Pade approximants for the transient optimization of hedging control policies in manufacturing

Part production is considered over a finite horizon in a single-part multiple-failure mode manufacturing system. When the rate of demand for parts is constant, for Markovian machine-mode dynamics and for convex running cost functions associated with part inventories or backlogs, it is known that optimal part-production policies are of the so-called hedging type. For the infinite-horizon case, such policies are characterized by a set of constant critical machine-mode dependent inventory levels that must be aimed at and maintained whenever possible. For the finite-horizon (transient) case, the critical levels still exist, but they are now time-varying and in general very difficult to characterize. Thus, in an attempt to render the problem tractable, transient production optimization is sought within the (suboptimal) class of time-invariant hedging control policies, a renewal equation is developed for the cost functional over finite horizon under an arbitrary time-invariant hedging control policy.