Solving Single-Sink, Fixed-Charge, Multi-Objective, Multi-Index Stochastic Transportation Problem

Abstract

SYNOPTIC ABSTRACTThe aim of this article is to present a fuzzy programming approach to a single-sink, fixed-charge, multiobjective, multi-index stochastic transportation problem (SSMISTP). This article focuses on the minimization of the transportation cost, deterioration rate, and underused capacity for transportation of raw materials from different sources to the ”Single-Sink” by different transportation modes. The parameters of the proposed problem are transportation cost, fixed-charge, deterioration rate, and underused capacity. These parameters are to be treated here as random variables. Because of the globalization of the market, assume that the “Sink” demand is an interval representing the inexact demand component for the SSMISTP. By considering the uncertainties of these parameters, we formulate the mathematical model of the proposed problem. Using a stochastic programming approach, all the stochastic objective functions are converted into deterministic objective functions. Again using the interval concept, the proposed interval-valued sink constraint decomposes into two deterministic constraints. Finally, using all deterministic objective functions and constraints, we design a multiobjective transportation problem(MOTP). The optimal compromise solution to the MOTP has been obtained by using a fuzzy programming technique. We demonstrate the feasibility of the proposed problem using a real-life practical example.