Two Stage Transportation Problem in Different Types of Fuzzy Environments: An Industrial Case Study

Abstract

In this paper, we have considered modeling and optimization of a two-stage transportation problem with some realistic set of constraints for an industry. The primary objective of the decision maker is to allocate the manufactured goods to different warehouses and retailers in such a manner which minimizes the total transportation cost and time. The two-stage transportation problem of a similar type in the past had been formulated under a certain environment where the input information’s are precisely known to the decision maker. However, in most of the situations, the input information is not precisely known. In such circumstances, the fuzzy set theory plays a vital role in the modeling of the problem where the input data has some vagueness. In this paper, vagueness in the input parameters are handled by the concept of fuzzy set theory by considering these parameters as type 1 fuzzy numbers, type 2 fuzzy numbers, LR fuzzy numbers, and intuitionistic fuzzy numbers respectively. Different types of ranking function approaches are used to obtain the equivalent crisp form of the fuzzy parameters. Then, the equivalent deterministic form of the formulated problems are solved by employing the Interactive fuzzy satisfying method to obtain the optimal solution. A case study has been given to illustrate the solution procedure for solving the two-stage transportation problem.