# IEOR4405, Spring 2003: Homework 06

Assigned: Thursday, February 27, 2003
Due: Thursday, March 6, 2003, in class

## General Instructions

1. 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.
2. Numbered problems are all from the textbook Scheduling: Theory, Algorithms and Systems

## Problems

1. Problem 5.8.
2. Problem 5.15
3. In the book and in class, we saw a linear program for P|pmtn|Cmax. In this linear program the variable xij only described which machine a job should run on. Suppose we wanted to write a linear program in which we actually assign each job to particular time period(s) on each machine.
1. Write an integer program for P|pmtn|Cmax in which the variables are xijs, where xijs is 1 if job j runs on machine i during the time interval (s,s+1), and 0 otherwise.
2. Write an integer program for P|pmtn|Cmax in which the variables are xijst, where xijst is 1 if job j begins running on machine i at time s and finishes running on machine i at time t.
3. What are the advantages and disadvantages of each integer program (You should consider issues such as number of variables and number of constraints in the formulation and the number of nonzero variables in the solution. Express your answers in terms of n, m and Cmax.)?
4. Write a proposal for your project. See the web page about the project for more information. Hand in this proposal on a separate sheet of paper.

### Switch to:

cliff@ieor.columbia.edu