Fuzzy Variable Linear Programming Problems

Abstract

During the last four decades, a large number of mathematical tools have been developed in Operational Research. For the linear programming problems in the crisp scenario, the aim is to maximize or minimize a linear objective function subject to linear constraints. But in many practical situations, the decision maker may not be in a position to specify the objective and/or constraint functions precisely but rather can specify them in a \fuzzy sense". In such situations , it is desirable to use some fuzzy variable linear programming type of modeling. This thesis is devoted to solve fuzzy variable linear programming problems. The main topics are fuzzy simplex method , fuzzy dual simplex method and sensitivity analysis for fuzzy variable linear programming problems. The chapter-wise summary of the thesis is as follows: Chapter 1 is introductory in nature. This chapter includes basic de¯nitions, arithmetic operations and concepts used throughout the work. A brief review of the work done in the area of fuzzy variable linear programming problem is also presented. In Chapter 2 , fuzzy simplex method for solving fuzzy variable linear pro- gramming problem , is presented . In Chapter 3, some duality results and fuzzy dual simplex method for solv- ing fuzzy variable linear programming problem , is presented . To illustrate the presented method, a numerical example is solved. In Chapter 4, a method to deal with sensitivity analysis for fuzzy variable linear programming problems is presented . To illustrate this method some numer- ical examples are solved.