Operation Research

Paper Code: 
24STT222
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course is meant for exposing the students to the mathematical details of the techniques for obtaining optimum solutions under constraints for desired output. They will be taught numerical methods of optimization, linear programming techniques and multiple objective programming. Students will also be exposed to practical applications of these techniques.

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT222

Operation Research

(Theory)

CO  41: Outline the principles, scope, and phases of operation research. Identify and formulate real-world problems into mathematical models and apply appropriate optimization techniques to find optimal solutions. 

CO 42: Develop proficiency in decision-making under uncertainty and risk using decision theory techniques and understand the principles of dynamic programming.

CO 43: Determine the inventory level of an industry for the smooth functioning and understand the concept of probability inventory problems.

CO 44: Analyzing queuing systems to optimize system performance and improve customer service.

CO 45: Explain problems related to sequencing and PERT-CPM to solve network analysis problems.

CO 46: Contribute effectively in course-specific interaction.

Approach in teaching: 

Interactive Lectures, 

Group Discussion, 

Classroom Assignment,

Problem Solving Sessions.

 

Learning activities for the students:

Assignments,

Seminar,

Presentation,

Subject based Activities.

Classroom Quiz,

Assignments,

Class Test,

Individual Presentation.

 

18.00
Unit I: 
Introduction to OR and Linear Programming

Operation Research: Definition and scope, phases, principles, models and their solutions. Review of linear programming problem, Duality Problems, Concept of simulation: Monte Carlo Simulation technique and its applications.

 

18.00
Unit II: 
Decision Theory and Dynamic Programming

Decision theory: Decision making under uncertainty and risk, sensitivity analysis. Dynamic programming: Introduction, decision tree, Bellman principle of optimality, solution of problems with finite number stages, concept of dynamic programming, minimum path problem.

 

18.00
Unit III: 
Inventory Control Models

Inventory control: Introduction, costs, advantages, Static Economic-Order-Quantity (EOQ) models with and without shortage, Deterministic models of price break, probabilistic inventory model, ABC Analysis.

 

18.00
Unit IV: 
Queuing Systems and Models

Queuing System: Definition, Characteristics of queuing system, Markov chain, Markov process, Poisson process: pure birth and pure death process. Kendall’s notations, Steady state solution of (M/M/1) and (M/M/s) models with associated distributions of queue length and waiting time. (M/G/1) model–Pollaczek Khintchine formula.

 

18.00
Unit V: 
Sequencing Problems and Project Management Techniques

Sequencing Problems: Notations, terminology, and assumptions, processing n jobs through 2 machines, n jobs through 3 machines, 2 jobs through m machines with graphical method, processing n jobs through m machines. PERT and CPM: basic concepts, probability of projection completion, travelling salesman problem, replacement problems- block and age replacement policies.

 

Essential Readings: 
  • Taha, H.A. (2007): Operation Research, McMillan Publishing Co. Inc 8thEdition,
  • Kanti Swaroop et. al (2007): Operation Reseach, Sultan chand & Sons, 13th edition.
  • Gross, D. & Harris C.M. 1975): Fundamentals of Queueing Theory, John Wiley & Sons.

 

SUGGESTED READINGS:

  • Sharma, S.D. (2000):  Operation Research, Kedar Nath Pub. Meerut.
  • Bronso, R. et.al.(1983), Schaum’s outlines Operation Research, Tata McGraw Hill Edition
  • Klienrock, L. (1975): Queueing System, Vol. 1 Theory, John Wiley.
  • Starr, M.K. and Miller, D.W. (1962): Inventory Control-Theory and Practice, Prentice Hall

 

e-RESOURCES:

 

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association

 

 

Academic Year: 
2024-2025
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