Value- and Ambiguity-Based Approach for Solving Intuitionistic Fuzzy Transportation Problem with Total Quantity Discounts and Incremental Quantity Discounts

Abstract

The cost of goods per unit transported from the source to the destination is considered to be fixed regardless of the number of units transported. But, in reality, the cost is often not fixed. Quantity discount is often allowed for large shipments. Furthermore, the transportation cost and the price break quantities are not deterministic. In this study, we introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and incremental quantity discounts. Here, the cost and quantity price breakpoints are represented by trapezoidal intuitionistic fuzzy numbers. The Values and Ambiguities are defined as the degree of acceptance and rejection for trapezoidal intuitionistic fuzzy numbers. The trapezoidal intuitionistic fuzzy transportation problem is converted to a parametric transportation problem based on their Value indices and Ambiguity indices. Then, for different Values of the parameter, the transformed problem is reduced to the linear programming problem. Then, the linear programming problem is solved by using the classical methods. The proposed method is demonstrated with a numerical example. In conclusion, the intuitionistic fuzzy transportation problem with total quantity discounts is compared with the intuitionistic fuzzy transportation problem with incremental quantity discounts.