Deck 6: Business Analytics With Integer Programming

Question 1

The divisibility assumption in the mathematical programming model is an acceptable and often reasonable assumption in many applications.

Answer 1

True

Question 2

The impact of rounding a fractional solution into an integer solution on the objective function is always minimal.

Answer 2

False

Question 3

Integer programming models have an objective function to be optimized, a set of constraints to be satisfied, and a set of constraints that forces some or all decision variables to be integers.

Answer 3

True

Question 4

Adding integer constraints to regular linear programming models significantly changes the problem.

Question 5

The finite nature of integer programming models leads to simpler solution algorithms.

Question 6

Nonlinear integer programming models offer additional challenges for solution algorithms because the values of reduced gradients are valid only at the point of the optimal solution.

Question 7

Linear integer programming models offer additional challenges for solution algorithms because the dual values are valid only at the point of the optimal solution.

Question 8

Searching for the optimal integer solution becomes easier for non-smooth nonlinear models.

Question 9

Solver's evolutionary solving method is suggested for seeking optimal integer solutions for non-smooth integer models.

Question 10

The assignment method is a special case of an integer programming model.

Question 11

In the assignment method, the decision maker seeks to assign each available resource to a specific task.

Question 12

The objective function of the assignment method always seeks to minimize cost.

Question 13

The objective function of the assignment method in business settings always seeks to maximize revenue, profit, or another organizational metric.

Question 14

The knapsack problem is a special case of integer programming models.

Question 15

The decision variables for the knapsack problem are defined as the number of items to be included in the knapsack from each of n potential items.

Question 16

The knapsack problem is a special case of the binary linear programming model.

Question 17

The number of decision variables in the assignment problem does not change significantly when the number of resources or tasks increases.

Question 18

In order to strictly enforce integer values for the final solution, the decision maker must set the tolerance level for integer constraints to zero.

Question 19

When determining the number of pounds of lumber to be produced, decision variables must be enforced as integer values.

Question 20

Nonlinear integer programming models have the same structure as integer programming models.

Question 21

Non-negativity constraints belong to an integer programming model, but not necessarily to a linear programming model.

Question 22

While a regular linear programming model has an infinite number of possible solutions, the integer counterpart has an infinite but different set of possible solutions.

Question 23

Nonlinear integer programming models offer additional challenges for solution algorithms because the values of reduced gradients are valid only at the point of the optimal solution.

Question 24

Nonlinear integer programming models offer additional challenges for solution algorithms because the values of Lagrange multipliers are valid only at the point of the optimal solution.

Question 25

When solving an integer linear programming model, the value of the objective function will not be better than the objective function of the respective non-integer model.

Question 26

In the assignment model, the number of resources and tasks must always be equal.

Question 27

In a mathematical programming model, the divisibility assumption allows decision variables to take:

A) Integer values.
B) Fractional values.
C) Negative values.
D) All of the above

Question 28

Which of the following definitions of decision variables requires the decision maker to not enforce an integer solution?

A) The number of houses to build in a new neighborhood
B) The number of pounds of products to be produced in a week's time
C) The number of airplanes to produce during a year
D) All of the above

Question 29

Integer programming models have the same structure as:

A) Linear programming.
B) Nonlinear programming.
C) Goal programming.
D) All of the above

Question 30

Which of the following constraints belongs to an integer programming model but not necessarily to a linear programming model?

A) Non-negativity constraints
B) Integer constraints
C) Non-integer constraints
D) All of the above

Question 31

Which of the following constraints belongs to an integer programming model, but not necessarily to a goal programming model?

A) An objective function
B) Integer constraints
C) System constraints
D) Both a and b

Question 32

While a regular linear programming model has an infinite number of possible solutions, the integer counterpart has:

A) An infinite and identical set of possible solutions.
B) An infinite but different set of possible solutions.
C) A limited number of possible solutions.
D) All of the above are possible solution sets for the integer counterpart of a regular linear programming model.

Question 33

Which of the following is not a type of integer programming model?

A) An all-integer programming model
B) A mixed-integer programming model
C) A linear integer programming model
D) All of the above are types of integer programming models.

Question 34

Which of the following is not a type of integer nonlinear programming model?

A) An all-integer nonlinear programming model
B) A mixed-integer nonlinear programming model
C) A nonlinear integer goal programming model
D) All of the above are types of integer programming models.

Question 35

Nonlinear integer programming models offer additional challenges for solution algorithms because:

A) The values of reduced gradients are valid only at the point of the optimal solution.
B) The values of Lagrange multipliers are valid only at the point of the optimal solution.
C) The generalized reduced gradient algorithm cannot differentiate local and global optima.
D) All of the above

Question 36

Which of the following situations suggests that the decision maker impose binary values for decision variables?

A) The decision maker wants to determine how many units of a product to produce.
B) The decision maker wants to determine whether or not to produce a production lot.
C) The decision maker wants to seek the minimum production cost.
D) All of the above

Question 37

0-1 linear programming is a special case of:

A) Integer programming.
B) Nonlinear programming.
C) Nonlinear integer programming.
D) All of the above

Question 38

Which of the following is a result that the decision maker should anticipate when solving an integer linear programming model with a minimization objective?

A) The value of the objective function will not be less than the objective function of the non-integer model.
B) The value of the objective function will be greater than the objective function of the non-integer model.
C) The value of the objective function will not be greater than the objective function of the non-integer model.
D) All of the above

Question 39

Which of the following is a result that the decision maker should anticipate when solving an integer linear programming model with a maximization objective?

A) The value of the objective function will not be less than the objective function of the non-integer model.
B) The value of the objective function will be greater than the objective function of the non-integer model.
C) The value of the objective function will not be greater than the objective function of the non-integer model.
D) All of the above

Question 40

Which of the following is a result that the decision maker should anticipate when solving an integer nonlinear programming model with a minimization objective?

A) The value of the objective function will not be less than the objective function of the non-integer model.
B) The value of the objective function will be greater than the objective function of the non-integer model.
C) The value of the objective function will not be greater than the objective function of the non-integer model.
D) All of the above

Question 41

Which of the following is a result that the decision maker should anticipate when solving an integer nonlinear programming model with a maximization objective?

A) The value of the objective function will not be less than the objective function of the non-integer model.
B) The value of the objective function will be greater than the objective function of the non-integer model.
C) The value of the objective function will not be greater than the objective function of the non-integer model.
D) All of the above

Question 42

In the assignment method, the decision maker seeks to assign:

A) Each available resource to a specific set of tasks.
B) One resource to only one task.
C) Several available resources to one set of tasks.
D) Several available resources to only one task.

Question 43

Which of the following is a context that may require the use of the assignment method?

A) There are m machines and n workers to be assigned at the beginning of production period (m ? n).
B) There are m machines and n workers to be assigned at the beginning of production period (m = n).
C) Both a and b
D) Neither a nor b

Question 44

Which of the following is a context that may require the use of the knapsack problem?

A) Selecting a project from a given list in which each project is characterized by its own budget and return on investment
B) Selecting items from a list of products to be shipped, considering that each item has a volume and revenue
C) Both a and b
D) Neither a nor b