hw2 - IE 418 Integer Programming Problem Set#2 Due Date...

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IE 418 – Integer Programming Problem Set #2 Due Date: February 23 Do the following problems. You may work with one other classmate. If you work alone, you will receive a 10% bonus. You are allowed to examine outside sources, but you must cite any references that you use. Please don’t discuss the problems with other members of the class (other than your partner, if you are working with one). For the instances you are required to solve, data files for most (if not all) of the instances can be found on the course web site. Right now data files are in AMPL data format. If you create a Mosel data file (before I do) and email it to me, I will give you extra credit! Only one person can get the extra credit. Please hand in printouts of any code, AMPL models, or Mosel models that you build 1 Nonconvex Regions 1.1 Problem Consider the following polyhedra: P 1 = { x R 4 + | 2 x 1 + 2 x 2 - x 3 + 2 x 4 10 , 4 x 1 + x 2 - x 3 + x 4 10 } P 2 = { x R 4 + | 8 x 1 + 2 x 2 - x 3 + 14 x 4 70 , x 1 + x 2 - x 3 + x 4 2 } P 3 = { x R 4 + | 4 x 1 + x 2 + x 3 + 5 x 4 20 , 2 x 1 + x 2 - 2 x 3 + x 4 15 } P 4 = { x R 4 + | 0 x 10 e } and objective function c def = (6 , 3 , - 1 , 5) T . Formulate as a mixed integer linear program the problem: max { c T x | x P 4 ( P 1 P 2 P 3 ) } . 1.2 Problem Solve your formulation from Problem 1.1 using the software tool of your choice.

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