JNTUA B.Tech. R20 Regulations

########## JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR B.Tech (ME) - IV-I Sem L T P C 3 0 0 3 (20A03701c) OPERATIONS RESEARCH (Professional Elective-III) Course Objectives:

- ● To impart the basic concepts of modelling, models and statements of the operations research.
- ● Formulate and solve linear programming problem/situations.
- ● Model strategic behaviour in different economic situations.
- ● To solve transportation problems to minimize cost.
- ● Apply Queuing theory to solve problems of traffic congestion, counters in banks, railway bookings etc.
- ● Explain scheduling and sequencing of production runs and develop proper replacement policies.

########## Course Outcomes:

At the end of the course, the student will be able to

- ● Develop mathematical models for practical problems. (L3)
- ● Apply linear programming to transportation problems. (L3)
- ● Solve games using various techniques. (L3)
- ● Solve production scheduling and develop inventory policies. (L6)
- ● Apply optimality conditions for constrained and unconstrained nonlinear problems. (L3)
- ● Apply dynamic programming methods. (L3)

UNIT I Introduction to OR OR definition - Classification of Models, modeling - Introduction to Operations Research (OR): OR definition - Classification of Models, modeling - Introduction to Operations Research (OR): Methods of solving OR Models, limitations and applications of OR models Problem Formulation, Graphical Method, Simplex Method, Big-M Linear Programming Programming (LP): Method, Two - Phase Simplex Method, Special Cases of LP- Degeneracy, Infeasibility and Multiple Optimal Solutions; Concept of dual theorem

########## UNIT - II Transportation and Assignment Problems

Transportation Problem - Formulation; Different Methods of Obtaining Initial Basic Feasible Solution - North West Corner Rule, Least Cost Method, Vogel's Approximation Method; Optimality Method - Modified Distribution (MODI) Method; Special Cases - Unbalanced Transportation Problem, Degenerate Problem. Assignment Problem - Formulation, Hungarian Method for Solving Assignment Problems, Traveling Salesman problem.

UNIT - III Game theory &Job Sequencing Optimal solution of two person zero sum games, the max min and min max principle. Game theory: Optimal solution of two person zero sum games, the max min and min max principle. Game theory: Games without saddle points, mixed strategies. Reduction by principles of dominance, arithmetic, algebraic method and graphical method. Introduction to Job shop Scheduling and flow shop scheduling, Solution of Job Job Sequencing: Sequencing: Sequencing Problem, Processing of n Jobs through two machines, Processing of n Jobs through m machines, graphical method.

UNIT - IV Queuing Theory &Inventory Control Introduction - Terminology, Arrival Pattern, Service Channel, Population, Departure Queuing Theory: Introduction - Terminology, Arrival Pattern, Service Channel, Population, Departure Queuing Theory: Pattern, Queue Discipline, Birth & Death Process, Single Channel Models with Poisson Arrivals, Exponential Service Times with infinite and finite queue length; Multichannel Models with Poisson Arrivals, Exponential Service Times with infinite queue length. Introduction, Deterministic models - EOQ model with and without shortages, Inventory Control: Control: Production model, Buffer stock and discount inventory models with single price breaks. Selective inventory control.

UNIT - V Replacement and Maintenance Analysis &DP Introduction - Types of Maintenance, Make or buy Replacement and Maintenance Analysis: Introduction - Types of Maintenance, Make or buy Replacement and Maintenance Analysis: decision. Types of Replacement Problems, Determination of Economic Life of an Asset, and Simple Probabilistic Model for Items which completely fail-Individual Replacement Model, Group Replacement Model. Introduction -Bellman's Principle of Optimality Dynamic Programming (DP): - Applications of Dynamic Programming - Shortest Path Problem - Capital Budgeting Problem -