Joint optimization of maintenance and inventory policies for a simple system

We examine age replacement and ordering decisions for a system with only one component subject to random failure and with room for only one spare in stock. The system incurs costs for replacement, shortage, holding, and breakage; the lead time for receipt of an ordered spare is constant. We consider the solvability and desirability of jointly optimizing these two traditionally separate decisions. We show that the problem has some convexity properties that make it amenable to minimization. For our data set, we find that using separate optimization gives an average loss of 3% relative to the joint minimum; about a tenth of die time the difference was more than 10%, but in general this loss can vary from zero to arbitrarily large.