A MANUFACTURING SYSTEM WITH GENERAL STATIONARY FAILURE PROCESS - STABILITY AND IPA OF HEDGING CONTROL POLICIES

The present paper concerns a new methodology for the adaptive optimiza tion of piecewise deterministic non Markovian systems via a simple exa mple of interest in manufacturing, This methodology takes into account the fact that piecewise deterministic systems are rarely Markovian an d that, consequently, classical control theory based on dynamic progra mming of Markovian systems cannot provide quantitative answers in most realistic situations, although it does provide useful insights. The e xample considered in this paper, which allows us to push the analysis sufficiently far and with enough details to understand the foundations and to appreciate the scope and limitations of the method, is that of a single-machine/single-part production system, first studied from th e point of view of control theory by Kimemia and Gershwin [23]. We obt ain stochastic gradient estimates via the perturbation analysis of Ho and Cao [18] by the ''regenerative'' method of Konstantopoulos and Zaz anis [24], in view of stochastic optimization, Its mathematical justif ication requires a careful study of the ''regenerative'' structure of the process, In particular, we give the necessary and sufficient condi tions of stability of this system via the method of Loynes [29].