A compensatory approach to multi-objective interval transportation problem

Abstract

The data of real life problems generally cannot be expressed strictly. An efficient way of handling this situation is expressing the data as intervals. Thus this paper focus on the Multi-objective Interval Transportation Problem (MITP) whose parameters i.e. cost coefficients of the objective functions, supply and demand quantities are expressed as intervals. This problem is transformed to a traditional Multi-objective Transportation Problem (MOTP) with crisp parameters. First, interval supply-demand quantities are converted into deterministic ones by means of the convex combination of left and right limits. By an order relation that represents the decision maker’s preferences between interval costs, each objective is turned into crisp form within the right limit and centre of the costs. Finally, using Werners’ “fuzzy and” operator, a compensatory fuzzy approach to MITP is presented. And to our knowledge, combining compensatory ( and ) operator with MITP has not been published up to now. Our approach generates compromise solutions which are both compensatory and Pareto-optimal. Also a numerical example is given to illustrate the presented approach.