Operations Research

By Prof. Kusum Deep   |   IIT Roorkee
Learners enrolled: 1840   |  Exam registration: 225
Optimization is the most important sub area of the discipline Operations Research. Optimization problems arise in all walks of human activity- particularly in engineering, business, finance and economics. The simplest optimization problems are linear in nature which may be subject to a set of linear constraints. This course will equip the student with the expertise to mathematically model real life optimization problems as Linear Programming (Optimization) Problems and subsequently educate the student to solve these models with the help of the available methods.

INTENDED AUDIENCE: Any student who wants to learn the basic concepts of Operations Research

INDUSTRY SUPPORT:  All industries who have to minimize cost of production or maximum output 
Course Status : Completed
Course Type : Core
Duration : 8 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate
Start Date : 24 Jul 2023
End Date : 15 Sep 2023
Enrollment Ends : 07 Aug 2023
Exam Registration Ends : 21 Aug 2023
Exam Date : 24 Sep 2023 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Introduction to OR Models, More OR Models, Graphical Method for LPP, Convex sets, Simplex Method
Week 2: Big M Method, Two Phase, Multiple solutions of LPP, Unbounded solution of LPP, Infeasible solution of LPP
Week 3: Revised Simplex Method, Case studies and Exercises-I, Case studies and Exercises-II, Case studies and Exercises - III, Primal Dual Construction
Week 4: Weak Duality Theorem, More Duality Theorems, Primal-Dual relationship of solutions, Dual Simplex Method, Sensitivity Analysis-I
Week 5: Sensitivity Analysis-II, Case studies and Exercises - I, Case studies and Exercises - II, Integer Programming Goal Programming
Week 6: Multi-Objective Programming, Dynamic Programming, Transportation Problem, Assignment Problem, Case studies and,Exercises
Week 7: Processing n Jobs on Two Machines, Processing n Jobs through Three Machines, Processing two jobs through m machines, Processing n jobs through m machines, Case studies and Exercises
Week 8: Two Person Zero-Sum Game, Theorems of Game Theory, Solution of Mixed Strategy Games, Linear Programming method for solving games, Case studies and Exercises

Books and references

  1. Mohan, C. and Deep, Kusum: “Optimization Techniques”, New Age, 2009. 
  2. Mittal, K. V. and Mohan, C. “Optimization Methods in Operations Research and Systems Analysis”, New Age, 2003. 
  3. Taha, H.A. : “Operations Research – An Introduction”, Prentice Hall, (7th Edition), 2002. 
  4. Ravindran, A. , Phillips, D. T and Solberg, J. J. “Operations Research: Principles and Practice”, John Willey and Sons, 2nd Edition, 2009.

Instructor bio

Prof. Kusum Deep

IIT Roorkee
Dr. Kusum Deep, is a full Professor, with the Department of Mathematics, Indian Institute of Technology Roorkee, India. She is Gold Medalist, International and national scholarship holder and has many awards , including best paper awards, to her credit. With a vast experience in the teaching she has authored a text book on Optimization Techniques. In research she is an Internationally renowned personality having supervised 18 PhDs and published over 110 research papers in good quality journals and equal number of papers published in proceedings of International Conferences. She is a Senior Member of Operations Research Society of India, IEEE, Computer Society of India, Indian Mathematical Society and Indian Society of Industrial Mathematics. She is on the Expert Panel of the Department of Science and Technology, Govt. of India. She is the Executive Editor of International Journal of Swarm Intelligence, Inderscience. She is the Founder President of Soft Computing Research Society, India and the secretary of Forum of Interdisciplinary Mathematics. She has a number of research projects and consultancy projects. She has travelled widely including Australia, United Kingdom, Russia, Korea, Iraq, Singapore, The Netherlands and France.Her areas of specialization are nature inspired optimization techniques and their applications to engineering, science, finance and industry. Her contribution is noteworthy in Genetic Algorithms, Memetic Algorithms, Particle Swarm Optimization, Grey Wolf Optimization, Artificial Bee Colony, Gravitational Search Algorithm, Ant Lion Algorithm, Biogeographical Based Optimization, Glowworm Optimization, Harmony Search Algorithm, and their applications to solve real life problems.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 
24 September 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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