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Unformatted text preview: 21 Scheduling problems In this section we consider a very important class of problems involving integer variables, arising from scheduling. We suppose we have n jobs, where job j takes time p j 0 to process. We cannot process two or more jobs simultaneously. We must choose an order in which to schedule the jobs, and our goal is minimize the average completion time for the jobs. For example, consider five jobs with processing times shown below. j 1 2 3 4 5 p j 13 4 19 20 3 If we chose the scheduled order 5 , 2 , 1 , 3 , 4, then the completion times would be 3 , 7 , 20 , 39 , 59, giving an average completion time of 128 5 . Suppose we now add the following precedence constraints: (1 , 3) , (1 , 4) , (2 , 4) , (2 , 5) , (4 , 5) . The pair (1 , 3), for example, means that job 1 must be finished before job 3 starts. We will try to model such problems as mixed integer programs : some variables must be integers....
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This note was uploaded on 01/09/2009 for the course ORIE 320 taught by Professor Bland during the Fall '07 term at Cornell University (Engineering School).
- Fall '07