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

Accepted Answer

A mutually exclusive decision means that if one decision is yes, the other must be no, and vice versa; it does not depend on both decisions being yes.

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

Accepted Answer

Binary integer programming problems can answer questions related to decision making, such as whether or not to undertake a project, make an investment, or locate a plant at a particular location. Therefore, all choices listed are correct.

Question 3

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

Accepted Answer

In a product mix problem with setup costs, the linear programming formulation needs to be modified to include the setup costs as well. The modified formulation is known as mixed integer linear programming (MILP) or mixed integer programming (MIP). Therefore, the statement is true that a linear programming formulation is not valid for a product mix problem with setup costs.

Question 4

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

Accepted Answer

Variables whose only possible values are 0 and 1 are typically called binary variables, not integer variables. Integer variables can take on any integer value, not just 0 or 1.

Question 5

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

Accepted Answer

Binary variables are also known as boolean variables and their only possible values are 0 and 1.

Question 6

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

Accepted Answer

A parameter analysis report can indeed be used to perform sensitivity analysis for integer programming problems. Sensitivity analysis involves examining how changes in the input parameters (such as the objective function coefficients, right-hand side values, or constraint coefficients) affect the optimal solution and associated values (such as shadow prices and reduced costs). A parameter analysis report can provide information on the range of values over which the optimal solution and associated values remain unchanged, as well as the impact of changes beyond these ranges. This can be useful in decision-making and management under uncertainty.

Question 7

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

Accepted Answer

Binary variables have only two possible values, usually 0 and 1, making them ideal for representing 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

Accepted Answer

The answer of An auxiliary binary variable is an additional...

Question 9

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

Accepted Answer

A pure BIP problem is a binary integer programming problem where all the variables are binary variables.

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

Accepted Answer

Binary variables can only have two possible values: 0 and 1.

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

Accepted Answer

This statement is false. The algorithms available for solving linear programming problems are generally more efficient than those for BIP problems. However, there are certain types of BIP problems that have faster algorithms available than linear programming alternatives, so the advantage of formulating a problem as BIP depends on the specific problem structure.

Question 12

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

Accepted Answer

This is the definition of mutually exclusive alternatives.

Question 13

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

Accepted Answer

It is possible to have a constraint in a BIP that forces at least one of the alternatives to be chosen, thus excluding the possibility of choosing none of them.

Question 14

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

Accepted Answer

The constraint allows for combinations of x1, x2, and x3 to sum up to 3, which means they are not mutually exclusive as more than one variable can be 1 simultaneously.

Question 15

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

Accepted Answer

The constraint x₁ ≤ x₂ means that alternative 1 cannot be selected unless alternative 2 is also selected, not the other way around.

Question 16

BIP can be used to determine the timing of activities

Accepted Answer

BIP (Business Integration Process) can be used to determine the timing of activities in order to improve the efficiency and effectiveness of business processes.

Question 17

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

Accepted Answer

The answer of A BIP problem considers one yes-or-no decision...

Question 18

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

Accepted Answer

The Excel sensitivity report can only be used for linear programming problems, not 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

Accepted Answer

Binary integer programming problems are those where all the decision variables are restricted to integer values that are either 0 or 1.

Question 20

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

Accepted Answer

BIP (Benefit-cost ratio or Benefit-to-cost ratio) can help in determining whether the benefits of an investment outweigh its costs. This information can be useful in capital budgeting decisions, where the goal is to allocate resources to projects that will generate the highest returns for the company.

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