Deck 7: Using Binary Integer Programming to Deal With Yes-Or-No Decisions

Question 1

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

Answer 1

True

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

BIP can be used to determine the timing of activities.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

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

Solver Table can be used to perform sensitivity analysis for integer programming problems.
Multiple Choice Questions

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

The constraint x₁ + x₂ + x₃ $\le$ 3 in a BIP represents mutually exclusive alternatives.

Question 18

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.

Question 19

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

Question 20

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

Question 21

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 $\le$ 1.
B)x₁ + x₂ = 1.
C)x₁ - x₂ $\le$ 1.
D)x₁ - x₂ = 1.
E)None of the above.

Question 22

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.

Question 23

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 $\le$ 1.
B)x₁ + x₂ +x₃ = 1.
C)x₁ - x₂ -x₃ $\le$ 1.
D)x₁ - x₂ -x₃= 1.
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 $\le$ 1.
B)x₁ + x₂ $\ge$ 1.
C)x₁ - x₂ $\le$ 1.
D)x₁ - x₂ = 1.
E)None of the above.

Question 25

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)Solver Table.
D)All of the above.
E)b and c only.

Question 26

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 $\le$ 1.
B)A+ B + C + D $\le$ 2.
C)A+ B + C + D $\le$ 4.
D)A+ B + C + D = 2.
E)None of the above.