Optimization Analysis In Stochastic Models

Abstract

The optimization problems are generally studied in stochastic models and operation research techniques. Linear programming problems and their applications play a vital role among optimization problems. This research work mainly deals with linear programming models. In the first chapter the basic definitions, properties, applications and formulation of linear programming models are presented. The second chapter is devoted to the previous research works relative to the topic of the thesis. The content of the chapters three, four and five are the contributions of the candidate. The Third chapter describes a study on optimization using stochastic linear programming. The Self Help Group of rural poor who have organized themselves into group for eradication poverty. A self help Group consists of two categories namely magalier thittam and non-magalier thittam. The factors of self help group categories are random in nature. These factors can be analyzed using stochastic linear programming problem. The optimization technique such as two stage programming and chance constrained programming are adopted for stochastic linear programming problem. Here, chance constrained programming is used to obtain optimal solution. In the fourth chapter Inverse stochastic Linear Programming has been analyzed.Stochastic linear programming problems with two stages are considered. Inverse optimization objective function of the models discussed and interval coefficients of constraints are introduced. Deterministic inverse Linear Programming is extended to Two stochastic linear programming problem with interval model coefficients. Dantzig-Wolfe and Bender s decomposition methods are utilized to obtain the feasible solutions of the two stage models. The upper and lower bounds of the optimal solution are generated by Bender s composition algorithm. This solution is terminated only when the differences between the bounds is less than are equal to pre specified value. Optimization model with interval valued functions has been studied in th