Engineering Optimization: Operations Research JNTU Anantapur syllabus

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR

B.Tech. IV-I Sem (M.E) (13A03701) OPERATIONS RESEARCH R-13

UNIT – I

Introduction to OR and Linear Programming-1 OR definition– Classification of Models –Types of Operations Research models; Linear Programming- Problem Formulation, Graphical Method, Simplex Method, Two–Phase Simplex Method, Big-M Method Special Cases of LP- Degeneracy, Infeasibility and Multiple Optimal Solutions

UNIT – II

Linear programming-2: Duality- Principle, Economic Interpretation of Duality, Dual Simplex Method Transportation Problem – Formulation; Different Methods of Obtaining Initial Basic Feasible Solution- North-West Corner Rule, Least Cost Method, Vogel’s Approximation Method; Optimality Methods-Stepping Stone Method and Modified Distribution (MODI) Method; Special Cases -Unbalanced Transportation Problem, Degenerate Problem; Assignment Problem – Formulation; Optimal Solution -Traveling Salesman problem.

UNIT – III

Game Theory: Introduction – Minimax (Maximin) Criterion and Optimal Strategy, Saddle Point, Solution of Games with Pure Strategy –Games with Mixed Strategies – 2 X 2 Games – Dominance Principle– Solution by Graphical Method of m X 2 & 2 X n games Queuing Theory: Introduction –Terminology, Service Channel, Arrival Pattern, Population, Departure Pattern(Service Pattern), Queue Discipline, Birth & Death Process, Balking, Reneging, Jockeying; Single Channel Models with Poisson Arrivals, Exponential Service Times with finite queue length and non-finite queue length; Multichannel Models with Poisson Arrivals, Exponential Service Times with finite queue length and non finite queue length.

UNIT – IV

Sequencing -Assumptions-n-jobs-2 Machines model, n-jobs-3-machines models. PERT & CPM: Introduction to Project Management, Activities, Events, Predecessor Relationships, AOA Diagram, Early Start, Early Finish, Late Start & Late Finish Times, Earliest Occurrence and Latest Occurrence of the Event, Total Float, Free Float, Independent Float CPM- Deterministic Model- Critical Path, Crashing, Optimal Project Duration, Least Possible Project Duration PERT- Probabilistic Model- Various types of Activity Time Estimates, Standard Deviation and Variance of the Activities and Projects, and Probability of Completing the Project within scheduled time

UNIT – V

Dynamic Programming : Introduction – Bellman’s Principle of Optimality – Applications of Dynamic Programming- Capital Budgeting Problem – Shortest Path Problem – Solution of Linear Programming Problem by DP Replacement and Maintenance Analysis: Introduction – Types of Maintenance, Types of Replacement Problem, Determination of Economic Life of an Asset, and Simple Probabilistic Model for Items which completely fail-Individual Replacement Model, Group Replacement Model.

TEXT BOOK :

1. Introduction to operations Research,Taha,PHI

2. Introduction to O.R,Hiller & Libermann (TMH).

REFERENCES :

1. Operations Research ,A.M.Natarajan,P.Balasubramani,A.

Tamilarasi,Pearson Education.

2. Operations Research: Methods & Problems , Maurice

Saseini, Arhur Yaspan & Lawrence Friedman

3. Operations Research , R.Pannerselvam,PHI Publications.

4. Operations Research , Wagner, PHI Publications.

5. Operation Research ,J.K.Sharma,MacMilan.

6. O.R,Wayne L.Winston,Thomson Brooks,cole