MG1402 – OPERATIONS RESEARCH VII –SEMESTER

DEPARTMENT OF E.E.E - S.SIVARAJA DEPARTMENT OF MATHEMATICS

CONTENT… SYLABUS UNIT WISE DETAILS REFERENCE LESSON PLAN ASSIGNMENT TOPICS SEMINAR TOPICS

SYLLABUS…

UNIT I LINEAR PROGRAMMING (LP) 9 Basic concepts and scope of OR – Phases of OR – Formulation of LP Problems – Limitations of LP – Solutions to LPP – Graphical Solution – Standard LP form and its Basic solutions – The simplex algorithm – Artificial Variable Technique – Big-M method, Two-phase method – Variants of the Simplex Method – Degeneracy, unbounded solution, infeasible solution – Application for business and Industrial problems UNIT II DUALITY, TRANSPORTATION MODEL AND ASSIGNMENT MODEL 9 Primal – Dual models – Dual simplex method – Mathematical formulation of the problem – Methods for finding an initial solution – North-West corner method, Least-cost method, Vogel’s Approximation Method (VAM) – Test for optimality – Variants of the transportation problem – Mathematical Formulation of the problem – Solution of an assignment problem – Hungarian algorithm – Variants of the assignment problem – Traveling salesman problem UNIT III INTEGER DYNAMIC PROGRAMMING 9 Types – Concept of a cutting plane – Gomory’s cutting plane method – Branch and bound method – Concepts – Terminology – Bellman’s principle of optimality – Application in Network, allocation and inventory

UNIT IV PROJECT MANAGEMENT AND THEORY OF GAMES 9 Concept of Network – PERT, CPM – Construction of Network – Critical path analysis – Probability in PERT analysis – Cost trade-off analysis – Two-person zero-sum game – Pure strategies – Mixed strategies – Games with dominance – Solution methods of games without saddle point – Algebraic method, arithmetic method, matrix method and Graphical method UNIT V INVENTORY CONTROL AND QUEUING 9 Deterministic model – Costs – Decision variables – EOQ – Instantaneous receipt of goods with and without shortages – Non-instantaneous receipt of goods without shortages – Price breaks – Probabilistic inventory model – Single period without setup cost – Inventory systems – Lead time – Safety stock – ROL, ROP determination – Characteristics of Queuing system – Symbols and Kendall’s notation – Poisson arrival and exponential service – Single and multi channel model – Infinite population

UNIT-WISE DETAILS

LINEAR PROGRAMMING

INTRODUCTION SOLUTION TO LPP GRAPHICAL METHOD SIMPLEX METHOD BIG-M METHOD TWO-PHASE SIMPLEX METHOD

DUALITY,TRANSPORTATION AND ASSIGNMENT MODEL

PRIMAL-DUAL DUAL SIMPLEX METHOD NORTH –WEST CORNER RULE LEAST COST METHOD VAM TEST FOR OPTIMAL SOLUTION ASSIGNMENT PROBLEM HUNGARIAN METHOD TRAVELLING SALESMEN PROBLEM

INTEGER DYNAMIC PROGRAMMING

INTRODUCTION CUTTING PLANE GOMORY’S CUTTING PLANE METHOD BRANCH AND BOUND METHOD BELLMAN’S PRINCIPLE OF OPTIMALITY

PROJECT MANAGEMENT AND THEORY OF GAMES

PERT CPM CRITICAL PATH ANALYSIS PROBABILITY IN PERT ANALYSIS COST TRADE –OFF ANALYSIS TWO-PERSON ZERO SUM GAME DOMINANCE PROPERTY MIXED STRATERGY SADDLE POINT

INVENTORY CONTROL AND QUEUEING

DETERMINISTIC MODEL EOQ INSTANTANEOUS RECEIPT OF GOODS NON-INSTANTANEOUS RECEIPT OF GOODS PROBABILISTIC INVENTORY MODEL LEAD TIME SAFETY STOCK ROL DETERMINATION ROP DETERMINATION

INTRODUCTION SINGLE-SERVER QUEUEING SYSTEM KENDALL’S NOTATION LITTLE’S FORMULA M/M/1:INFINITY/FIFO M/M/C:INFINITY/FIFO

REFERENCE….

1. Sharma, J.K., “Operations Research: Theory and applications”, Macmillan India Ltd., Reprint, Hamdy A. Taha, “Operations Research – An Introduction”, 7th Edition, Prentice Hall of India, Don, T. Philips, Ravindran, A. and James Solnerg, “Operations Research: Principles and Practice”, John Wiley and Sons, Bobby Srinivasan and Sandblom, C.L., “Quantitative Analysis for Business Decisions”, Tata McGraw Hill Edition, Chandrasekhar Rao, Shanti Lata Misra, “Operations Research”, Alpha Science International Ltd, Nita H. Shah, Ravi M. Gor, Hardik Soni, “Operations Research”, Prentice Hall of India, 2007.

LESSON PLAN…

UNIT UNIVERSITY/ PLANNED I II III IV V TOTAL 9/15 9/14 9/13 9/12 9/16 45/80

ASSIGNMENT AND SEMINAR TOPICS

ASSIGNMENTSEMINAR GRAPHICAL METHOD GAME THEORY MIXED STRATERGY SIMPLEX METHOD NORTH WEST CORNER RULE TRAVELLING SALESMEN PROBLEM