Uncertain Multi –Objective Multi –Item Four Dimensional Fractional Transportation Model

Abstract

In day to day real-life situations we often tend to face problems which contain parameters which are mutually non-commensurable. In transportation problems where goods are transported from origin to destination, when trying to establish a relationship between parameters, we observe that few of them come out as fractions with linear nature. In this work, we have proposed a four dimensional multi-objective multi-item fractional transportation model whose parameters in both objective functions and constraints are considered as an uncertain variables. As it is difficult to handle such type of problem directly, an equivalent deterministic model is obtained by using chance constraint and expected value property of uncertain variable. Furthermore, all the uncertain linear fractional objective functions of the proposed model are converted to a single objective function and obtained an optimal solution for the proposed model. An illustrative example is given to demonstrate the proposed model.