Deck 7: Using binary integer programming to deal withy es-Or-No decisions

Question 1

A yes-or-no decision is a mutually exclusive decision if it can be yes only if a certain other yes-or-no decision is yes

Answer 1

False

Question 2

Binary integer programming problems can answer which types of questions?

A)Should a project be undertaken?
B)Should an investment be made?
C)Should a plant be located at a particular location?
D)All of the above
E)None of the above

Answer 2

D

Question 3

A linear programming formulation is not valid for a product mix problem when there are setup costs for initiating production

Answer 3

True

Question 4

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

Question 5

Binary variables are variables whose only possible values are 0 or 1

Question 6

A parameter analysis report can be used to perform sensitivity analysis for integer programming problems

Question 7

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

Question 8

An auxiliary binary variable is an additional binary variable that is introduced into a model to represent additional yes-or-no decisions

Question 9

A problems where all the variables are binary variables is called a pure BIP problem

Question 10

Binary variables can have the following values:

A)0
B)1
C)any integer value
D)a and b only
E)All of the above

Question 11

The algorithms available for solving BIP problems are much more efficient than those for linear programming which is one of the advantages of formulating problems this way

Question 12

If choosing one alternative from a group excludes choosing all of the others then these alternatives are called mutually exclusive

Question 13

It is possible to have a constraint in a BIP that excludes the possibility of choosing none of the alternatives available

Question 14

The constraint x₁ + x₂ + x₃? ≤ 3 in a BIP represents mutually exclusive alternatives

Question 15

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

Question 16

BIP can be used to determine the timing of activities

Question 17

A BIP problem considers one yes-or-no decision at a time with the objective of choosing the best alternative

Question 18

The Excel sensitivity report can be used to perform sensitivity analysis for integer programming problems

Question 19

Binary integer programming problems are those where all the decision variables restricted to integer values are further restricted to be binary variables

Question 20

BIP can be used in capital budgeting decisions to determine whether to invest a certain amount

Question 21

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

A)x₁ + x₂ +x₃ ≤ 1
B)x₁ + x₂ +x₃ = 1
C)x₁ - x₂ -x₃ ≤ 1
D)x₁ - x₂ -x₃ = 1
E)None of the above

Question 22

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)A + B ≤ 1
B)A + B = 1
C)A ≤ B
D)B ≤ A
E)None of the above

Question 23

In a BIP problem,1 corresponds to a yes decision and 0 to a no decision If there are 4 projects under consideration (A,B,C,and D)and at most 2 can be chosen then the following constraint needs to be added to the formulation:

A)A + B + C + D ≤ 1
B)A + B + C + D ≤ 2
C)A + B + C + D ≤ 4
D)A + B + C + D = 2
E)None of the above

Question 24

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

A)x₁ + x₂ ≤ 1
B)x₁ + x₂ ≥ 1
C)x₁ - x₂ ≤ 1
D)x₁ - x₂ = 1
E)None of the above

Question 25

In a BIP problem,1 corresponds to a yes decision and 0 to a no decision If there are two projects under consideration,A and B,and either both projects will be undertaken or no project will be undertaken,then the following constraint needs to be added to the formulation:

A)A ≤ B
B)A + B ≤ 2
C)A ≥ B
D)A = B
E)None of the above

Question 26

Which of the following techniques or tools can be used to perform sensitivity analysis for an integer programming problem?

A)The sensitivity report
B)Trial-and-error
C)A parameter analysis report
D)All of the above
E)b and c only

Question 27

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

A)x₁ + x₂ ≤ 1
B)x₁ + x₂ = 1
C)x₁ - x₂ ≤ 1
D)x₁ - x₂ = 1
E)None of the above

Question 28

.
Binary integer programming can be used for:

A)capital budgeting
B)site selection
C)scheduling asset divestitures
D)assignments of routes
E)All of the above