# Operations Research for SPPU 19 Course (BE - SEM VII - MECH - 402045D) - Elective-IV

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Unit 1 Introduction to OR, Theory of Games and Decision Analysis Introduction to OR : Origin of Operations Research, Definition, Evolution and Classification of Quantitative methods, Operations Research Techniques and Methodology, Advantages and Limitations, Scope and Applications of OR Theory of Games : Introduction, Classification of Games, Two-person Zero Sum Games, Solution of 2 x 2 Game with no Saddle Point, Dominance in Games, Subgame Method to Solve (2 x n or m x 2) Mixed Strategy Games, Graphical Method to Solve (2 x n or m x 2) Games Decision Analysis : Introduction, Decision Under Certainty, Decision Under Risk, Decision Under Uncertainty (Maximin, Minimax, Maximax, Minimin Criterions, Hurwicz Criterion, Laplace Criterion, Savage or MiniMax Regret Criterion), Decision Tree. (Chapters - 1, 2, 3) Unit 2 Queuing Theory and Sequencing Model Queuing Theory : Introduction, Elements of Queuing, Characteristics of Waiting Lines, Service discipline, Service Mechanism, Terminology and Kendall’s Notation of Queuing system, Single Channel systems M/M/1: FCFS// and M/M/1: FCFS/N/ Sequencing Models : Solution of Sequencing Problem - Processing of n Jobs Through Two Machines, Processing of n Jobs Through Three Machines, Processing of Two Jobs Through m Machines, Processing of n Jobs Through m Machines. (Chapters - 4, 5) Unit 3 Linear Programming Introduction, Formulation of LPP, LPP by Graphical Method, Solution of LPP by Simplex Method, Big M Method and Two-phase method (Limited to 2 variables only), Conversion of Primal to Dual problems (Chapter - 6) Unit 4 Transportation and Assignment Model Transportation Model : Introduction, Formulation of Transportation problem, Methods to Find Basic Feasible Solution (Vogel’s Approximation Method (VAM), Least Cost Method (LCM), North West Corner Rule (NWCR)), Unbalanced Transportation Problem, Degeneracy in Transportation Problem (Theoretical treatment only), Optimality Test- Modified Distributed Method Assignment Model : Introduction, Mathematical Formulation of Assignment Problem Difference between Transportation and Assignment problem Assignment Problem, Hungarian Method, Balanced and Unbalanced Assignment problem, Maximization in Assignment Problems, Travelling Salesman Problem (Mathematical Formulation and Numerical) (Chapters - 7, 8) Unit 5 Project Management Network Models : Fulkerson's Rule, Concept and Types of Floats, CPM and PERT, Crashing Analysis and Resource Scheduling Replacement Analysis : Replacement of Items that Deteriorate, Replacement of Items that Fail Suddenly. (Chapters - 9, 10) Unit 6 Simulation and Dynamic Programming Simulation : Introduction, Simulation Definition, Types of Simulation, Steps of Simulation, Advantages and Disadvantage of simulation, Stochastic Simulation and Random numbers, Monte Carlo simulation, Random number Generation Dynamic Programming : Introduction, Dynamic Programming Model, Applications of Dynamic Programming Model to Shortest Route problems, Bellman Optimality Principle, Resource Allocation problem by Dynamic Programming. (Chapters - 11, 12)

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