European Journal of Operational Research

There has been extensive academic research on the optimisation of reverse logistics (RL) and closed-loop supply chain (CLSC) network design. However, the existing literature is lacking in several features of practical relevance, and the simultaneous consideration of dynamic characteristics, including the multi-period setting, inventory factors, environmental footprints, and scalability of the application. This shortcoming is primarily due to the challenges associated with computation complexity, mathematical formulation, and the need for a faster solution method to solve such large-scale problems in real-time. In this research, we address these challenges and investigate the multi-facility green RL network design problem, integrating carbon footprint and vehicle selection, entailing allocation between the facilities in the multi-period setting to incorporate the dynamic characteristics. We formulate a mixed-integer linear programming (MILP) model to minimise the total cost, comprising the carbon emission cost due to transport and production at the facilities. We also investigate the effects of carbon emissions and the choice of the vehicle fleet on the network's structure. The novelty of our research lies in the development and application of an exact solution method, namely “Improved Benders Decomposition (IBD)” with several algorithmic enhancements, including a strengthened master problem, valid inequalities, a heuristic, and a multi-stage strategy to accelerate the convergence of the Benders decomposition method. By combining these elements, the proposed IBD solves the MILP model, provides a faster solution methodology with improved convergence of the bounds, and addresses the inherent intractability of the existing problem. We apply our proposed heuristic on a set of 12 problem configurations under distinct scenarios. We show that the proposed IBD heuristic outperforms existing traditional methods in terms of solution quality, computational time, and robustness.

Multi-period green reverse logistics network design: An improved Benders-decomposition-based heuristic approach