# IEOR4405, Spring 2009: Homework 7

Assigned: Thursday, March 26, 2009
Due: Thursday, April 2, 2009, in class

## 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 the following project scheduling network, which can be found here .

In the table below, let pj be the processing time associated with activity j and let cj be the cost of reducing pj by one unit.
 j pj cj 1 1 6 2 1 4 3 5 1 4 6 3 5 6 1 6 4 1 7 2 2 8 4 3 9 6 7

1. List critical paths in the network.
2. List 5 different minimal cut sets in the network.
3. Suppose that you want to reduce the project length by 1 unit of time while spending the smallest amount of money. What would you do, and how much would it cost?
4. List all critical paths with the new processing times.
5. Suppose that you had \$10 to spend on reducing the project and you have the restrictions that no processing time can decrease by more than 2 units, and that no processing time can decrease below 1. What would you do and what would the resulting schedule length be.
2. Problem 6.11
3. Problem 6.12 (hint: use an exchange argument)
4. Continue working on your project

### Switch to:

cliff@ieor.columbia.edu