Solving Different Types of Transportation Problems in Fuzzy Environment

Abstract

In todays highly competitive market, the pressure on organizations to nd better ways to create and deliver value to customers become stronger. How and when to send the products to the customers in the quantities, they want in a cost-e ective manner, become more challenging. Transportation models provide a powerful frame- work to meet this challenge. Transportation models ensure the e cient movement and timely availability of raw materials and nished goods. The solid transportation problem can be considered as extension of transporta- tion problem. In solid transportation problem, di erent modes of transport called conveyances, such as truck, cargo ights etc. are used to transport a homogeneous product from di erent sources to various destinations. This thesis is devoted to solving di erent types of transportation problems in fuzzy environment. The main topics are transportation problem and solid trans- portation problem in fuzzy environment. 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. Chapter 2 presents brief review of the work done in the area of fuzzy trans- portation problem and fuzzy solid transportation problem. In Chapter 3, fuzzy transportation problem is studied. Fuzzy vogel's ap- proximation method is used to nd the fuzzy initial basic feasible solution and fuzzy modi ed distribution method is used to nd fuzzy optimal solution of the said prob- lem. To illustrate the presented method, a numerical example is solved. In Chapter 4, two types of fuzzy transportation problems are studied. The problems are solved using extension principle. To illustrate the presented methods, two numerical examples are solved. In Chapter 5, the solution procedure of fuzzy solid transportation prob- lem using extension principle is presented. To illustrate the presented method, a numerical example is solved.