The closed-loop supply chain network (CLSCN) contains reverse flows that collect products from customers and recycle or remanufacture usable parts. The CLSCN design problem is becoming more and more prominent under the context of Sustainable Development and Circular Economy. Parameters associated with a CLSCN including customer demands, transportation costs, or disposal rates are usually subject to uncertainty. Furthermore, natural or man-made disruptions may cause part of the CLSCN to malfunction. We herein propose a hybrid stochastic and distributionally robust optimization (DRO) approach to hedge against discrete disruption scenarios and uncertain customer demands. We also tailor a Benders decomposition-based algorithm to efficiently solve the resulting large-scale mixed integer linear programming reformulations. Computational experiments demonstrate that the proposed algorithm can outperform commercial solvers such as CPLEX, and the DRO approach can produce solutions with low average costs and low variance in out-of-sample tests.

中文翻译：

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不确定条件下闭环供应链设计的分布式鲁棒优化

闭环供应链网络 (CLSCN) 包含从客户那里收集产品并回收或再制造可用零件的逆向流程。在可持续发展和循环经济的背景下，CLSCN 设计问题越来越突出。与 CLSCN 相关的参数（包括客户需求、运输成本或处置率）通常存在不确定性。此外，自然或人为的中断可能导致部分 CLSCN 发生故障。我们在此提出了一种混合随机和分布稳健优化 (DRO) 方法，以对冲离散中断场景和不确定的客户需求。我们还定制了一个基于 Benders 分解的算法，以有效地解决由此产生的大规模混合整数线性规划重构。