A Study on Transportation Problems with Imprecise Parameters

Abstract

The classical transportation problem is one of the many well-structured problems in Operations Research that has been extensively studied in literature. The transportation problem is one of the subclass of the linear programming problems for which simple and practical computational procedures have been developed that take the advantage of the special structure of the problem. The transportation problem is amongst the most important special linear programming problem – in terms of the frequency with it appears in the applications and also in the simplicity of the procedure developed for its solutions. In solving real life transportation problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the fuzzy/intuitionistic fuzzy representation for the data. In this thesis, it is shown that it is not necessary to use the arithmetic operations of fuzzy/intuitionistic fuzzy numbers to find the fuzzy/intuitionistic fuzzy optimal solution of fuzzy/intuitionistic fuzzy transportation problems. The same can also be obtained by using the arithmetic operations of real numbers. Also, as it is much easy to apply arithmetic operations of real numbers as compared to arithmetic operations of fuzzy/intuitionistic fuzzy numbers so it is better to find the use method based on arithmetic operations of real numbers as compared to method based on arithmetic operations of fuzzy numbers.