Introduction:
Evolution of OR, Definitions of OR, Scope of OR, Applications of OR, Phases in OR study. Characteristics and limitations of OR, models used in OR, Linear Programming Problem (LPP), Generalized LPP- Formulation of problems as L.P.P. Solutions to LPP by graphical method (Two Variables).
LPP:
Simplex method, Canonical and Standard form of LP problem, slack, surplus and artificial variables, Solutions to LPP by Simplex method, Big-M Method and two-phase Simplex Method, Degeneracy in LPP. Concept of Duality, writing Dual of given LPP. Solutions to L.P.P by Dual Simplex Method.
Transportation Problem:
Formulation of transportation problem, types, initial basic feasible solution using North-West Corner rule, Vogel’s Approximation method. Optimality in Transportation problem by Modified Distribution (MODI) method. Unbalanced T.P. Maximization T.P. Degeneracy in transportation problems, application of transportation problem. Assignment Problem-Formulation, Solutions to assignment problems by Hungarian method, Special cases in assignment problems, unbalanced, Maximization assignment problems. Travelling Salesman Problem (TSP). Difference between assignment and T.S.P, Finding best route by Little’s method. Numerical Problems.
Network analysis:
Introduction, Construction of networks, Fulkerson’s rule for numbering the nodes, AON and AOA diagrams; Critical path method to find the expected completion time of a project, determination of floats in networks, PERT networks, determining the probability of completing a project, predicting the completion time of project; Cost analysis in networks. Crashing of networks- Problems. Queuing Theory: Queuing systems and their characteristics, Pure-birth and Pure-death models (only equations), Kendall & Lee’s notation of Queuing, empirical queuing models – Numerical on M/M/1 and M/M/C Queuing models.
Game Theory:
Definition, Pure Strategy problems, Saddle point, Max-Min and Min-Max criteria, Principle of Dominance, Solution of games with Saddle point. Mixed Strategy problems. Solution of 2X2 games by Arithmetic method, Solution of 2Xn m and mX2 games by graphical method. Formulation of games. Sequencing: Basic assumptions, Johnson’s algorithm, sequencing ‘n’ jobs on single machine using priority rules, sequencing using Johnson’s rule-‘n’ jobs on 2 machines, ‘n’ jobs on 3 machines, ‘n’ jobs on ‘m’ machines. Sequencing of 2 jobs on ‘m’ machines using graphical method.
Course Outcomes:
At the end of the course, the student will be able to:
CO1: Understand the meaning, definitions, scope, need, phases and techniques of operations research.
CO2: Formulate as L.P.P and derive optimal solutions to linear programming problems by graphical method, Simplex method, Big-M method and Dual Simplex method.
CO3: Formulate as Transportation and Assignment problems and derive optimum solutions for transportation, Assignment and travelling salesman problems.
CO4: Solve problems on game theory for pure and mixed strategy under competitive environment.
CO5: Solve waiting line problems for M/M/1 and M/M/K queuing models.
CO6: Construct network diagrams and determine critical path, floats for deterministic and PERT networks including crashing of Networks
CO7: Determine minimum processing times for sequencing of n jobs-2 machines, n jobs-3 machines, n jobs-m machines and 2 jobs-n machines using Johnson’s algorithm.
Question paper pattern:
Textbook/s
1 Operations Research P K Gupta and D S Hira S. Chand and Company LTD. Publications, New Delhi 2007
2 Operations Research, An Introduction Hamdy A. Taha PHI Private Limited Seventh Edition, 2006
Reference Books
1 Operations Research, Theory and Applications J K Sharma Trinity Press, Laxmi Publications Pvt.Ltd. Sixth Edition, 2016
2 Operations Research Paneerselva n PHI
3 Operations Research A M Natarajan, P Balasubram ani Pearson Education, 2005
4 Introduction to Operations Research Hillier and Lieberman McGraw Hill 8thEd