Applied Statistical and Optimization Models

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Applied Statistical and Optimization Models

Applied Statistical and Optimization Models

Applied Statistical and Optimization Models

Presentation transcript:

Applied Statistical and Optimization Models Topic 04: Integer Programming

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.

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

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

Integer Linear Programming Solve the linear programming model graphically

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

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

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.