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**Unformatted text preview: **Math 482 (Lecture 18): Integer linear programming (introduction) This lecture discusses Chapter 13 of the textbook. Definition: An integer linear programming problem (ILP) is the optimization problem: min c'x Ax=b x≥ 0 x is integral . * All transformations to/from standard to canonical form, that we introduced for LP's remain valid. * In general one cannot hope to come close to the correct solution to (ILP) by rounding, although this can be a useful strategy sometimes. Example/in class exercise: Consider the assignment problem: a software company has n employees and m tasks (say, owners of the software sending in an "SR"=service request). All of the owners have paid a one time fee for service, so the only difference is the time it takes to complete the job. Say c i,j is the time it takes for employee i to solve task j. The problem is to assign employees to tasks so that the total amount of time spent is as small as possible....

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