An approach to solve an unbalanced fully rough multi-objective fixed-charge transportation problem

Nowadays, rough set theory has become an invaluable tool to represent the uncertainty in different optimization problems because of its aspect of considering agreement and knowledge of all the experts and hence addressing more realistic decisions. Motivated by the nature of rough sets, in this study we investigate an unbalanced multi-objective fixed-charge transportation problem in which all the decision variables as well as coefficients of the objective functions and constraints are represented by rough intervals. A new method has been proposed to solve an unbalanced fully rough multi-objective fixed-charge transportation problem in which, firstly, an unbalanced fully rough multi-objective fixed-charge transportation problem transformed into a balanced fully rough multi-objective fixed-charge transportation problem. Then three approaches, namely, fuzzy programming technique, goal programming technique and weighted-sum method are applied for obtaining the Pareto-optimal solution of the transformed balanced fully rough multi-objective fixed-charge transportation problem. In weighted-sum method, analytic hierarchy process has been used to determine the weights corresponding to objective functions. A comparison is drawn between the Pareto-optimal solutions which are derived from different approaches. Since the obtained solution is in a rough environment, it provides a wide range to help the decision maker to extract the best compromise solution. Finally, a case study is solved to show the contribution of the article in the field of decision-making and transportation.