Breakable fuzzy multi-stage transportation problem

In this paper, we investigate two new transportation models with breakability and restriction on transportation. Sometime in transportation process the items which are transported, have got damaged due to bad conditions of the road and vehicle. Here we consider the problem that there are so many plants and customers and the goods are transported in n-stages. We formulate two transportation models under crisp and fuzzy environment where we consider the transportation parameters are crisp and fuzzy in nature, respectively. We also consider the breakability (takes the deterministic value for the respective models) at each stages. For the fuzzy model, generalized triangular fuzzy number and mean of α-cut method are considered. Numerical illustration is provided to illustrate the developed models. © 2015, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press and Springer-Verlag Berlin Heidelberg 2015.