IEOR4405, Spring 2016: Homework 1

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. Find the optimal schedule for P4||C_max for the following instance.

   j	pj
   1	9
   2	9
   3	8
   4	8
   5	7
   6	7
   7	6
   8	6
   9	5
   10	4

   Do not read ahead, but come up with the best schedule that you can. Also, give the optimal schedule for when you have 3 machines and 2 machines.
2. Consider the problem 1|p_j=1|L_max. Show how to solve this problem by formulating an assignment problem, the solution of which gives a solution to your scheduling problem.
3. What is the optimal algorithm for 1 |pmtn| Σ C_j? Prove that your algorithm is optimal.
4. Give an example of an instance of 1|r_j|Σ C_j in which there is exactly one job that has r_j = 0 but the optimal schedule does not run any job at time 0.

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