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.
Highlights
In conventional transportation problems, it is assumed that the decision-maker is certain about the exact values of the cost of transportation, availability, and demand for the product
Solving the above Value- and Ambiguity-based linear programming problems by using classical methods, we obtain the solution of the Value and Ambiguity for both Model I and Model II, which is provided in Tables 12 and 13
All quantity discount scheme is usually less than the incremental quantity discount scheme, but in this research, there is a difference in the trapezoidal all quantity discount scheme
Summary
It is assumed that the decision-maker is certain about the exact values of the cost of transportation, availability, and demand for the product. We introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and with incremental quantity discounts. Ebrahimnejad [27] provided a new way to solve the fuzzy transfer problem (FTP) In this method, transportation cost, supply, and demand are represented by a nonnegative flat fuzzy number LR. Ebrahimnejad and Verdegay [28] have proposed an efficient computational solution approach for solving intuitionistic fuzzy transportation problems in which costs are triangular intuitionistic fuzzy numbers (TIFN) and availabilities and demands are taken as exact numerical values. E main objective of this study is to solve the new transportation problem with total quantity discounts and incremental quantity discounts in the intuitionistic fuzzy environment without using the ranking function. 0 to qIijF1N, the qIijF2N, cost is is scheme is called transportation problem with incremental intuitionistic fuzzy quantity discounts
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