Asymptotic Optimality of Hierarchical Controls in Stochastic Manufacturing Systems: a Review

نویسنده

  • S. P. Sethi
چکیده

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of diierent types of events in the system results in decisions that are asymptotically optimal as the rates of some events become large compared to those of others. Manufacturing systems that are addressed include single machine systems, owshops, and jobshops producing multiple products, incorporate random production capacity and demands, and involve such decisions as production rates, capacity expansion, and promotional campaigns. The paper concludes with a review of computational results and areas of applications. An appropriate place to begin this survey on this occasion is with the paper by Thompson and Sethi (1980), which considers a continuous-time, deterministic, single machine, single product production planning model whose purpose is to obtain production rates over time to minimize an integral representing a discounted quadratic loss function. The model is solved both with and without nonnegative production constraints. It is shown that there exists a time-dependent threshold termed the turnpike level of inventory such that production takes place in order to reach the threshold if the inventory is below it and no production takes

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تاریخ انتشار 1994