Profit Maximization Solid Transportation Problem with Trapezoidal Interval Type-2 Fuzzy Numbers

Abstract

This paper proposes a new concept on transportation problem in which, we maximize the profit and minimize the transportation time while transporting an amount of quantity from a source to the destination. Here, we design two transportation models, in both the models; we maximize the profit and minimize the time of transportation. Here model-I having the unit purchase cost, unit selling price, unit transportation cost and transportation time as trapezoidal interval type-2 fuzzy number, while in model-II all the parameters are trapezoidal interval type-2 fuzzy number. To reduce these model-I and model-II into crisp equivalent, we use the expected value of a trapezoidal interval type-2 fuzzy number. Then the crisp equivalent problems are solved by employing the Interactive fuzzy satisficing method and LINGO 13.0 software to get the optimal solution. A numerical example is provided to demonstrate the models.