A multi-objective transportation problem under quantity dependent credit period and cost structure policies in triangular intuitionistic fuzzy environment

Abstract

One of the major economic activities of a business concern is transportation of its products without any hassle. Therefore, the research on a transportation problem is very important now-a-days. In a classical transportation problem, the amount incurred for shipping the goods from the source to a destination is determined on the basis of unit transportation cost. But now, in many practical cases, it is seen that the unit transportation cost is settled on the basis of transported amount. In such a direction, this article develops a transportation problem to transport the produced items from a production house to some retailers through some distributors. The system has two cost parameters, one is actual unit transportation cost and other is demanded unit transportation cost. The actual unit transportation cost is the cost incurred during the transportation while the demanded unit transportation cost is the cost demanded by the distributors. Here, the demanded unit transportation cost has been decided depending on the amount of transported item. Since in the system, there are more than one distributor, distributors offer a credit period policy to attract the retailers. On the basis of the deterioration of the loaded amount, the transported items are classified into two categories. For the higher deteriorated items, the transportation cost is relatively larger and for the lower deteriorated items, the transportation cost is relatively lower with the increase in the loading amount. Considering the above two categories, two crisp models are developed. Due to the uncertain information of the actual unit transportation cost, the models are illustrated considering the actual unit transportation cost as a triangular intuitionistic fuzzy number. The main objective of this research is to minimize the total cost of the retailers and to maximize the total profit of the distributors simultaneously under the above circumstances. For crispification, two different methods have been used here — one is an existing method namely ordered weighted average operator and other is a developed average value approach. Also, the elitist non-dominated sorting genetic algorithm (NSGA-II) and the fuzzy programming technique have been used to get the optimal solution of this problem. To justify the impact and significance of the proposed models on this decision making system, some numerical studies have been done and it is observed that distributors and retailers both benefit more under the credit period policy than the policy without credit period. This study discusses the situation under which the uncertain parameters are to be expressed in terms of triangular intuitionistic fuzzy numbers. Also, it is identified that more accurate crispification has been done by the average value approach than the existing approach.