1. Applied Statistical and Optimization Models
Topic 04: Integer Programming

2. Objectives
Identify the solution to a linear programming model that only allows for integers as solutions.
Solve integer linear programming problems graphically.
Solve integer linear programming problems using Excel solver.

3. Integer Linear Programming
Consider the following example: Magic Cookies produces Chocolate (C) and Vanilla (V) cookies. A chocolate cookie sells for $2 and a vanilla cookie for $1. The production of cookies requires eggs, flour, chocolate, and vanilla. The following table summarizes the required units of each input factor for a chocolate and vanilla cookie.
Chocolate
Vanilla
Maximum
Eggs 1 2 20
Flour 5
100
Chocolate Powder 9
Vanilla Powder

4. Integer Linear Programming
Define the linear programming model:
Z = _____ ∙ C + _____ ∙ V
s.t.
_____ ∙ C + _____ ∙ V ≤ _____ Eggs constraints
_____ ∙ C + _____ ∙ V ≤ _____ Eggs constraints
_____ ∙ C + _____ ∙ V ≤ _____ Chocolate powder constraint
_____ ∙ C + _____ ∙ V ≤ _____ Vanilla powder constraint

5. Integer Linear Programming
Solve the linear programming model graphically

6. Integer Linear Programming
Solve the integer linear programming model using Excel solver
Make sure to “tell” solver that the optimum values must be integers!

7. Integer Linear Programming
Comparison of “fractional” and “integer solution”
If half cookies could be sold, then the optimum solution would be
Chocolate Cookies = 5.5, Vanilla Cookies = 9
Chocolate Cookies = 5, Vanilla Cookies = 9

8. What you Should Have Learned
Advance your linear programming skills in Excel, understanding especially the nature of integer linear programming
Run Excel solver with even more confidence
Interpret answer output, sensitivity analysis, and limits report.