Week 8 - Integer programming

Question 1

What are the 4 types of integer programming problems?

Answer 1

• Pure integer solutions - all decisions must have integer solutions
• Mixed integer programming - Some must have decision variables
• Pure binary integer programming - all decisions variables are binary (0 or 1)
• Mixed binary programming - (some decision variables are binary, other decision variables are integer or continuous

Question 2

What are the two basic properties of an integer linear program?

Answer 2

• The objective function and all constraints are linear functions of the decision variables
• Variables may be continuous, meaning that they may assume any real value

Question 3

How to answer integer programming questions? (5)

Answer 3

• Write down max profit formula: max profit = (x) product a + (x) product b
• list the constraints such as the tasks in the question with the time each product uses for each task and the max they can use
• Plot graph with the two products either side
• plot the curves with the tasks and market mix constraints
• Find feasible region and optimal solution

Question 4

What is the half-space?

Answer 4

Is where a set of points are on one side and points lying there can be potential solutions to the optimisation problem

Question 5

Where is the feasible region

Answer 5

Below the finishing constraint and above marketing constraint

Question 6

How to find the optimal solution? (2)

Answer 6

• Find the last point in feasible region that the profit line will cross
• Use that coordinate and put into max profit formula