Closed-loop supply chains (CLSCs) have received considerable attention because of various economic and regulatory factors. A CLSC is characterized by more complicated network structures and higher uncertainties compared to traditional supply chain networks. Therefore, reliable CLSCs are being increasingly emphasized in academic circles due to the vast impacts of disruptions such as natural disasters and terrorist attacks. This paper studies a reliable location-inventory problem in a CLSC considering the mutual effects between failures of forward and reverse distribution centers (DCs) when they are co-located. The disruption probability of a co-located forward DC is different from that of a standalone forward DC, i.e., probabilistic disruptions are dependent on facility type. The problem is formulated as a nonconvex mixed-integer programming problem. A decomposition approach based on the outer approximation (DOA) algorithm is proposed to address the resulting model. The algorithm alternately solves relaxed master problems (mixed-integer linear programs, MILPs) and two nonlinear programming (NLPs) problems. Extensive numerical experiments are conducted to evaluate the performance of the proposed solution approach, after which managerial insights are explored.

由于各种经济和监管因素，闭环供应链（CLSC）受到了广泛的关注。与传统的供应链网络相比，CLSC的特点是网络结构更加复杂，不确定性更高。因此，由于自然灾害和恐怖袭击等破坏的巨大影响，学术界越来越重视可靠的CLSC。考虑到正向和反向分配中心（DC）并置时的故障之间的相互影响，本文研究了CLSC中的可靠位置库存问题。位于同一位置的前向DC的破坏概率与独立的前向DC的破坏概率不同，即，概率破坏取决于设施类型。该问题被表述为非凸混合整数编程问题。提出了一种基于外部逼近（DOA）算法的分解方法来解决生成的模型。该算法交替解决松弛主问题（混合整数线性程序，MILP）和两个非线性规划（NLP）问题。进行了广泛的数值实验，以评估所提出的解决方案方法的性能，然后探索管理的见解。