# Operation Research

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# 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

Session-5:

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

Session-6:

Introduction to Duality in Linear Programming

Session-7:

General primal-dual pair

Session-8:

Formulating primal-dual problem

Session-9:

Duality in simplex method

Session-10:

Dual simplex method

Session-11:

Introduction to Inventory Controls

Session-12:

Introduction to Inventory decision

Session-13:

Cost associate with inventories

Session-14:

Factor affecting inventory control

Session-15:

Introduction to Economic order quantity (EOQ)

Session-16:

Deterministic inventory problem with no shortages

Session-17:

Problems of deterministic inventory problem with no shortages

Session-18:

Deterministic inventory problem with shortages

Session-19:

Problems of deterministic inventory problem with shortages

Session-20:

Economic order quantity (EOQ) problem with price breaks.

Session-21:

Introduction to elementary queuing theory

Session-22:

Introduction to Queuing system

Session-23:

Elements of queuing system

Session-24:

Problems on Elements of queuing system

Session-25:

Operating characteristics of queuing system

Session-26:

Probability distribution in queuing systems

Session-27:

Problems of probability distribution in queuing systems

Session-28:

Classification of queuing models

Session-29:

Problems of queuing models

Session-30:

Definition of transient and steady state.

Session-31:

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

Session-32:

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

Session-33:

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

Session-34:

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

Session-35:

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

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## Session

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## Case Studies

### 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 […]