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.
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References
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.
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.
J.A. Buzacott, ‘Optimal’ operating rules for automated manufacturing systems, IEEE Trans. Automatic Control, AC-27(1982)80.
J.A. Buzacott and J.G. Shanthikumar, Models for understanding flexible manufacturing systems, AIIE Trans. 12(1980)339.
D. Dubois, A mathematical model of a flexible manufacturing system with limited in-process inventory. Eur. J. Oper. Res. 14(1983)66.
W.J. Gordon and G.F. Newell, Closed queueing networks with exponential servers, Oper. Res. 15(1967)252.
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.
J. Hatvany, Ed.,World Survey on CAM (Butterworths, Kent, U.K., 1983).
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.
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.
G.K. Hutchinson, Flexible manufacturing systems in the United States. Management Research Center, University of Wisconsin-Milwaukee, Milwaukee, 1979.
J. Keilson,Markov Chain Models: Rarity and Exponentiality (Springer-Verlag, New York, 1979).
F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).
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.
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.
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.
M. Reiser, Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks, Performance Evaluation 1(1981)7.
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.
J.G. Shanthikumar and R.G. Sargent, A unifying view of hybrid simulation/analytic models and modeling, Oper. Res. 31(1983)1030.
J.J. Solberg, A mathematical model of computerized manufacturing systems,Proc. 4th Int. Conf. on Production Research, Tokyo, Japan, 1977.
K.E. Stecke, Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems, Management Sci. 29(1983)273.
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.
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.
D. Towsley, Queueing network models with state-dependent routing. J. Ass. Comp. Mach. 27(1980)323.
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.
W. Whitt, Deciding which queue to join, Bell Laboratories, Holmdel, NJ, 1983.
W. Whitt, Open and closed models for networks of queues, Bell Syst. Tech. J. 63(1984)1911.
D.D. Yao, Queueing models of flexible manufacturing systems, Ph.D. Dissertation, Dept. of Industrial Engineering, University of Toronto, Toronto, Canada, 1983.
D.D. Yao and J.A. Buzacott, Modeling the performance of flexible manufacturing systems, Int. J. Prod. Res. (1984), to appear.
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.
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Yao, D.D., Buzacott, J.A. Modeling a class of state-dependent routing in flexible manufacturing systems. Ann Oper Res 3, 153–167 (1985). https://doi.org/10.1007/BF02024744
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DOI: https://doi.org/10.1007/BF02024744