A multi-objective robust optimization model for a facility location-allocation problem in a supply chain under uncertainty

S. Mohammad Arabzad, Mazaher Ghorbani, Sarfaraz Hashemkhani Zolfani


This paper presents a mathematical model for a facility location-allocation problem in order to design an integrated supply chain. We consider a supply chain consisting of multiple suppliers, multiple products, multiple plants, multiple transportation alternatives and multiple customers. The problem is to determine a number and capacity level of plants, allocation of customers demand, and selection and order allocation of suppliers. A scenario approach is used to handle the uncertainty of demand and cost parameters. The formulation is a robust multi-objective mixed-integer linear programming (MOMILP) that considers two conflicting objectives simultaneously. The first objective is to minimize the total costs of a supply chain including raw material costs, transportation costs and establishment costs of plants. The second objective function aims to minimize the total deterioration rate occurred by transportation alternatives. Then, the problem transformed into a linear one. Finally, by applying the LP-metric method, the model is solved as a single objective mixed-integer programming model. An experiment study shows that the proposed procedure can provide a promising result to design an efficient supply chain.

DOI: http://dx.doi.org/10.5755/j01.ee.26.3.4287


Supply chain design, Facility location-allocation, Robust multi-objective optimization, Uncertainty

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Print ISSN: 1392-2785
Online ISSN: 2029-5839