A multi objective solid transportation problem in fuzzy, bi-fuzzy environment via genetic algorithm

In this paper, we concentrate on developing a bi-fuzzy multi objective transportation problem (MOSTP) according to bi-fuzzy expected value method (EVM). In a transportation model, the available discount is normally offered on items/criteria, etc., in the form all unit discount (AUD) or incremental quantity discount (IQD) or combination of these two. Here transportation model is considered with fixed charges and vehicle costs where AUD, IQD or combination of AUD and IQD on the price depending upon the amount is offered and varies on the choice of origin, destination and conveyance. To solve the problem, multi objective genetic algorithm (MOGA) based on Roulette wheel selection, arithmetic crossover and uniform mutation has been suitably developed and applied. To illustrate the models, numerical examples have been presented. Here, two types of problems are introduced and the corresponding results are obtained. To provide better customer service, the entropy function is considered.