Ma 416: Operations Research

• Syllabus.txt The syllabus in a txt file
• Table of contents This worksheet grows as the semester wears on.
• Syllabus.mws The syllabus in a worksheet.
• Introduction to Maple This worksheet is the first worksheet in the calculus handbook
• pigfarm.mws Typical minimum cost diet problem.
• The graphical method for solving 2 variable linear programming problems
• The simplex package in Maple and how to use it.
• The simplex algorithm. The simplex algorithm carried out 'by hand'.
• Automating the simplex algorithm Look at 'tabular' and 'mymax' in this worksheet.
• Unbounded objective and multiple optima Homework solutions.
• Surplus and artificial variables Homework exercise on Big M and Phase 1 / Phase 2 methods.
• The pigfarmer problem revisited This worksheet sets up the pigfarmer problem and works it
• 'by hand'.
• Yet another example Here is a problem with artificial variables and multiple optimal points.
• Sensitivity Analysis This worksheet takes a typical maximize profit linear programming problem and describes how to do a 'sensitivity analysis' of the right hand sides and the coefficients of the objective function.
• Exam 1 This exam is due by class time on 2/19/97
• A matrix form of the simplex method. 1 This worksheet shows how to use matrices to reduce the arithmetic in sensitivity analysis.
• The matrix form of the simplex algorithm automated This worksheet defines 'gauss', 'getpiv', and 'matmax' which automate (somewhat) the matrix form of the simplex method.
• Exam 1 Solutions
• A problem and its dual are solved. This worksheet uses the word 'dual' in the simplex package to set up the dual problem. Then it sets it up in matrix form and uses 'matmax' from the previous worksheet.
• The usefulness of the dual This worksheet corrects an impression given in class about the usefulness of the dual.
• Project 1 Due the Friday before spring break.
• More uses of the matrix form of the simplex algorithm This worksheet shows how to add a new decision variable or a new constraint without starting over. The dual simplex algorithm is 'discovered'.
• Project 1: A solution to problem 2. This problem exercised much of what we have learned to this point.
• Parametric programming: an example. This worksheet takes off on a question that arises in the above worksheet.
• Parametric programming: another example. This worksheet 'discovers' the dual simplex algorithm which is needed whenever you are varying the right hand sides.
• Transportation problems. This worksheet discusses the transportation problem and implements the streamlined simplex algorithm described in our text.
• Assignment problems . This worksheet looks at assignment problems.
• Exam topics This worksheet contains a very brief listing of the exam topics for Friday's exam.
• Exam 2. Handin portion due Monday.
• Networks 1 This worksheet finds a minimum spanning tree in a weighted graph.
• Minimum Cost Flow Problems I In this worksheet we generate and work some random minimum cost flow problems.
• Exam2 solutions.
• Tilings I. In this worksheet, tiling problems are defined and we show how to use networks to construct solutions.
• Tilings II. In this worksheet, we show how to use the simplex method to solve tiling problems.