Uncertain Multi Level Four Dimensional Multi Item Fractional Transportation Problem

Abstract

This work will be illustrating a model for dealing with multi level four dimensional fractional multi item transportation problem whose parameters in both objectives and constraints are considered as uncertain variables. The Fractional programming technique is useful in dealing with real life situations where the decision maker has to maximize or minimize the ratios of two objective functions. In any hierarchical system or decentralized system, multi level programming problem can be used to obtain efficient solution based on the preferences of each decision maker at each level. The usage of fractional method and level wise preference in real life problems helps us to obtain the efficiency of system and also enables hierarchical decision making which is common in day to day transportation firms. An equivalent deterministic model has been obtained for the multi level four dimensional fractional multi item transportation problem under uncertain environment by using expected and chance constrain model of uncertainty theory. Then the deterministic model is solved by using the modified fuzzy goal programming technique to obtain the compromise solution of the proposed model. The validity of the proposed model has been explained using the numerical example