Failure-prone production systems with uncertain demand

We consider a failure-prone manufacturing system with bursty demand arrivals. We prove that the hedging-point policy is optimal for this problem and provide analytical expressions to compute the hedging point. This allows us to compare our exact results to approximations provided by diiusion limits and large deviations. We also show that our result leads to the solution for the constant demand rate problem under an appropriate scaling of the demand process. We also provide a necessary and suucient condition under which the just-in-time (JIT) policy is optimal for the case of linear, absolute value instantaneous cost.