Optimizing simultaneously inspection interval and inventory levels (s, S) for a k-out-of-n system

In this paper, we will present a model for joint optimization of periodic inspection and inventory levels for a k-out-of-n system. The component failures follow a Non-Homogeneous Poisson Process and failed components can only be revealed at inspection times. We have two types of inspections; planned periodic inspections and non-planned opportunistic inspections. Opportunistic inspections are performed when the system fails, which occurs when n-k+1 components are down at the same time. Failed components are either minimally repaired or replaced with spare parts from the inventory. The inventory policy needs to support the inspection policy so that spare parts are available when needed. The inventory is replenished to level S at periodic inspections, after a random lead-time. However, when the system fails within an inspection interval, the inventory is replenished to level s, with no lead-time (because it is an emergency order). We assume that placing an emergency order is more expensive, and that it depends on the number of spares which is ordered. A simulation model is developed to find the expected total cost for given inspection interval τ and inventory levels S and s. In order to find the combination of τ, s and S, that minimizes the total cost over the system life cycle, we use a genetic algorithm. It is necessary to use a search heuristic method because the size of the search space makes it not feasible to find the optimal solution by trying all combinations of τ, s and S.