IEOR4405, Spring 2019: 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	9
   4	8
   5	7
   6	6
   7	5
   8	5
   9	3
   10	1

   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. Problem 2.3. Please do not read ahead to Chapter 3 before doing this problem. The purpose is to get you to try to figure out how to solve this problem by yourself.
3. 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.
4. 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. That is, given an instance of 1|p_j=1|L_max, you should give an algorithm to convert it into an assignment problem (minimum weight bipartite matching). Then you should show that an optimal solution to the resulting assignment problem can be used to construct an optimal solution to the scheduling problem.

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