IE 501 : Optimization models

Professor when you took the course:

Prof. Narayan Rangraj

Motivation behind the course:

  1. To learn the art of mathematically modeling optimization problems.
  2. Writing models for computers.
  3. To understand the mathematics behind solution techniques for some classes of optimization problems.

Course Content:

The following topics are taught in this course –                                                                                                             

  1. Modeling of allocation and control problems in industry and social systems.
  2. Framework and overview of optimization with examples of continuous and discrete optimization, unconstrained and constrained problems.
  3. Single stage and multistage models.Formulations and equivalences. Examples from science, engineering, and business.
  4. Linear programming.
  5. Geometry and algebra of the simplex method.
  6. Duality & sensitivity.
  7. Combinatorial optimization problems with emphasis on applications, a notion of large feasible spaces and neighborhood solutions, representation of solution space, search tree, search techniques, branch and bound method.
  8. Examples of mixed-integer programming models.
  9. Decision problems involving network flows, assignment models, transportation models, multi-stage flows.

Prerequisites:

The course doesn’t have any prerequisites.

Feedback on lectures:

Attendance is not compulsory but is necessary to keep up with the course and the course is taught in such a way that it becomes very easy to understand the concepts in class and hence saves time spent trying to understand them later.

Feedback on tutorials, assignments, and exams:

Several assignments are uploaded on Moodle during the duration of the course. These are usually good practice for exams.  Quizzes are relatively simple whereas the Mid-Semester and End-Semester are easy if you have worked out all the assignments and class notes carefully.

Exams are a combination of theoretical and numerical questions. Questions in the exam are from the things taught in class itself hence it is better to be attentive in class and take down notes.

Difficulty level:

3/5

How is the grading?

AA – 4, AB – 7, AU – 1, BB – 11, BC – 9, CC – 9, CD – 8, DD – 5, FR – 2

Total students – 56

Study Material and References:

  1. G. Hadley. Linear Programming, Narosa, 2000 – classic reference
  2. Bazaraa, Jarvis and Sherali, Linear Programming and Network Flows, Wiley Student Edition, 2004 – quite comprehensive
  3. Howard Karloff, Linear Programming, Modern Birkhauser Classics, 1991 – a very compact book which has material on LP over and above

Note: I personally prefer Howard Karloff as it sometimes explains the theory with the help of numerals.

Online Resources (Not necessary for the course)

  1. Mathematical Programming Glossary

http://glossary.computing.society.informs.org

  1. NEOS Guide

http://www.neos-guide.org/NEOS

  1. MIT Open Course Ware

Ocw.mit.edu

  1. Bradley, Hax, and Magnanti

Applied Mathematical Programming,

http://web.mit.edu/15.053/www

  1. Jon Lee, A First Course in Linear Optimization, First Edition,

https://sites.google.com/site/jonleewebpage/home/publications

Miscellaneous:

This course is important as it proves helpful while doing IE 504(not a prerequisite but helps a little bit to know some concepts already). This course might also help you if you are doing an operations intern.

We thank “Swapnil Agashe” for sharing the course review

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