FUZZY LINEAR PROGRAMMING: SOLUTION TECHNIQUES

Abstract

One of the most important daily problems is to model and solve the optimization problem. The linear programming (LP) is a useful tool for this purpose. But in many real-life practical problems such as diet, management problems, network optimization, etc it is often difficult to precisely define objectives and(/or) constraints for LPP in crisp scenarios. In such cases Fuzzy Linear Programming (FLP) type of modeling comes into play, providing more flexibility. In LPP fuzziness may arise in various ways. In this dissertation, Firstly various types of fuzzy linear programming models are introduced. Then we study FLPP with fuzzy parameters, FLPP with fuzzy decision variables, and fully fuzzy LPP. We give the methodologies to solve these FLPPs based on ranking function, duality results, etc. In such methods, we see how FLPP can be defuzzified into the crisp LPP using the ranking function. We have discussed some standard methods such as Primal, Dual, primal-dual simplex algorithms, duality results, etc.