ExerciseSet5.pdf - Linear Programming 2013-2014 Exercise...

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Linear Programming 2013-2014 Exercise Set 5 Modeling LP problems Exercise 1 Machine scheduling A factory needs to complete n jobs by using m machines. To complete each job j , j = 1 , . . . , n , an amount of r j > 0 processing units is required. Each machine i has a processing speed p ij > 0 (in processing units/time unit) that depends on job j . Moreover, each job may be completed by using different machines. As an example, suppose there is a job requiring r = 10 processing units. Furthermore, assume there are two machines with processing speeds 2 and 6, respectively. Then we can use 2 time units of machine 1 and 1 time unit of machine 2 to complete the job (since 2 · 2 + 1 · 6 = 10). The factory wants to assign the jobs to the machines in such a way that the time point at which the latest machine finishes is minimized. Model this problem as a linear programming problem. The dual simplex method Exercise 2 a. Describe the general idea of the dual simplex method.
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