IE 525 - System Synthesis and Design

Brief Course Description

Production and other systems can be modeled as networks of transmission links interconnecting sources, processing points, and destinations. Additionally, many problems, such as scheduling, machine replacement, distribution systems, and even roller coaster design, can be formulated as network problems. Such a formulation can vastly reduce the time required to find an answer. For example, one recent graduate student reduced the solution time for one problem from 1054
years (much longer than the estimated life of the Universe) to about half an hour.

IE 525 focuses on modeling situations as networks, using computers to find results, then interpreting those results. In addition, students will gain skill in choosing appropriate models and algorithms in a variety of situations.

Course Objectives

Students successfully completing IE 525 will:

• develop skill in observing and representing the structure, as well as the data, in a variety of situations,
• develop knowledge and skill in exploiting the special structure of these situations leading to more efficient, or even feasible, methods of solution, and
• demonstrate an ability to use a hand computations to solve small problems and a computer to solve moderately large ones.

Main Topics

The course material is organized into four units:

• Fundamentals: An overview of the course approach, as well as notation and conventions that will be used throughout the course. This unit also includes an introduction to the computer tools you will use.
• Shortest Path Problems: Here, the main task is to find a shortest or cheapest route through a network.
• Maximum Flow Problems are ones in which the main problem is to find out the greatest amount of material that can be moved through the network from one specific node to another.
• Minimum Cost Flow Problems are ones in which the main task is to move a specified amount of material through the network at the lowest possible cost.

Within each unit, the following topics will be addressed.

• Modeling: the task of abstracting key elements of the situation to form an analytical model
• Representation: the problem of depicting the elements of the model in graphical, mathematical, and computer-usable forms.
• Algorithms: which are the step-by-step processes that lead to a solution.
• Transformations: which allow us to use the method for one problem to solve a larger class of problems.
• Basic Problem Types: which include shortest path, maximum flow, lowest-cost flow, and minimal spanning trees. We will examine the nature of real-world problems of these types as well as algorithms that may solve them.
• Efficiency: which arises as an issue in the timely solution of practical problems. This includes the problem of collecting and processing data as well as computer time to solve it.
• Computer resources: which includes the trade-off of using general-purpose vs. special-purpose software.
• Interpretation of algorithm results or computer output in the context of the original problem.
• Sensitivity of solutions to inaccuracies or changes in the data.

Details:

 Instructor: John Mullen, Tel: (575) 646-2958, email: jomullen@nmsu.edu Texts: Network Flows: Theory, Algorithms, and Applications, by R. K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Prentice Hall, 1993, ISBN 0-13-617549-X. We will use parts of chapters 1 through 9 and 11 through 13. Additional resources are available through the WebCT site. Computer: Web-CT Site: https://salsa.nmsu.edu/ MatLab LINDO and LINGO

Note: Your primary computer tool in this course will be MatLab. In addition, you will do a few problems in LINDO and LINGO. All of these are are commercial problem-solving tools which are available in the IE computer lab. If you want to install these programs on your own computer, moderately-priced student versions are available. See the WebCT site for details. You can also download free evaluation copies of LINDO and LINGO which are not as capable as the student version, but adequate for IE 525.

Revision Date: November 13, 2008 by jpm.