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Annals of Operations Research

, Volume 3, Issue 3, pp 153–167 | Cite as

Modeling a class of state-dependent routing in flexible manufacturing systems

  • David D. Yao
  • J. A. Buzacott
Analytical Performance Models

Abstract

We develop a closed queueing network model for flexible manufacturing systems (FMSs), where parts routing follows a probabilistic shortest-queue (PSQ) scheme, i.e. parts are routed to the shortest queue (or the most empty station) with the highest probability. We allow limited local buffer at each work station. We prove that with the PSQ routing, the Markovian queue-length process satisfies time reversibility and has a product-form equilibrium distribution. An algorithm is developed to compute the solutions to the model. The model can be used as a performance evaluation tool to study FMSs.

Keywords and phrases

Closed queueing network reversible Markov process state-dependent routing flexible manufacturing 

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References

  1. [1]
    R. Akella, Y. Choong and S.B. Gershwin, Performance of hierarchical production scheduling policy. Report LIDS-FR-1357, Laboratory of Information and Decision Systems, MIT, Cambridge, MA, 1984.Google Scholar
  2. [2]
    F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed and mixed networks of queues with different classes of customers, J. Ass. Comp. Mach. 22(1975)248.Google Scholar
  3. [3]
    J.A. Buzacott, ‘Optimal’ operating rules for automated manufacturing systems, IEEE Trans. Automatic Control, AC-27(1982)80.Google Scholar
  4. [4]
    J.A. Buzacott and J.G. Shanthikumar, Models for understanding flexible manufacturing systems, AIIE Trans. 12(1980)339.Google Scholar
  5. [5]
    D. Dubois, A mathematical model of a flexible manufacturing system with limited in-process inventory. Eur. J. Oper. Res. 14(1983)66.Google Scholar
  6. [6]
    W.J. Gordon and G.F. Newell, Closed queueing networks with exponential servers, Oper. Res. 15(1967)252.Google Scholar
  7. [7]
    E.H. Hahne, Dynamic routing in an unreliable manufacturing network with limited storage. Report LIDS-TH-1063, Laboratory for Information and Decision Systems, MIT, Cambridge, MA, 1980.Google Scholar
  8. [8]
    J. Hatvany, Ed.,World Survey on CAM (Butterworths, Kent, U.K., 1983).Google Scholar
  9. [9]
    R.R. Hildebrant, Scheduling flexible machining systems when machines are prone to failure, Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, MIT, Cambridge, MA, 1980.Google Scholar
  10. [10]
    Y.C. Ho, R. Suri, X.R. Cao, G.W. Diehl and J.W. Dille, Optimization of large multi-class (NON-product-form) queueing networks using perturbation analysis. Division of Applied Sciences, Harvard University, Cambridge, MA, 1983.Google Scholar
  11. [11]
    G.K. Hutchinson, Flexible manufacturing systems in the United States. Management Research Center, University of Wisconsin-Milwaukee, Milwaukee, 1979.Google Scholar
  12. [12]
    J. Keilson,Markov Chain Models: Rarity and Exponentiality (Springer-Verlag, New York, 1979).Google Scholar
  13. [13]
    F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).Google Scholar
  14. [14]
    J.G. Kimemia, Hierarchical control of production in flexible manufacturing systems. Ph.D. Dissertation, Report LIDS-TH-1215, Laboratory for Information and Decision Systems, MIT, Cambridge, MA, 1982.Google Scholar
  15. [15]
    J.G. Kimemia and S.B. Gershwin, Multicommodity network flow optimization in flexible manufacturing systems. Report ESL-FR-834-2, Electronic Systems Laboratory, MIT, Cambridge, MA, 1980.Google Scholar
  16. [16]
    G.J. Olsder and R. Suri, Time-optimal control of parts-routing in a manufacturing system with failure-prone machines,Proc. 19th IEEE Conf. on Decision and Control, 1980.Google Scholar
  17. [17]
    M. Reiser, Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks, Performance Evaluation 1(1981)7.Google Scholar
  18. [18]
    A. Seidmann and P.J. Schweitzer, Real-time on-line control of an FMS cell. Working Paper Series No. QM8217, Graduate School of Management, University of Rochester, Rochester, New York, 1982.Google Scholar
  19. [19]
    J.G. Shanthikumar and R.G. Sargent, A unifying view of hybrid simulation/analytic models and modeling, Oper. Res. 31(1983)1030.Google Scholar
  20. [20]
    J.J. Solberg, A mathematical model of computerized manufacturing systems,Proc. 4th Int. Conf. on Production Research, Tokyo, Japan, 1977.Google Scholar
  21. [21]
    K.E. Stecke, Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems, Management Sci. 29(1983)273.Google Scholar
  22. [22]
    K.E. Stecke and J.J. Solberg, The CMS loading problem. The optimal planning of computerized manufacturing systems. Report No. 20, School of Industrial Engineering, Purdue University, West Lafayette, Indiana, 1981.Google Scholar
  23. [23]
    R. Suri and G.W. Diehl, A variable buffer-size model and its use in analyzing closed queueing networks with blocking. Division of Applied Sciences, Harvard University, Cambridge, MA, 1983.Google Scholar
  24. [24]
    D. Towsley, Queueing network models with state-dependent routing. J. Ass. Comp. Mach. 27(1980)323.Google Scholar
  25. [25]
    J.N. Tsitsiklis, Optimal dynamic routing in an unreliable manufacturing system. Report LIDS-TH-1069, Laboratory for Information and Decision Systems, MIT, Cambridge, MA, 1981.Google Scholar
  26. [26]
    W. Whitt, Deciding which queue to join, Bell Laboratories, Holmdel, NJ, 1983.Google Scholar
  27. [27]
    W. Whitt, Open and closed models for networks of queues, Bell Syst. Tech. J. 63(1984)1911.Google Scholar
  28. [28]
    D.D. Yao, Queueing models of flexible manufacturing systems, Ph.D. Dissertation, Dept. of Industrial Engineering, University of Toronto, Toronto, Canada, 1983.Google Scholar
  29. [29]
    D.D. Yao and J.A. Buzacott, Modeling the performance of flexible manufacturing systems, Int. J. Prod. Res. (1984), to appear.Google Scholar
  30. [30]
    D.D. Yao and J.A. Buzacott, Queueing models for a flexible machining station, Part I: Diffusion approximations; Part II: The method of coxian phases, Eur. J. Oper. Res. 19(1984) 233; 241, resp.Google Scholar

Copyright information

© J.C. Baltzer A.G., Scientific Publishing Company 1985

Authors and Affiliations

  • David D. Yao
    • 1
  • J. A. Buzacott
    • 2
  1. 1.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA
  2. 2.Department of Management SciencesUniversity of WaterlooWaterlooCanada

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