Linear Programming Class Project Spring 2007

with A ∈ IRm×n, b ∈ IR, and x, c ∈ IR. We will assume that the number of columns n of matrix A is so large that it is impossible to generate and store the matrix A in memory. The revised simplex method in Chapter 7 of Chvátal can be appropriately modified to solve linear programs of the form (1); the resulting method is known as the column generation method where columns of A are generated as needed. One such LP arises in the cutting stock problem (see Chapter 13 in Chvátal). A short description of the cutting stock problem is also given below. Our goal in this project is a to develop a computer implementation of the column generation method in MATLAB to solve the cutting stock problem. You will work in groups of 3 students. The entire project is due in class on Tuesday, 24 April, 2007. If you have questions on any parts of the project, please send me an email. Note: Your sources on the project are Chvátal, the codes and papers posted on the course webpage, and your group members. If you consult anything else, please remember to cite it in your report. Moreover, passing off someone else’s work (from the previous semesters or an online website) as your own is regarded as plagiarism, and will fetch you a zero for the project.