Interval Oriented Entropy Based Multi-item Solid Transportation Problem with Budget and Breakability

To maximization the total profit andminimization the total cost we investigate two transportationmodels with interval transportation parameters and we present a solution of our newly developed models using appropriate methods. The solid transportation problem has been formulated with and without interval entropy function defined by Shannon’s measure of entropy. Also an additional constraint on the total budget at each destination is imposed. When we transport the goods from plants to destination then few items should be damage due to bad condition of route and vehicles, for this reason we introduce the breakability in our respective models. We employ two different approaches (Hu and Wang’s Approach and Mahato and Bhunia’s Approach) based on interval ranking and made a comparison on it. To convert the multi-objective programming problem into single-objective problem we apply weighted sum method. The models are illustrated with numerical examples and solved using the LINGO.13 optimization software. The results of the models with and without entropy are also obtained and compared.