# Chapter 5 - ManagementScience ManagementScience BIT2406...

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Management Science Management Science BIT 2406 BIT 2406 Chapter 5 Chapter 5 Integer Programming Integer Programming 1 BIT 2406

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Reading Questions Reading Questions What are the three different kinds of integer programming models and how do they differ? What is a mutually exclusive constraint? What is a multiple-choice constraint and how is it different from a mutually exclusive constraint? What is a conditional constraint? Be able to explain how you formulate a conditional constraint. What is a corequisite constraint and how is it different from a conditional constraint? Rounding noninteger solutions up to the nearest integer value may result in what? What happens if you round down noninteger solutions values? What is the traditional approach for solving integer programming problems? What is the major principle of this method? Who is credited with being the first individual to develop a systematic (algorithmic) approach for solving linear integer programming problems? What was this approach called? Searching through all possible integer solutions is what type of approach? What is an example of this type of approach that conducts this search in an intelligent manner? What are three popular applications of 0-1 integer programming? Be able to describe and model each type of problem. BIT 2406 2
Chapter Topics Chapter Topics Integer Programming (IP) Models Integer Programming Graphical Solution Computer Solution of Integer  Programming Problems With Excel BIT 2406 3

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Integer Linear Programming Models Integer Linear Programming Models In some problems, we need to solve the  problem so that an optimal integer  solution is guaranteed. In our previous linear programming  models, the assumption was solutions  could be fractional or real numbers. BIT 2406 4
Three Basic Types of Integer Linear  Three Basic Types of Integer Linear  Programming Models Programming Models Total Integer Model – all the decision variables are  required to have integer solution values 0-1 Integer Model – all the decision variables have  integer values of zero or one (binary values; choice  selection and rejection) Mixed Integer Model – some of the decision variables  (but not all) are required to have integer solutions BIT 2406 5

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A Total Integer Model Example:  A Total Integer Model Example:  Problem Definition Problem Definition Owner is buying new presses and lathes. Each press purchased will increase profit by \$100 per day and each lathe by \$150.   Budget: \$40,000 and 200 square feet Owner wants to know how much of each type of machine to purchase to max profit BIT 2406 6 Machine Required Floor Space (ft.
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