Abstract
We derive estimators of throughput sensitivity to changes in buffer capacity for continuous flow models of a transfer line comprising two machines separated by a buffer of finite capacity, where machines are subject to operation-dependent failures, i.e., a machine cannot fail when it is idle. Both repair times and failure times may be general, i.e., they need not be exponentially distributed. The system is hybrid in the sense that it has both continuous dynamics—as a result of continuous material flow—and discrete events: failures and repairs. The combination of operation-dependent failures and buffer capacity as the parameter of interest make the derivative estimation problem difficult, in that unlike previous work on continuous flow models, careful use of conditional expectation (i.e., smoothed perturbation analysis) is required to obtain unbiased estimators.
Similar content being viewed by others
References
Bashyam, S., and Fu, M. C. 1994. Application of perturbation analysis to a class of periodic review (s,S) inventory systems. Naval Research Logistics 41(1): 47–80.
Brémaud, P., Malhamé, R. P., and Massoulié, L. 1997. A manufacturing system with general stationary failure process: stability and IPA of hedging control policies. IEEE Trans. Automatic Control 42: 155–170.
Buzacott, J. A., and Shanthikumar, J. G. 1992. Stochastic Models of Manufacturing Systems. Englewood Cliff, NJ: Prentice-Hall.
Caramanis, M., and Liberopoulos, G. 1992. Perturbation analysis for the design of flexible manufacturing system flow controllers. Operations Research 40: 1107–1125.
Dallery, Y., and Gershwin, S. B. 1992. Manufacturing flow line systems: a review of models and analytical results. Queueing Systems 12: 3–94.
Fu, M. C., 1994. Sample path derivatives for (s,S) inventory systems. Operations Research 42(2): 351–364.
Fu, M. C., and Hu, J. Q. 1997. Conditional Monte Carlo: Gradient Estimation and Optimization Applications. Boston: Kluwer Academic Publishers.
Fu, M. C., and Xie, X.-L. 1998. Gradient estimation of two-stage continuous transfer lines subject to operation-dependent failures. Research Report TR 98–57, Institute for Systems Research, University of Maryland, College Park, U.S.A.
Haurie, A., L'Ecuyer, P., and Van Delft, Ch. 1994. Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models. Discrete Event Dynamic Systems: Theory and Applications 4: 87–111.
Plambeck, E. L., Fu, B.-R., Robinson, S. M., and Suri, R. 1996. Sample-path optimization of convex stochastic performance functions. Mathematical Programming 75: 137–176.
Shi, L., Fu, B.-R., and Suri, R. 1999. Sample path analysis for continuous tandem production lines. Discrete Event Dynamic Systems: Theory and Applications 9: 211–239.
Suri, R., and Fu, B.-R. 1994. On using continuous flow lines to model discrete production lines. Discrete Event Dynamic Systems: Theory and Applications 4: 127–169.
Wardi, Y., and Melamed, B. 1996. IPA gradient estimation for loss measures in continuous flow models. submitted.
Xie, X. L. 1998. Evaluation and optimization of two-stage continuous transfer lines subject to time-dependent failures. Proceedings of the International Workshop on Discrete Event Systems, 112–117.
Yan, H., Yin, G., and Lou, S. X. C. 1994. Using stochastic optimization to determine threshold values for the control of unreliable manufacturing systems. J. Optimization Theory and Applications 83: 511–539.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fu, M., Xie, X. Derivative Estimation for Buffer Capacity of Continuous Transfer Lines Subject to Operation-Dependent Failures. Discrete Event Dynamic Systems 12, 447–469 (2002). https://doi.org/10.1023/A:1019759524969
Issue Date:
DOI: https://doi.org/10.1023/A:1019759524969