Operation Research

Teacher

Dr. Mohammed Siddique

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Course Name : Operation Research

Code(Credit) : CUNT2483 (3-0-1)

Objectives

  • To introduce a brief understanding of Linear Programming
  • To cater to the characteristics of Linear Programming Problems and its
  • To demonstrate the utilization of Linear Programming Problems in industry and business.

Course Outcomes

COs Course outcomes Mapping Cos with POs (High-3, Medium-2, Low-1)
CO1 Can formulate the necessary and sufficient optimality conditions for linear programming and demonstrate the geometrical interpretation of these conditions. PO1(3), PO9(3)
CO3 Can use various techniques inventory and queuing theory to solve real-life application problems. PO4(3), PO2(2),
CO5 Can use the mathematical foundations learned in this course to formulate new applications as optimal decision problems and seek appropriate solutions algorithms. PO5(2), PO9(2)

Course Syllabus

Module-I:

Linear programming problem & Simplex method: Introduction to linear programming problem,

Formulation of linear programming problem, Graphical solution of linear programming problem, Solution of linear programming problem using simplex method, Artificial variables, Solution of linear programming problem using Big-M and two-phase method

 

Module -II:

Duality in Linear Programming: Introduction, General primal-dual pair, formulating primal-dual problem, Duality in simplex method, Dual simplex method.

 

ModuleIII:

Inventory Controls: Introduction, Inventory decision, Cost associate with inventories, Factor affecting inventory control, Economic order quantity (EOQ).

Module - IV:

Deterministic inventory problem with no shortages, Deterministic inventory problem with shortages, Economic order quantity (EOQ) problem with price breaks.

Module – V:

Elementary queuing theory: Introduction, Queuing system, Elements of queuing system, Operating characteristics of queuing system.

Module – VI:

Probability distribution in queuing systems, Classification of queuing models, Definition of transient and steady state.

 

Module – VII:

Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.

 

Projects:

 

  1. Project on Inventory management system
  2. Project on queuing theory

 

Text Books:

 

  1. KantiSwarup, P.K. Gupta and Man Mohan-Operations Research, S. Chand and Co. Pvt.Ltd.

 

  1. Engineering Optimization Theory and Practice by Singiresu S. Rao, JOHN WILEY & SONS, INC., Fourth Edition

 

Reference Book:

 

Mathematical Programming by N. S. Kambo, East West Press.

Session Plan

Session-1:

 

Introduction to linear programming problem

 

https://in.video.search.yahoo.com/search/video?fr=mcafee&ei=UTF-8&p=Introduction+to+Random+variables&vm=r&type=E210IN714G0#id=0&vid=e878bfaa6a2d0dec8ce0b504175d7016&action=click

 

Session-2:

 

Formulation of linear programming problem

 

https://in.video.search.yahoo.com/search/video?fr=mcafee&ei=UTF-8&p=What+is+a+univariate+distribution+in+statistics%3F&type=E210IN714G0#id=2&vid=eb412c34f71af2d2408462604dcd49bb&action=click

 

Session-3:

 

Graphical solution of linear programming problem

 

https://in.video.search.yahoo.com/search/video?fr=mcafee&ei=UTF-8&p=What+is+a+univariate+distribution+in+statistics%3F&type=E210IN714G0#id=2&vid=eb412c34f71af2d2408462604dcd49bb&action=click

 

Session-4:

 

Solution of linear programming problem using simplex method

 

https://www.youtube.com/watch?v=H2Ji-Q4MfqU&list=PLU6SqdYcYsfIaokdZTmptaf-PK7s-B0ju&index=4

 

Session-5:

 

Artificial variables, Solution of linear programming problem using Big-M and two-phase method

 

https://www.youtube.com/watch?v=L0zWnBrjhng

 

Session-6:

 

Introduction to Duality in Linear Programming

https://www.youtube.com/watch?v=Ag8XJuskG78&list=PLRNL7AjA6rjxW80He0tS0Xv1l2PEvAQNZ

 

Session-7:

 

General primal-dual pair

 

https://www.youtube.com/watch?v=z0Ry_3_qhDw

 

Session-8:

 

Formulating primal-dual problem

 

https://www.youtube.com/watch?v=4kDScWSaEWs

 

Session-9:

 

Duality in simplex method

 

 

https://www.youtube.com/watch?v=Za1YxRJL-SA&list=PLwJRxp3blEvZBAn3bwAAtdJqotRPBWBlP

 

Session-10:

 

Dual simplex method

 

https://www.youtube.com/watch?v=pJh1oZ401NI

 

Session-11:

 

Introduction to Inventory Controls

 

https://www.youtube.com/watch?v=9vwucf8RZH0

 

Session-12:

 

Introduction to Inventory decision

 

https://www.youtube.com/watch?v=Cq9Jr6v8p0M

 

Session-13:

 

Cost associate with inventories

 

https://www.youtube.com/watch?v=E-S-E6HsR_k

 

Session-14:

 

Factor affecting inventory control

 

https://www.youtube.com/watch?v=HdUul6xIocg

 

Session-15:

 

Introduction to Economic order quantity (EOQ)

 

https://www.youtube.com/watch?v=y5nxiL6civU

 

Session-16:

 

Deterministic inventory problem with no shortages

 

https://www.youtube.com/watch?v=UwzuJW4P2Jw

 

Session-17:

 

Problems of deterministic inventory problem with no shortages

 

https://www.youtube.com/watch?v=8e0zaHhTHyY

 

Session-18:

 

Deterministic inventory problem with shortages

 

https://www.youtube.com/watch?v=lzGKRSvs5HM

 

Session-19:

 

Problems of deterministic inventory problem with shortages

 

https://www.youtube.com/watch?v=dQNpSa-bq4M

 

Session-20:

 

Economic order quantity (EOQ) problem with price breaks.

 

https://www.youtube.com/watch?v=zAULhNrnuL4

 

Session-21:

 

Introduction to elementary queuing theory

 

https://www.youtube.com/watch?v=UVvuwv-ne1I

 

Session-22:

 

Introduction to Queuing system

 

https://www.youtube.com/watch?v=0WY9WYZGl9c

 

Session-23:

 

Elements of queuing system

 

https://www.youtube.com/watch?v=nkTZ7XdIp-A

 

Session-24:

 

Problems on Elements of queuing system

 

https://www.youtube.com/watch?v=2J8pVynRZ8A

 

Session-25:

 

Operating characteristics of queuing system

 

https://www.youtube.com/watch?v=HIiBoL-z0cU&list=PLHRHy1-UoGh2pdh2hqTAUKtb0bCjttby8

 

Session-26:

 

Probability distribution in queuing systems

 

https://www.youtube.com/watch?v=0l3tzQI_ApM

 

Session-27:

 

Problems of probability distribution in queuing systems

 

https://www.youtube.com/watch?v=F5DhWBsp8J4

 

Session-28:

 

Classification of queuing models

 

https://www.youtube.com/watch?v=osgqQy9Hr8s

 

Session-29:

 

Problems of queuing models

 

https://www.youtube.com/watch?v=2EjGJXzsC2U

 

Session-30:

 

Definition of transient and steady state.

 

https://www.youtube.com/watch?v=3MnVCX94jJM

 

Session-31:

 

Steady-state solutions of Markovian queuing model: M/M/1

 

https://www.youtube.com/watch?v=KLAEwukvuZs

 

Session-32:

 

Steady-state solutions of Markovian queuing model: M/M/1 with limited waiting space

 

https://www.youtube.com/watch?v=O5TjsbZBs2E

 

Session-33:

 

Steady-state solutions of Markovian queuing model: M/M/C

 

https://www.youtube.com/watch?v=O5TjsbZBs2E

 

Session-34:

 

Steady-state solutions of Markovian queuing model: M/M/C with limited waiting space

 

https://www.youtube.com/watch?v=O5TjsbZBs2E

 

Session-35:

 

Steady-state solutions of Markovian queuing model: M/G/1.

 

https://www.youtube.com/watch?v=nuOtA2TwouU

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Case Studies

Case Studies

Our Main Teachers

Dr. Mohammed Siddique

Asst. Prof. Department of Mathematics
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Dr. Mohammed Siddique, received Ph. D in Mathematics in the area of Optimization Techniques and Machine Learning from KIIT, Deemed to be University, Bhubaneswar and completed his M.Sc in Mathematics and M.Tech in Computer Science from Utkal University, Bhubaneswar.  He is having more than 16 years of teaching experience. He is having more than 50 […]