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Chapter+5+-+Integer+Programming

Chapter+5+-+Integer+Programming - Chapter 5 Integer...

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Integer Programming Chapter 5

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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.
Introduction When one or more variables in an LP problem must assume an integer value we have an Integer Linear Programming (ILP) problem. ILPs occur frequently Scheduling Manufacturing Integer variables also allow us to build more accurate models for a number of common business problems.

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Three Types of ILP Models All Integer Model 0-1 Integer Model (Binary Variables) Mixed Integer Model
Manufacturing Example Machine shop is expanding and plans to buy lathes and presses Owner estimates that profit will be \$100/day for each press and each lathe will yield a profit of \$150/day Machine Floor Space Cost Press 15 \$8,000 Lathe 30 4,000 Budget of \$40,000 and 200 ft2 floor space Owner wants to determine the # of lathes & presses to buy to maximize profit.

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Integrality Conditions Let X1 = # Presses, X2 = # Lathes Max Z = 100X1 + 150X2 } profit subject to: 15X1 + 30X2  200 ft2 } floor space \$8,000X1 + 4,000X2  \$40,000 } Price X1, X2  0 } nonnegativity X1, X2 must be integers } integrality Integrality conditions are easy to state but make the problem much more difficult (and sometimes impossible) to solve.
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Chapter+5+-+Integer+Programming - Chapter 5 Integer...

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