Hedging policies for failure-prone manufacturing systems: optimality of JIT and bounds on buffer levels

In this paper, we consider a multiple part-type, single machine manufacturing system that is subject to failures. We provide necessary conditions and sufficient conditions for the optimality of Just-In-Time manufacturing, and further show that the necessary and sufficient conditions coincide when the negative buffer costs for all the parts are equal. In general, finding optimal hedging policies for multiple part type problems is extremely difficult. Despite this, we provide bounds on the optimal hedging points, and also prove that, under an optimal hedging policy, the buffer levels will be upper bounded. The existence of a computable upper bound on the buffer levels is significant for two reasons: (i) It provides the maximum buffer capacity required to operate the system optimally, (ii) It restricts the choice of switching curves and hedging points to be considered for numerical evaluation of optimal hedging policies.