Question 1

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

Accepted Answer

The constraint x₁ + x₂ + x₃ ≤ 1 ensures that at most one of the mutually exclusive alternatives can be selected.

Question 2

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

Accepted Answer

If project A can be undertaken only if project B is also undertaken, then A can only be 1 if B is 1. This is represented by the constraint A ≤ B.

Question 3

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

Accepted Answer

The constraint should ensure that at most 2 projects are chosen. The term "_{" means that if project A is chosen (represented by 1), then at least one of B, C, or D must be chosen (represented by the term "}+ B + C + D"). This ensures that at least two projects are chosen if A is chosen. The entire constraint states that the total number of chosen projects should be at most 2. Thus, the correct constraint is "A+ B + C + D ≤ 2".

Question 4

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

Accepted Answer

In a BIP (Binary Integer Programming) problem, if two alternatives are mutually exclusive, it means that at most one of them can be chosen. The constraint x₁ + x₂ ≤ 1 ensures that either x₁ or x₂ can be 1, but not both.

Question 5

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

Accepted Answer

The constraint A = B ensures that both projects are either undertaken together (A = 1, B = 1) or not undertaken at all (A = 0, B = 0).

Question 6

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

Accepted Answer

The sensitivity report is not applicable for integer programming problems, as it is based on the assumption of continuous variables. Therefore, only options B and C remain. Trial-and-error involves testing different solutions to see their effect on the objective function, whereas a parameter analysis report involves examining the impact of changes in the problem parameters on the optimal solution. Both techniques can be useful in performing sensitivity analysis for integer programming problems.

Question 7

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

Accepted Answer

The constraint should ensure that only one of the two alternatives is chosen. Therefore, the sum of the decision variables for the two alternatives needs to be equal to 1, meaning that exactly one alternative is chosen. Thus, option B correctly represents this requirement.

Question 8

.
-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

Accepted Answer

Binary integer programming can be used for a variety of applications that involve making decisions about whether or not to select a given option. Capital budgeting, site selection, scheduling asset divestitures, and assignments of routes are all examples of problems that can be framed as binary integer programming problems. By using binary variables, we can represent the decision of choosing or not choosing a particular option, which allows us to optimize our solution for multiple objectives. Therefore, the best choice is E, as it includes all the above options.

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

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

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:

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:

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

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:

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

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:

. -Binary integer programming can be used for: