Solving the sustainable supply chain network design problem by the multi-neighborhoods descent traversal algorithm

A multi-period, multi-echelon, multi-product, and multi-modal sustainable supply chain network design problem is considered. The problem is formulated as a multi-objective Mixed-Integer Linear Programming (MILP) model that explicitly considers the environmental footprint and social responsibilities. We introduce the Multi-Neighborhood Descent Traversal Algorithm (MNDTA), which can solve this problem efficiently. The MNDTA begins with a structured initial solution of the model and improves the incumbent solution by sequentially traversing several specifically designed neighborhoods over generations. A lower-bound-based evaluation method is introduced to reduce the computational complexity involved in solving the integer programming problem. Experimental results demonstrate that the proposed MNDTA can provide high-quality solutions that are close to the optimal solutions with a negligibly small (relative) gap and can solve large instances much more quickly than CPLEX can. In addition, the MNDTA outperforms existing solution algorithms. A numerical comparison of the results of the proposed model with those of a model that only considers financial aspects demonstrates that explicitly using our model when designing a supply chain network can substantially reduce the environmental impact and increase social responsibility at a negligible cost increase.