On Optimization of Unreliable Material Flow Systems

  • Yu. Ermoliev
  • S. Uryasev
  • J. Wessels
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 49)


The paper suggests an approach for optimizing a material flow system consisting of two work-stations and an intermediate buffer. The material flow system may be a production system, a distribution system or a pollutant-deposit/removal system. The important characteristics are that one of the work-stations is unreliable (random breakdown and repair times), and that the performance function is formulated in average terms. The performance function includes random production gains and losses as well as deterministic investment and maintenance costs. Although, on average, the performance function is smooth with respect to parameters, the sample performance function is discontinuous. The performance function is evaluated analytically under general assumptions on cost function and distributions. Gradients and stochastic estimates of the gradients were calculated using Analytical Perturbation Analysis. Optimization calculations are carried out for an example system.


Performance Function Buffer Size Perturbation Analysis Repair Time Continuous Optimization Problem 
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  1. [1]
    J.A. Buzacott (1982): “Optimal” operating rules for automated manufacturing systems. IEEE — Transactions on Automatic Control 27, pp. 80–86.CrossRefGoogle Scholar
  2. [2]
    Ermoliev, Yu. (1988): Stochastic Quasi-Gradient Methods. In: “Numerical Techniques for Stochastic Optimization” Eds. Yu. Ermoliev and R.J-B Wets, Springer- Verlag,393–401.CrossRefGoogle Scholar
  3. [3]
    Yu. Ermoliev, S. Uryasev, and J. Wessels (1992): On Optimization of Dynamical Material Flow Systems Using Simulation. International Institute for Applied Systems Analysis, Laxenburg, Austria, Report WP-92–76, 28 p. 59Google Scholar
  4. [4]
    P. Glasserman (1991): Gradient Estimation Via Perturbation Analysis. Kluwer Academic Publishers, Boston-Dordrecht-London.zbMATHGoogle Scholar
  5. [5]
    W.B. Gong, Y.C. Ho (1987) Smoothed (conditional) perturbation analysis of discrete event dynamic systems. IEEE — Transactions on Automatic Control 32, pp. 858–866.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    A.M. Gupal, L.T. Bazhenov. (1972): A Stochastic Analog of the Methods of Conjugate Gradients. Kibernetika, 1, 124–126, (in Russian).Google Scholar
  7. [7]
    Ho Y.C. and X.R. Cao (1991): Perturbation Analysis of Discrete Event Dynamic Systems. Kluwer, Boston.zbMATHCrossRefGoogle Scholar
  8. [8]
    M.B.M. de Koster (1989) Capacity oriented analysis and design of production systems. Springer-Verlag, Berlin (LNEMS 323).zbMATHCrossRefGoogle Scholar
  9. [9]
    H.J. Kushner, Hai-Huang. (1981): Asymptotic Properties of Stochastic Approximation with Constant Coefficients. SI AM Journal on Control and Optimization, 19, 87–105.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    H.J. Kushner, G.G. Jin (1997): Stochastic Approximation Algorithms and Applications. Appl. Math. 35, Springer.zbMATHGoogle Scholar
  11. [11]
    Yin G. and Q. Zhang. (Eds) (1996): Mathematics of Stochastic Manufacturing Systems. Lectures in Applied Mathematics, Vol. 33.Google Scholar
  12. [12]
    D. Mitra (1988) Stochastic fluid models, in: P.-J. Courtois, G. Latouche (eds.) Performance ′87. Elsevier, Amsterdam, pp. 39–51.Google Scholar
  13. [13]
    Pflug G. Ch. (1996): Optimization of Stochastic Models, The Interface Between Simulation and Optimization. Kluwer Academic Publishers, Boston-Dordrecht-London.zbMATHCrossRefGoogle Scholar
  14. [14]
    Rubinstein, R. and A. Shapiro (1993): Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization via the Score Function Method. Wiley, Chichester.Google Scholar
  15. [15]
    Saridis, G.M. (1970): Learning applied to successive approximation algorithms. IEEE Trans. Syst. Sei. Cybern., 1970, SSC-6, Apr., pp. 97–103.CrossRefGoogle Scholar
  16. [16]
    Bashyam, S. and M.S. Fu (1994): Application of Perturbation Analysis to a Class of Periodic Review (s,S) Inventory Systems. Naval Research Logistics. Vol. 41, pp.47–80.MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    Syski, W. (1988): A Method of Stochastic Subgradients with Complete Feedback Stepsize Rule for Convex Stochastic Approximation Problems. J. of Optim. Theory and Applic. Vol. 39, No. 2, pp. 487–505.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Uryasev, S.P. (1988): Adaptive Stochastic Quasi-Gradient Methods. In “Numerical Techniques for Stochastic Optimization”. Eds. Yu. Ermoliev and R. J-B Wets. Springer Series in Computational Mathematics 10, (1988), 373–384.CrossRefGoogle Scholar
  19. [19]
    Uryasev, S. (1991): New Variable-Metric Algorithms for Nondifferential Optimization Problems. J. of Optim. Theory and Applic. Vol. 71, No. 2, 1991, 359–388.MathSciNetCrossRefGoogle Scholar
  20. [20]
    Uryasev, S. (1992): A Stochastic Quasi-Gradient Algorithm with Variable Metric, Annals of Operations Research. 39, 251–267.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Uryasev, S. (1994): Derivatives of Probability Functions and Integrals over Sets Given by Inequalities. J. Computational and Applied Mathematics. Vol. 56, 197–223.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Uryasev, S. (1995): Derivatives of Probability Functions and Some Applications. Annals of Operations Research, Vol. 56, 287–311.MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    Uryasev, S. (1997): Analytic Perturbation Analysis for DEDS with Discontinuous Sample-path Functions. Stochastic Models. Vol. 13, No. 3.Google Scholar
  24. [24]
    J. Wijngaard (1979) The effect of interstage buffer storage on the output of two unreliable production units in series with different production rates. AIIE -Transactions 11, pp. 42–47.CrossRefGoogle Scholar
  25. [25]
    S. Yeralan, E.J. Muth (1987) A general model of a production line with intermediate buffer and station breakdown. AIIE — Transactions 19, pp. 130–139.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Yu. Ermoliev
    • 1
  • S. Uryasev
    • 2
  • J. Wessels
    • 3
  1. 1.International Institute for Applied Systems AnalysisLaxenburgAustria
  2. 2.University of FloridaGainesvilleUSA
  3. 3.Technical University EindhovenEindhovenThe Netherlands

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