A Capacitated Three-Echelon Supply Chain Location-Allocation Problem in a Continuous Space: A Hybrid Grasp-Vns

Abstract

Location decisions are among the fundamental building blocks of supply chain network design. This paper investigates the location problem in a three-echelon supply chain network with simultaneously considering primary suppliers, mid-tier distributors, and end consumers. Each of these layers is assumed to have a finite demand and/or capacity with the option of acquiring their products from multiple sources. Here, we cover an often-neglected aspect of three-layer systems where the facilities are allowed to be located on a continuous two-dimensional space. This can be the case for many realistic supply chains in both private and public sectors. The challenge here is to develop a practical framework capable of efficiently organising real-scale networks with a large number of customers. An optimisation mathematical model is developed to minimise the total transportation cost of the system, expressed using Mixed-Integer Non-Linear Programming (MINLP). As the problem is difficult to solve exactly, we put forward a hybrid metaheuristic approach that reinforces the greedy randomised adaptive search procedure (GRASP) with an efficient local search based on the variable neighbourhood search (VNS). To further improve the efficiency of the hybrid approach, another version with a customised method for identifying the restricted candidate lists (RCL) is also offered. A variety of benchmark datasets, from small to large real-scale ones, are used to demonstrate the performance of the proposed mathematical model and algorithms. The reported results of five solution methods revealed a substantial success for the proposed approach, with the quality of our solutions outperforming other heuristic and exact benchmark algorithms by up to 77.9%

Keywords: Location-allocation, Continuous space, Three-echelon systems, GRASP, VNS