We will use computer programs to help us solve many of the optimization problems we encounter in this course. Some of these programs are available online.

  AMPL
  Stefan Waner's Online Pivot Tool

  Robert Vanderbei's Linear Programming: Foundations and Extensions textbook
  George Dantzig Memorial Site
  J. E. Beasley's OR-Notes

  Thursday, 1/10/2008

• AMPL Code for the Farmer Problems
• Maple 11 Document for the Farmer Problems

  Tuesday, 1/15/2008

• The GGMC and KC Problems

  Thursday, 2/7/2008

• Duality Worksheet
• Notes On Unbounded Problems   These notes provide a correction to what was said in class.

  Tuesday, 2/19/2008

• Today we talked about three possible combinations for the primal and the dual. There is actually one more possibility that we will cover in class on Thursday. The complete list is as follows:

  Primal	Dual
  Infeasible	Unbounded
  Unbounded	Infeasible
  Optimal Solution	Optimal Solution
  Infeasible	Infeasible

  Tuesday, 3/4/2008

• Maple Worksheet, Revised Simplex Method

  Thursday, 3/20/2008

• Maple Worksheet, Revised Simplex Method using some procedures
• Maple Language File (a text file with some procedures)
• NOTE: These files will not work in Maple 9.5. You need Maple 10 or higher.

  Tuesday, 4/21/2008

• Carla Laffra's Applet for Dijkstra's ALgorithm

• Lab #1   Due: Thursday, 1/17
• Lab #2   lab2.mod   Due: Thursday, 1/24
  • NOTE: You may assume that all slack variables are nonnegative. In standard form, the inequalities have the form a₁x₁+ a₂x₂ + . . . + a_nx_n ≤ b. We can add a nonnegative slack varialbe, s₁, to the righthand side of this inequality to obtain an equation and a new nonnegative variable: a₁x₁+ a₂x₂ + . . . + a_nx_n+s₁ = b, s₁ ≥ 0. When the inequality takes the form a₁x₁+ a₂x₂ + . . . + a_nx_n ≥ b. We can subtract a nonnegative slack variable (sometimes called a surplus variable), t₁, from the righthand side of this inequality to obtain an equation and a new nonnegative variable: a₁x₁+ a₂x₂ + . . . + a_nx_n-t₁ = b, t₁ ≥ 0.
• Lab #3   Due: Tuesday, 2/5
  • CORRECTION: 1. (e) iv. should say, "no. of probs: 10." I have made this correction and posted an updated version of the lab.
  • If you are having difficulty submitting the problems for the pivot tool, do not worry. If you cannot submit the problems, simply write down the solutions that I asked you to record. You do not have to submit the problems. Some people are experiencing a glitch with the progrmam. Sorry. Jakayla
• Lab #4   Due: Thursday, 2/14
  • In class, I made an error in the objective function of the Klee-Minty problem. When n=4, the objective function should be z=1000x1+100x2+10x3+x4. I reversed the variables in class.
• Lab #5   Due: Tuesday, 3/18
  • The following files were created by Robert Molzon.
    • basic.mod
    • basic.dat
    • general.mod
    • general.dat
  • Make sure that you do the first item on the lab. It will help you understand how to run models that have both a .mod and a .dat file.
  • In the lab report, I want the *optimal* objective function values.
• Lab #6   Due: Tuesday, 4/1

• Homework #1     Some Sample Problems   Due: Thursday, 1/17
• Homework #2   Due: Wednesday, 1/30
• Homework #3   Due: Tuesday, 2/5
• Homework #4   Due: Thursday, 2/14
• Homework #5   Due: Bring to class on Thursday, 2/21.
• Homework #6   Due: Thursday, 4/3.
• Homework #7   Due: Wednesday, 4/16.
  • HINT: For number 11.2, do some smaller examples. See what happens if you can only choose numbers between 1 and 3. See what happens if you can only choose numbers between 1 and 4. See what happens if you can only choose numbers between 1 and 6. Do you see a pattern? Make a guess as to the optimal strategy. Can you use duality theory to show that it is optimal?