Robust sustainable bi-directional logistics network design under uncertainty

Reverse logistics networks are often implemented to ensure a sustainable product or material recovery and to improve a company's sustainability footprint. The most common approach for designing bi-directional networks is the independent design of reverse and forward networks. The joint integration of both networks is rarely considered. Here we study a strategic capacitated facility location problem with integrated bi-directional product flows through a network of multiple supply stages, including production allocations, uncertain data development, facility locations and flexible capacity adjustments. We extend the location and capacity problem by including the decision on the type of depot to install. Forwarding or collecting depots only process one designated direction. Hybrid sites process products of both flow directions. We first introduce a detailed deterministic model assessing the impact of incorporating reverse logistics into a forward-oriented supply chain. This is then extended to a robust capacitated facility location model, which minimizes the expectations of relative regrets for a set of scenarios over a multi-period planning horizon, while considering uncertainty regarding supplying and collecting goods. Example settings show the superior performance of the robust model compared to the deterministic model. The resulting network design mitigates the risks of higher costs and of not being able to fully satisfy demand. This is achieved at costs not significantly higher than the individual optimal solution and with solution times that are promising for applications in practice. The approach supports practitioners in assessing the flexibility of their supply chain, independent of its product flow direction, when operating under uncertainty.