Capacitated inspection scheduling of multi-unit systems

We consider the inspection scheduling problem of multi-unit systems where the inspections of individual units are coupled via a capacity constraint. Although the optimal inspection policy of the majority of single-unit systems can be characterized by a threshold policy, finding an optimal policy for multi-unit systems is significantly harder. Therefore, the current state-of-the-practice uses a periodical inspection policy for all units. Instead, we propose using a dynamic programming (DP) approach to solve small-scale problem instances to optimality and use solutions optimized for a single-unit system in an approximation scheme to obtain near optimal solutions for large-scale problems. Our results show that taking individual properties of the units to be inspected into account and incorporating the single-unit solutions within an approximate DP framework significantly decrease the inspection cost compared to a periodical inspection policy. The proposed methods can help resource-constrained regulatory agencies such as US Food and Drug Administration (FDA) to optimize their inspection activities.