Multi-directional local search for sustainable supply chain network design

In this paper, we propose a bi-objective MILP formulation to minimise logistics costs as well as ${{\rm CO}_2} $CO2 emissions in a supply chain network design problem with multiple layers of facilities, technology levels and transportation mode decisions. The proposed model aims at investigating the trade-off between cost and ${{\rm CO}_2} $CO2 emissions through supply chain activities (i.e. raw material supply, manufacturing, warehousing, and transportation). To this end, a multi-directional local search (MDLS) metaheuristic is developed. The proposed method provides a limited set of non-dominated solutions ranging from a purely cost effective solution to a purely environmentally effective one. Each iteration of the MDLS consists in performing local searches from all non-dominated solutions. To do so, a Large Neighborhood Search (LNS) algorithm is used. Extensive experiments based on randomly generated instances of various sizes and features are described. Three classic performance measures are used to compare the set of non-dominated solutions obtained by the MDLS algorithm and by directly solving the MILP model with the epsilon-constraint approach. This paper is concluded by managerial insights about the impact of using greener technology on the supply chain topology.