Journal of Applied & Computational Mathematics

Breakable Solid Transportation Problem with Hybrid and Fuzzy Safety Factors using LINGO and Genetic Algorithm

Abstract

Abhijit Baidya, Uttam Kumar Bera and Manoranjan Maiti

nvironments. If we carrying the produce from sources to destination by the means of unlike conveyances then due to insurgency, land slide and bad road, there are some risks or difficulties to transport the items. By this motive we initiate “Safety Factors” in transportation problem. Due to this reason desired total safety factor is being introduced. Also our objective is to evaluate the solution of STP using expected value model. Here we develop six models where first three models are formulated taking crisp unit transportation cost but the remaining three models are formulated taking hybrid unit transportation cost. To build up the different models we consider breakability and safety factor which is taken as crisp, fuzzy and hybrid for assorted models. All the fuzzy and hybrid models are reduced into its crisp equivalent using expected value modeling. Finally by Generalized Reduced Gradient (GRG) method using LINGO.13 optimization software and Genetic Algorithm we solve the mathematical models and put a enlarge discussion on it.