A distributed approximation approach for solving the sustainable supply chain network design problem

This paper introduces a comprehensive Mixed Integer Linear Programming (MILP) model for a sustainable supply chain network design problem, and an efficient Distributed Approximation Approach (DAA) to solve it approximately. We study a multi-echelon, multi-product and multi-modal supply chain with different transportation modes. Besides relevant costs in the supply chain such as procurement, production and distribution cost, we also explicitly consider the environmental footprint, represented by carbon emissions and water consumption from production and transportation. The approximation approach is a decomposition-based method. First, the original problem is divided into a partner selection sub-problem and a transportation planning sub-problem. Then multiple filter mechanisms are used to remove potentially infeasible solutions, and an approximate value of the objective function is calculated for each of the remaining solutions to perform a further selection. The one with the lowest approximation is chosen to be applied with a branch-and-bound method. Finally, the algorithm is paralleled and implemented in Apache Spark distributed computing framework to further improve efficiency. Experimental results show that the proposed DAA can provide high quality solutions compared to the optimal solutions of the MILP model with mostly a negligible relative gap and solve large instances in much shorter time than CPLEX. Moreover, in our numerical study, we also compare the results of our model with another version of the model that does not take the environmental footprint into consideration. The results show that explicitly incorporating environmental footprint results in a substantial decrease of CO₂ emissions and water consumption at a negligible cost increase. This insight may be of interest to managers and other decision makers and policy makers.