more unit of a resource were added?

shadow price

if the right-hand side of a constraint is increased by one unit, the amount that the objective function value will increase is given by

shadow price

Transshipment problems are essentially the same as transportation problems, but in the transshipment problem

shipments pass through intermediate nodes

a city to is trying to find tha fastest route for fire trucks. this is a

shortest path problem

Number of arcs

sources x destination

in a maximum flow problem, all of the flow in the network originate at a single _____ node and ends at a single _____ node

supply, demand

if the total change (as a percentage of the allowable change) for two or more changes to constraint right hand sides is more than 100 percent

the optimal solution may or may not change

if the total change (as a percentage of the allowable change) for two or more changes to constraint right hand sides is less than 100 percent

the shadow price remains valid

a firm is attempting to find the most efficient means of shipping a product from its five factories directly to its three warehouses. What model would be most appropriate?

transportation problem

in a network diagram, a node which has equal quantities flowing in and out is called

transshipment node

which of the following must conform to the conservation of flow principle?

transshipment node

a firm is attempting to find the most efficient means of shipping a product from its five factories directly to its three warehouses. The firm uses two warehouses to receive shipments from the factories before shipping the products to the customer. What model would be most appropriate?

transshipment problem

pure BIP model

uses only binary decision variables

The process of determining the effect of changing objective function coefficients, right-hand side values of constraints, and decision variable values on a linear program is known as

what-if analysis

when a product is produced, a setup cost of 500 is incurred and the capacity of the production is 25 units. If the binary decision variable Y is used to represent setup costs, which of the following would ensure X (quantity) does not exceed capacity

x <=25y

In a BIP problem with 3 mutually exclusive alternatives, x1 , x2 , and x3, the following constraint needs to be added to the formulation:

x1 + x2 + x3 ≤ 1

In a BIP problem with 2 mutually exclusive alternatives, x1 and x2, the following constraint needs to be added to the formulation:

x1 + x2 ≤ 1

In a BIP problem, which of the following constraints would enforce a mutually exclusive relationship between project 1 and project 2?

x1 + x2 ≤ 1

In a BIP problem, which of the following constraints will enforce a contingent relationship between project 1 and 2 such that project 1 can be accepted only if project 2 is also accepted and that project 2 can only be accepted is project 1 is accepted?

x2 = x1

when the only choice is to proceed or decline, it's known as a

yes or no decision

In the shortes path model with multiple destinations, a dummy destination can be used to force the network to have a single destination. The length of the arc from each destination to the dummy destination is

zero

when using binary integer decision variables to model the selection of facility locations, a decision variable value of ____ means the location was not selected.

zero