Diversification or pooling? Distributionally robust optimization approach for closed-loop supply chain network design

Establishing a reliable closed-loop supply chain is crucial for companies aiming to reduce costs and enhance sustainability. Two main structures are prevalent: one diversifies risk and logistics through a specific recycling distribution center, while the other pools risk and bidirectional logistics into the co-located distribution center. In this work, we propose a hybrid structure that integrates both types of distribution centers. We formulate this reliable closed-loop supply chain network design problem into a two-stage distributionally robust optimization (DRO) model to resist facility-correlated disruptions. We demonstrate the supermodularity of the second-stage problem and reformulate it into a mixed-integer second-order cone program, making it tractable for commercial solvers. To efficiently handle large-scale, long-horizon problems, we develop a Branch-and-Benders-Cut Decomposition algorithm and introduce Supermodular Cuts specifically tailored to our model. In numerical studies, we investigate risk diversification and pooling effects within different network structures. We found that utilizing the co-located distribution center, which pools risk and bidirectional logistics in a single facility, can effectively withstand high-disruption risks. Moreover, increasing facility capacity improves the flexibility of the network in addressing disruption scenarios. Additionally, we show that our algorithm outperforms the benchmark model in terms of efficiency. Finally, we consider the problem of independent facility disruption to enhance the robustness of our results.