Study of Multi Objective Mathematical Programming Problems in Uncertain Environment involving Multi Choice Parameters

Abstract

In the thesis we have tried to develop the methodologies to solve different types of fuzzy chance constrained programming models by converting the mathematical models into their equivalent deterministic models. Fuzziness is present in the chance constrained programming problem either in objective function or in constraint or in both in the form of fuzzy random variables and fuzzy numbers. Throughout the thesis we have considered the chance constrained programming problem under fuzzy environment. All the methodologies have been developed by using the concept of Buckley s fuzzy probability theory. newlineMulti-Choice programming (MCP) problem is a mathematical programming (MP) problem, in which decision maker is allowed to set multiple number of choices for a parameter. There is no direct methodology to solve MCPs. A linear programming problem involving multi-choice parameter is computationally expensive to obtain an optimal solution. Therefore, to develop a methodology that optimizes objective function and selects an appropriate multi-choice parameter, is one of the challenging problems in MCP. Keeping this in mind the core of the thesis is concentrated in building up solution procedures for fuzzy probabilistic programming problems involving multi-choice parameters. newlineMore than one objective function have also been considered in the proposed model. In this thesis we have considered, fuzzy programming approach, _-constraint method, and goal programming approach to handle the multi-objective mathematical programming problem. newlineAfter transforming multi-choice parameters into its equivalent mathematical expressions, the mathematical model is converted to a mixed integer non-linear programming problem. The mathematical model is then solved by using existing methodologies. newlineIn this thesis we have considered Multi-Objective Fuzzy Probabilistic Programming Problem Involving Multi-Choice Parameters, Computation of Multi-Choice Multi-Objective Fuzzy Probabilistic Programming Problem, Multi-Choice Multi- Objective Fuzzy Stochastic Transportation Problem, Computation of Multi-Choice Multi-Objective Fuzzy Probabilistic Two Stage Programming Problem and Multi-Objective Fuzzy Probabilistic Quadratic Programming Problem. In multi-choice multi-objective stochastic transportation problem, we have considered multi-choice demand which follows normal distribution. The probabilistic constraints are transformed to its equivalent deterministic mathematical model by chance constrained method. To deal with multiple objective function, we have used fuzzy programming approach than any other existing techniques. To deal with multi-choice parameters least square approximation technique is used. newlineIn all of our models we have verified the methodologies using numerical examples. newline newline