Available online at www.sciencedirect.com Automatica 40 (2004) 945–956 www.elsevier.com/locate/automatica Perturbation analysis for production control and optimization of manufacturing systems  Haining Yu , Christos G. Cassandras * Department of Manufacturing Engineering and Center for Information and Systems Engineering, Boston University, Brookline, MA 02446, USA Received 12 July 2002; received in revised form 20 January 2004; accepted 2 February 2004 Abstract We use stochastic uid models (SFM) to capture the operation of threshold-based production control policies in manufacturing systems without resorting to detailed discrete event models. By applying innitesimal perturbation analysis (IPA) to a SFM of a workcenter, we derive gradient estimators of throughput and buer overow metrics with respect to production control parameters. It is shown that these gradient estimators are unbiased and independent of distributional information of supply and service processes involved. In addition, based on the fact that they can be evaluated using data from the observed actual (discrete event) system, we use them as approximate gradient estimators in simple iterative schemes for adjusting thresholds (hedging points) on line seeking to optimize an objective function that trades o throughput and buer overow costs. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Manufacturing system; Perturbation analysis; Performance optimization 1. Introduction Production control problems in manufacturing systems have been widely studied, starting with the pioneering work in Kimemia and Gershwin (1983). In a typical manufactur- ing setting, a machine may either occasionally break down, or, in a multi-product environment, it may be temporarily inaccessible to a certain part buer because it is serving an- other one. In the latter case, from the point of view of a buer, the machine appears to be failure prone (in queue- ing theory, this is also referred to as a server that “takes vacations”). As a result, the buer content experiences uc- tuations and occasionally overows causing blocking phe- nomena that disrupt the smooth operation of the system and  This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Xiren Cao under the direction of Editor Tamer Ba sar. Supported in part by the National Science Foundation under grants ACI-98-73339 and EEC-00-88073, by AFOSR under grant F49620-01-0056, by ARO under grant DAAD19-01-0610, and by the Air Force Research Laboratory under contract F30602-99-C-0057. * Corresponding author. E-mail addresses: fernyu@bu.edu (H. Yu), cgc@bu.edu (C.G. Cassandras). incur signicant costs. To compensate, one can control the ow of parts into a buer so as to maintain a satis- factory throughput while minimizing buer overow. A common approach is to formulate appropriate stochastic control problems so that control-theoretic techniques can be applied, as in Akella and Kumar (1986); Bielecki and Kumar (1988); Perkins and Srikant (1999); Feng and Yan (2000). For certain problem formulations, under specic modeling assumptions, production control policies based on thresholds or hedging points have been identied as being optimal (Perkins & Srikant, 1998, 1999; Hu, Vakili, & Yu, 1994) for a general overview and a recent survey see Sethi and Zhang (1994); Sethi, Yan, Zhang, and Zhang (2002). Although in general such policies do not guarantee opti- mality, their implementation simplicity also makes them widely appealing in practice. These facts motivate us to further study their application to manufacturing systems. Unfortunately, the determination of optimal values for these hedging points is a dicult problem; see Akella and Kumar (1986); Perkins and Srikant (1998, 1999); Feng and Yan (2000). In this paper, we address this particular problem, aiming at methodologies which can be applied on-line and without any knowledge of the stochastic characteristics of machine behavior or supply processes. 0005-1098/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.automatica.2004.02.001