Optimal control of a simple manufacturing system with restarting costs

We consider the optimal control of an unreliable manufacturing system with restarting costs. In 1986 and 1988, Akella and Kumar (for the infinite horizon discounted cost) and Bielecki and Kumar (for the infinite horizon average expected cost) show that the optimal policy is given by an optimal inventory level (“hedging point policy”). Inspired by these simple systems, we explore a new class of models in which the restarting costs are explicitly taken into account. The class of models discussed often allow complete analytical discussions. In particular, the optimal policy exhibits an (s; S) type form.