IEOR4405, Spring 2018: Homework 6

General Instructions

1. Please review the course information.
2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
3. Numbered problems are all from the textbook Scheduling: Theory, Algorithms and Systems.

Problems

1. Consider an instance of R|pmtn|C_max for which the amount of processing time for each job on each machine (solution to the LP) is:

   	J1	J2	J3	J4
   M1	6	2	4	0
   M2	2	7	4	1
   M3	3	2	1	4

   Show the execution of the algorithm given in class on this instance.
2. Problem 5.8
3. We could define a variant of McNaughton's wrap-around rule for Q|pmtn|C_max which takes the machines in decreasing order of speed and also takes the jobs in decreasing order of processing time. It then tries to fill the first machine, and wraps around to the second machine if necessary, continuing through the machines in order. Does this rule give an optimal algorithm for Q|pmtn|C_max? Why or why not?
4. Write an integer linear program for P|pmtn,r_j|C_max in which a variable y_i,j,t is 1 if job j is running on machine i at time t. Your program should ensure that at each time on each machine, at most one job runs. Show that this program does NOT necessarily find an optimal schedule. Explain how to modify the program so that you can use the solution to get an optimal schedule.

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• Homework 5
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