Chapter 7 Using Binary Integer Programming to Deal with Yes-or-No decisions单词卡 | Quizlet

I. Yes-or-No decisions

Binary integer values are useful to model what types of decisions?

I. Yes-or-No decisions

II. The quantity of a product to produce

III. The amount of money to invest in a certain project

a. x1 + x2 ≤ 1

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

a. x1 + x2 ≤ 1

b. x1 + x2 ≥ 1

c. x1 − x2 ≤ 1

d. x1 − x2 = 1

e. None of the answer choices is correct.

x2 = x1

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?

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

Which of the following statements about integer programming is TRUE?

e. All of the answers choices is correct.

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

a. Whether or not to select a project

b. The minimum number of projects to select

c. The maximum number of projects to select

d. Selecting one project is only possible if some other project is also selected

e. All of the answers choices is correct.

True

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

t/f

False

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

t/f

False

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

t/f

True

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

t/f

d. All of the choices are correct.

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 choices are correct.

e. None of the choices is correct.

a. x1 + x2 ≤ 1.

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 choices is correct.

c. A ≤ B.

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 choices is correct.

a. x1 + x2 + x3 ≤ 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 choices is correct.

False

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

t/f

True

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

t/f

a binary variable that represents a yes-or-no decision by assigning a value of 1 for choosing yes and a value of 0 for choosing no

binary decision variable

a yes-or-no decision is this if it can be yes only if a certain other yes-or-no decision is yes

Contingent Decisions

where only some of the variables are restricted to be binary variables

Mixed BIP model

A group of alternatives where choosing any one alternative excludes choosing any of the others

mutually exclusive alternatives

a constraint that requires the sum of certain binary variables to be greater than or equal to 1

set covering constraint