Optimality of a hedging-point control policy for a failure-prone manufacturing system under a probabilistic cost criterion

Bielecki and Kumar (1988) established the optimality of a critical inventory policy (hedging policy) in a Markovian failure-prone manufacturing system subject to a constant rate of demand for parts, and for a long-term average cost structure including parts storage and demand backlog costs. Under the same conditions, and if instead of minimizing the long-term average cost, one aims at minimizing a long-term probabilistic risk measure of the running cost exceeding a given fixed barrier, we show that the optimal policy remains of the critical inventory type, albeit with different characteristics. Application of the Hamilton-Jacobi-Bellman (HJB) equation to establish optimality for this risk-averse criterion is particularly problematic. Instead, the result is established using novel, more direct arguments.