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Description: Development and application of fundamental deterministic analytical methods including linear programming, integer programming, dynamic programming and nonlinear optimization.
PREREQUISITES
MATH 304 or equivalent
COURSE OBJECTIVES
The objective of the course is to give the student experience in modeling, solving and analyzing problems using linear programming. Emphasis will be stressed on theory, applications, and computer usage. By the end of the course the student should have developed the skills to:
(1) consider real-world problems and determine whether or not linear programming is an appropriate modeling framework;
(2) formulate linear programming models that consider the important elements of the real world problem;
(3) solve the models for their optimal solutions;
(4) interpret the models' solutions and infer solutions to the real-world problems.
TEXTBOOK AND ADDITIONAL COURSE MATERIAL
Winston, Wayne L. and M. Venkataramanan, Introduction to Mathematical Programming, 4th Edition, Duxbury Press, Belmont, CA, 2003. ISBN 0-534-35964-7.
TOPICAL OUTLINE
Topics to be covered in the lectures: 1. Introduction to Linear Programming. 2. Model Formulation. 3. Solving Linear Programs (graphical method, simplex method, special cases). 4. Sensitivity Analysis. 5. Duality. 6. Transportation and Assignment Problems. 7. Network Problems. 8. Special Topics (e.g. integer programming, dynamic programming, nonlinear programming).
Semester Group Project
Part 1: Implement the simplex method in MATLAB.
Part 2: Model given problem instances using linear programming, solve the models using
MATLAB, CPLEX, LINDO, LINGO EXCEL Solver, MATLAB and perform sensitivity analysis.
Part 3: Project ReportCLASS SCHEDULE
Lectures: Three days a week, 50 minutes per day (No laboratory).
PROFESSIONAL COMPONENT
This course provides fundamental concepts, theory and procedures for modeling, solving and analyzing problems using linear programming. The knowledge learned in this course is used to develop a semester group project.
PROGRAM OUTCOMES
A. An ability to apply knowledge of mathematics, science, and engineering.
Specialized knowledge and analytical procedures are developed to enhance the decision-making process using linear programming. This included the following: (1) Formulate a problem in technical terms; (2) Determine and implement the appropriate modeling approach; (3) Perform sensitivity analysis and apply feedback to improve the system
B. An ability to design and conduct experiments, as well as analyze and interpret data.
Students are required to do a semester project in which they are given three real-life problem instances and they are to apply linear programming to model, solve as well as analyze and interpret (sensitivity analysis) the problems optimal solutions. The students are taught how to use state-of-the-art optimization software such as CPLEX, LINDO, LINGO, and the EXCEL Solver.
C. An ability to function on multi-disciplinary teams.
Students are required to do assignments and a semester project in groups. In order to promote the team approach, groups of two to three students are allowed for each assignment and semester project. The requirements for the semester project are as follows: (1) Implementation of the simplex method in Matlab; (2) Modeling of three real-life problem instances using linear programming; (3) Providing solutions to the problems using state-of-the-art software such as CPLEX, LINDO, LINGO; (4) Performing sensitivity analysis on the optimal solutions; (5) Providing recommendations via a project report
The selection of the problems is done by the instructor.
D. An ability to identify, formulate, and solve engineering problems.
ISEN 420 emphasizes on the importance of the following in industrial engineering: (1) Identify a real-world problem; (2) Determine whether or not linear programming is an appropriate modeling framework; (3) Formulate the problem as a linear program; (4) Solve the problem for its optimal solution; (5) Interpret the models' solutions and infer solutions to the real-world problem.
E. An ability to communicate effectively.
Students are encouraged to engage in group discussions in class concerning the subject matter. The semester group project requires a report to be reviewed and graded. After each section report is returned, with specific suggestions and recommendations, each team must revise it effectively to reflect those improvements identified in the review process. Time permitting each team makes a project presentation with specific areas presented by designated members of the group. The presentation takes approximately 15 minutes per team, including questions (about 5 minutes).
F. A recognition of the need for, and an ability to engage in life-long learning.
Throughout the development of the class, a great deal of lecture time is devoted to discussing real-life problems where operations research is an appropriate tool. This allows the students to recognize the importance of being life-long learners, particularly since most of the real-life problems are open-ended.
G.
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.
The following techniques, skills and tools are studied and used: MATLAB, CPLEX, LINDO, LINGO, and Excel Solver.
PREPARED BY: Lewis Ntaimo DATE: 8-18-04
