LESSON 6: INTEGER LINEAR PROGRAMMING

Question 1

A manufacturing company wants to optimize its production schedule to maximize profit. Which of the following is a primary goal of integer linear programming (ILP) in this situation?

A. Minimize production time
B. Maximize profit
C. Reduce raw material costs
D. Minimize machine maintenance costs

Answer 1

Maximize profit

Question 2

A logistics company needs to determine the most cost-effective route for delivering goods to various locations. What type of decision-making tool is best suited for this scenario?

A. Descriptive analytics
B. Predictive analytics
C. Prescriptive analytics
D. Diagnostic analytics

Answer 2

Prescriptive analytics

Question 3

An e-commerce company wants to allocate resources efficiently for order fulfillment, considering warehouse constraints. What technique would be most appropriate for this optimization problem?

A. Predictive modeling
B. Descriptive modeling
C. Prescriptive modeling
D. Diagnostic modeling

Answer 3

Descriptive modeling

Question 4

A retail chain wants to optimize shelf space for products to maximize sales. What mathematical approach is suitable for this scenario?

A. Linear regression
B. Integer linear programming
C. Decision trees
D. Cluster analysis

Answer 4

Integer linear programming

Question 5

A retail company wants to optimize its inventory management to reduce stockouts and excess inventory costs. Which prescriptive analytics approach is most suitable for this scenario?

A. Predictive modeling
B. Descriptive analytics
C. Simulation modeling
D. Optimization modeling

Answer 5

Optimization modeling

Question 6

In a production scheduling problem, which variable type is likely to be modeled as an integer in ILP?

A. Descriptive analytics
B. Predictive analytics
C. Prescriptive analytics
D. Diagnostic analytics

Answer 6

Prescriptive analytics

Question 7

A company wants to minimize transportation costs while distributing goods to various locations. What type of problem is this, and what kind of variables might be integer in nature?

A. Linear regression, continuous variables
B. ILP, binary variables
C. Clustering, categorical variables
D. Decision tree, discrete variables

Answer 7

ILP, binary variables

Question 8

Which of the following is a common constraint in ILP for resource allocation problems?

A. Profit maximization
B. Budget constraint
C. Market demand
D. Regression coefficient

Answer 8

Budget constraint

Question 9

A manufacturing company wants to determine the optimal production plan for maximizing profit. Which type of ILP variable might represent the choice of whether to produce a specific product or not?

A. Continuous variable
B. Binary variable
C. Integer variable
D. Dummy variable

Answer 9

Binary variable

Question 10

A manufacturing company wants to optimize its production schedule to maximize profit. It has identified three production options with associated profits: Option A ($5000 per unit), Option B ($7000 per unit), and Option C ($6000 per unit). The production capacity for each option is limited to 100 units. The objective is to maximize profit. What type of programming model is suitable for this scenario?

A. Linear Programming (LP)
B. Integer Linear Programming (ILP)
C. Quadratic Programming (QP)
D. Non-linear Programming (NLP)

Answer 10

Integer Linear Programming (ILP)

Question 11

A retail company wants to optimize shelf space allocation for products. What type of ILP constraint might be used to ensure that the total shelf space used does not exceed the available space?

A. Equality constraint
B. Inequality constraint
C. Budget constraint
D. Time constraint

Answer 11

Inequality constraint

Question 12

A company wants to allocate advertising budget across various channels for maximum reach. What type of ILP constraint might be used to ensure that the total budget is not exceeded?

A. Equality constraint
B. Inequality constraint
C. Budget constraint
D. Time constraint

Answer 12

Budget constraint

Question 13

In a project scheduling problem, if the goal is to minimize the project completion time, which type of ILP variable might be used to represent the duration of each task?

A. Continuous variable
B. Binary variable
C. Integer variable
D. Dummy variable

Answer 13

Continuous variable

Question 14

A logistics company wants to optimize the delivery routes for a fleet of vehicles. Each vehicle has a limited capacity, and the goal is to minimize the total distance traveled. What characteristic of the problem requires the use of Integer Linear Programming?

A. Limited capacity
B. Minimizing total distance
C. Multiple vehicles
D. Integer quantities of routes

Answer 14

Integer quantities of routes

Question 15

In an Integer Linear Programming problem, when do we use integer constraints?

A. When the decision variables can only take on integer values.
B. When the decision variables can take on any real values.
C. When the objective function is linear.
D. When the problem involves maximizing profit.

Answer 15

When the decision variables can only take on integer values.

Question 16

A company wants to minimize the total cost of production while meeting certain demand constraints for multiple products. Which type of objective function should be used?

A. Maximize profit
B. Minimize cost
C. Maximize revenue
D. Minimize production

Answer 16

Minimize cost

Question 17

In a production planning problem, if the decision variable represents the number of workers assigned to a shift, what type of constraint ensures that each shift is adequately staffed?

A. X ≥ Minimum staff requirement
B. X ≤ Maximum staff requirement
C. X × Minimum staff requirement = 1
D. X + Minimum staff requirement ≥ 0

Answer 17

X ≥ Minimum staff requirement

Question 18

A company is optimizing its supply chain, and the decision variable represents the quantity of raw materials purchased. What type of constraint ensures that the quantity does not fall below a certain threshold?

A. X ≥ Minimum quantity
B. X ≤ Minimum quantity
C. X + Minimum quantity ≥ 0
D. X × Minimum quantity = 1

Answer 18

X ≥ Minimum quantity

Question 19

In a manufacturing facility, a manager wants to optimize the production schedule to maximize profit. Which of the following is an appropriate use of integer linear programming (ILP) in this scenario?

A. Minimizing the number of machines used
B. Maximizing the production output
C. Reducing the production time
D. Minimizing the overall cost

Answer 19

Maximizing the production output

Question 20

In a project management context, a project manager wants to assign tasks to team members in a way that minimizes the total project completion time. What type of integer linear programming problem is this?

A. Assignment Problem
B. Scheduling Problem
C. Traveling Salesman Problem
D. Network Flow Problem

Answer 20

Scheduling Problem