Reliable closed-loop supply chain design problem under facility-type-dependent probabilistic disruptions

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.