Multi-directional local search for a sustainable supply chain network design model

International audience1. The problem consideredThe increasing importance of environmental issues has prompted decisionmakersto incorporate environmental factors into supply chain networkdesign (SCND) models. We propose a bi-objective SCND model to minimizetwo conflicting objectives: the total cost and the environmental impactexpressed by CO2 emissions.The logistics network consists of four layers: suppliers, plants, distributioncenters (DCs) and customers. The model considers several possibletransportations modes in the network, each transportation mode havinga lower and upper capacity limitation. Moreover, we consider differentcandidate technology levels at the plants and DCs. Each technology representsa type of service with associated fixed and variable costs and CO2emissions. A higher-level technology may reduce carbon emissions, but islikely to require more investment cost.The model considers CO2 emissions caused by all industrial and logisticsoperations as well as transportation. The main issues to be addressedin the sustainable SCND model includes determining the number, location,and technology level at plants and DCs, suitable transportation mode, andproduct flows between facilities.2. Solution methodWe solve the corresponding bi-objective mixed integer linear programmingmodel with the multi-directional local search (MDLS) framework. The efficiency of this recent framework has been proved on the multiobjectiveknapsack, set packing and orienteering problems, but to the bestof our knowledge, this is the first attempt to solve a facility location problemwith it. The MDLS is based on the principle of separately using independentsingle-objective local searches to iteratively improve the Pareto setapproximation. The motivation for using this framework is the capabilityof using already implemented single objective optimization components.In our case, we use a large neighborhood search algorithm as single objectivemethod. Our algorithm can be decomposed in the three followingsteps:Phase 1: look for an initial Pareto set approximation. The initialphase of the single objective LNS is executed separately for each objective.The output is an initial Pareto set approximation.Phase 2: Intensification around the Pareto set approximation. ThePareto set approximation is improved by exploring the neighborhoodof all the solutions in this set with a Multi-directional local search.Phase 3: optimization of product flows. After stabilizing the locationand transportation mode decisions for all Pareto set approximationsolutions in phase 2, we determine the optimal product flows by applyingthe Simplex algorithm to all solutions in the set.3. Computational resultsWe assess the performance of our approach through a comparison withthe well-known "-constraint method. In particular, we analyze the Paretofronts given by both solutions on a set of 60 generated instances and showthat the efficiency of our approach improves when the instance size grows