JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-requisites

Operations Research

Course Objectives

The main objectives of the course are: Learn

• Numerical optimization techniques for single variable and multi variable non- linear optimization problems.
• Sensitivity analysis on LPP queuing
• Simulation of annexing problem & inventory problem.
• Geometry cutting plane method & branch bound method for linear IPP.
• Meaning of stochastic programming problem simple problems for finding mean variance of random variables chance constrained algorithm.
• Formulation of GP model and solving it using arithmetic geometric inequality theorem.
• State of art nontraditional optimization technique, namely genetic algorithm simulated annealing & particle swarm optimization.

Course Outcomes

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

• apply appropriate optimization techniques and solve based on the type of optimization problem like single variable or multivariable
• Make sensitivity analysis to study effect of changes in parameters of LPP on the optimal solution without reworking.
• Simulate the system to estimate specified performance measures.
• Solve integer programming problem by either geometry cutting plane algorithm or branch band method.
• Apply chance constrained algorithm and solve stochastic linear programme.
• Formulate GP model and solve it.
• Solve given optimization problem by genetic algorithm or simulated annealing or PSO.

UNIT - I

Single Variable Non-Linear Unconstrained Optimization: Elimination methods: Uni-Model function- its importance, Fibonacci method & Golden section method. Interpolation methods: Quadratic & Cubic interpolation methods.

UNIT - II

Multi variable non-linear unconstrained optimization: Direct search methods – Univariant method, Pattern search methods – Powell’s, Hook -Jeeves, Rosenbrock search methods. Gradient methods: Gradient of function& its importance, Steepest descent method, Conjugate direction methods: Fletcher- Reeves method & variable metric method.

UNIT - III

Linear Programming: Formulation, Simplex method & Artificial variable optimization techniques: Big M & Two-phase methods. Sensitivity analysis: Changes in the objective coefficients, constants& coefficients of the constraints. Addition of variables, constraints. Simulation – Introduction – Types- steps – applications: inventory & queuing – Advantages and disadvantages.

UNIT - IV

Integer Programming: Introduction – formulation – Geometry cutting plane algorithm – Zero or one algorithm, branch and bound method

Stochastic Programming: Basic concepts of probability theory, random variables- distributions-mean, variance, correlation, co variance, joint probability distribution. Stochastic linear programming: Chance constrained algorithm.

UNIT - V

Geometric Programming: Posynomials – Arithmetic - Geometric inequality – unconstrained G.P- constrained G.P (≤ type only) Non-Traditional Optimization Algorithms: Genetics Algorithm-Working Principles, Similarities and Differences between Genetic Algorithm & Traditional Methods. Simulated Annealing-Working Principle- Simple Problems. Introduction to Particle Swarm Optimization (PSO) (very brief)

TEXT BOOKS:

• 1. Optimization theory & Applications by S. S. Rao, New Age International.
• 2. Optimization for Engineering Design by Kalyanmoy Deb, PHI

REFERENCE BOOKS:

• 1. Operations Research by S. D. Sharma
• 2. Operation Research by H. A. Taha, TMH
• 3. Optimization in operations research by R. L Rardin
• 4. Optimization Techniques by Benugundu & Chandraputla, Pearson Asia.
• 5. Optimization Techniques theory and practice by M.C. Joshi, K. M. Moudgalya, Narosa Publications. M. TECH. I Year I Sem. (AMS)