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

Abhijit Baidya Uttam Kumar Bera

doi:10.4172/2168-9679.1000185

Abstract

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.

Highlights

The transportation problem (TP) was developed by Hitchcock [1]
The transportation cost obtained by generalized reduced gradient technique (LINGO 13.0 Software) is greater than the cost obtained by using Genetic Algorithm
We conclude that to solve any solid transportation problem with and without breakability and safety factor Genetic algorithm (GA) is very useful than LINGO (Table 2)

Summary

Introduction

The transportation problem (TP) was developed by Hitchcock [1]. The classical transportation problem deals with transportation goods from some sources to some destinations. The solid transportation problem (STP) is a generalization of the well-known transportation problem (TP) in which three-dimensional properties is taken into account in the objective and constraint set instead of source and destination. A homogeneous product is delivered from an origin to a destination by means of different modes of transport called conveyances, such as trucks, cargo flights, goods trains, ships, etc. These conveyances are taken as the third dimension. Yang and Liu [12] applied expected value model, chance-constrained programming model and dependentchance programming in fixed charge solid transportation problem in fuzzy environment. Kundu et al [18] solve a multi-objective solid transportation problem with

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Results

Conclusion