IEOR 3608, Fall 2006: Homework 8

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 Introduction to Mathematical Programming, 4th Edition.

Problems

1. p. 419, B8. Formulate and solve by converting to a transshipment problem and using LINGO or LINDO to solve.
2. p. 430, A4 and A5. Please use the Ford-Fulkerson algorithm to find the maximum flow and show the residual graph after each step.
3. p. 430, A7. Formulate and solve using LINGO.
4. p. 430, B12.
5. p. 454, A3. Formulate and solve using LINGO
6. p. 455, B7. Formulate and solve using LINGO
7. The stable roommates problem is like the stable marriage problem, except that you are not restricted to pairing a man with a woman. In other words, you are given a set of n people, and each person has ranked the other n-1 people in order. You want to pair the people up. An unstable pair consists of 2 people, each of whom rank the other higher than their current roomate. A solution is stable if there are no unstable pairs. Give an example of an input to the stable roommates problem for which it is impossible to find a stable solution. (Hint: there is an example with four people).
8. Extra credit: Suppose that we have a stable marriage problem and we use the algorithm given in class. Prove that the resulting marriage is guaranteed to be stable.