Optimization Techniques

Unit 1

Introduction: Introduction to OR Modeling Approach and Various Real Life Situations Linear Programming Problems (LPP) : Basic LPP and Applications ; Various Components of LP Problem Formulation Solving Linear Programming Problems : Solving LPP : Using Simultaneous Equations and Graphical Method ; Simplex Method ; Duality Theory ; Charnes’ Big - M Method . Transportation Problems and Assignment Problems.

Unit 2

Network Analysis : Shortest Path : Dijkstra Algorithm ; Floyd Algorithm ; Maximal Flow Problem (Ford-Fulkerson); PERT-CPM (Cost Analysis, Crashing, Resource Allocation excluded) .

Unit 3

Inventory Control : Introduction ; EOQ Models ; Deterministic and probabilistic Models ; Safety Stock ; Buffer Stock.

Unit 4

Game Theory : Introduction ; 2- person Zero - sum Game; Saddle Point ; Mini-Max and 6L Maxi-Min Theorems (statement only); Games without saddle point ; Graphical Method ; Principle of Dominance.

Unit 5

Queuing Theory : Introduction ; Basic Definitions and Notations ; Axiomatic Derivation of the 7L Arrival & Departure (Poisson Queue ). Pure Birth and Death Models; Poisson Queue Models : M/M/1 : ∞ /FIFO and M/M/1: N/ FIFO.

REFERENCES:

1. H.A. Taha, “Operations Research”, Fifth Edn. Macmillan Publishing Company, 1992.

2. Hadley G., “Linear Programming” Narosa Publishers, 1987

3. Hillier F. & Liebermann G.J., “Introduction to Operations Research” 7/e (with CD), THM

4. Mustafi: Operations Research, New Age International DIGITAL IMAGE PROCESSING (