Reliable Flexibility Design of Supply Chains Via Extended Probabilistic Expanders

It is well-known that adding a little flexibility to the right place is an effective strategy to improve the performance of operations in the face of demand uncertainties, to ensure high level of capacity utilization. However, given that system disruptions are ubiquitous, the legacy flexibility designs may perform poorly under disruptions to supply or capacity installations. In this paper, we focus on the design of reliable and sparse flexibility structures that consistently meet a reasonable performance criterion under disruptions to both demand and supply. Specifically, we propose a class of structures termed as extended probabilistic expanders, based on the conjecture that the expansion property, rather than the global connectivity, is critical to good performance of the structures. We prove that for a system with n retailers, essentially only O(n) supply routes between suppliers and retailers are necessary to ensure good performance under disruption. In addition, we present an efficient randomized algorithm to construct extended probabilistic expanders, and demonstrate that the construction yields very good structure with the least number of edges asymptotically. We also investigate an extension to systems with structural constraints. Numerical results demonstrate that our design has not only a wide range of applications, but also better performance than a variety of known structures