A Multi-Objective Stochastic Solid Transportation Problem with the Supply, Demand, and Conveyance Capacity Following the Weibull Distribution

Amrit Das,Gyu M Lee

doi:10.3390/math9151757

Abstract

This study addresses a multi-objective stochastic solid transportation problem (MOSSTP) with uncertainties in supply, demand, and conveyance capacity, following the Weibull distribution. This study aims to minimize multiple transportation costs in a solid transportation problem (STP) under probabilistic inequality constraints. The MOSSTP is expressed as a chance-constrained programming problem, and the probabilistic constraints are incorporated to ensure that the supply, demand, and conveyance capacity are satisfied with specified probabilities. The global criterion method and fuzzy goal programming approach have been used to solve multi-objective optimization problems. Computational results demonstrate the effectiveness of the proposed models and methodology for the MOSSTP under uncertainty. A sensitivity analysis is conducted to understand the sensitivity of parameters in the proposed model.

Highlights

There have recently been an increasing number of natural or human-made disasters, including earthquakes, tsunamis, floods, typhoons, chemical explosions, and nuclear disasters
We have presented the optimal compromised solutions for multi-objective stochastic solid transportation problem (MOSSTP) models proposed in Section 3, using global criterion method (GCM) and fuzzy goal programming (FGP)
Note that the deterministic models converted from the MOSSTP are not balanced by nature

Summary

Introduction

There have recently been an increasing number of natural or human-made disasters, including earthquakes, tsunamis, floods, typhoons, chemical explosions, and nuclear disasters. During or after the disaster impact, the relief goods pre-located at relief warehouses must be distributed quickly to the people in need to save their lives or to help them recover from damages [1]. This critical task in disaster management is called the relief distribution problem, where various uncertainties exist in demand points, demand, and road networks. In relief distribution and redistribution problems, multiple objectives [3] are required to be achieved because of timeliness, fairness, and costs. These relief distribution and redistribution problems offer the motivation to propose MOSSTPs with uncertainties in supply, demand, and conveyance capacity

Objectives

Methods

Results

Conclusion