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Performance modeling of a manufacturing cell with a single material transporter: An approximation

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Abstract

We consider a flexible manufacturing system with a number of workstations, a single material transporter, and a common storage space of finite capacity. The material handling delay times are explicitly considered in the model and assumed to follow a two-stage Coxian distribution. The material processing times on a workstation also have a two-stage Coxian distribution. The routing of parts within the system follows a Markov chain. An approximate performance model is developed and the results are compared with the exact or simulation results. We also investigate how this performance model compares to a simulation with deterministic routing and processing times. Finally, we study the effect, on the performance measures, of ignoring the material transporter or of modeling the transporter as a central server with aggregation of routing information.

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References

  • Altiok, T., and Perros, M., “Open Networks of Queues with Blockings: Tandem Configuration”, IEEE Transactions On Software Engineering, Vol SE-12, No. 3, (1986).

  • Altiok,T., and Stidham,S., “The Allocation of Interstage Buffer Storage Capacities in Production Lines”, IIE Transactions, Vol. 15, pp 292–299 (1983).

    Google Scholar 

  • Bitran, G.R., and Tirapati, D., “Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference”, Management Science, Vol. 34, No. 1, (1988).

  • Buzacott,J.A., and Shanthikumar, J.G., “Models for Understanding Flexible Manufacturing Systems”, IIE Transactions, Vol. 12, pp 339–350 (1980)

    Google Scholar 

  • Buzacott, J.A., and Shanthikumar, J.G., “Approximate Queueing Models of Dynamic Job Shops”, Management Science, Vol. 31, No. 7, (1985).

  • Buzacott, J.A., and Yao, D., “On Queueing Network Models of Flexible Manufacturing Systems”, technical report, Department of Management Science, University of Waterloo, Ontario, Canada (1985).

    Google Scholar 

  • Gordon, W.J., and Newell, G.F. “Closed Queueing Networks with Exponential Services”, Operations Research, Vol. 15, pp 252–267, (1967).

    Google Scholar 

  • Hartley, J., FMS at Work, IFS Publications, Bedford, U.K. (1984).

    Google Scholar 

  • Jackson, J.R., “Jobshop-Like Queueing Systems”, Management Science, Vol. 10, pp 131–142, (1963).

    Google Scholar 

  • Jafari, M.A., “Performance Modeling of a Flexible Manufacturing Cell with Two Workstations and A Single Material Handling Device”, Proceedings of IEEE International Conference on Robotics and Automation, Raleigh, NC (1987).

  • Kelly, F.P., Reversibility and Stochastic Networks, Wiley, New York (1979).

    Google Scholar 

  • Kuchn, P.J., “Approximate Analysis of General Networks by Decomposition”, IEEE Transactions on Communications, COM-27, 1 (1979).

    Google Scholar 

  • Polleck, S., Birge, J., and Alden, J., “Approximate Analysis of Open Tandem Queues with Blocking: Exponential and General Service Times”, technical report No. 85-30, Dept. of IE&OR, University of Michigan, Ann Arbor, MI.

  • Ranky, P.G., “A Program Prospects for the Simulation, Design and Implementation of Flexible Assembly and Inspection Cells”, in Proceedings of the 2nd ORSA/TIMS Conference on FMS: Operations Research Models and Applications Ann Arbor, MI. K.E., Stecke and R., Suri (Eds.), Elsevier Science Publishers, Amsterdam, pp 157–168 (1986).

    Google Scholar 

  • Ranky, P.G., Computer Integrated Manufacturing, Prentice Hall, Englewood, NJ (1986).

    Google Scholar 

  • Reiser, M., and Lavenberg, S.S., “Mean Value Analysis of Closed Multichain Queueing Networks”, Journal of Association for Computing Machinery, Vol. 27, No. 2, (1980).

  • Schweitzer, P., “Maximum Throughput in Finite-Capacity Open Queueing Networks with Product-Form Solutions”, Management Science, Vol. 24, pp 217–223 (1977).

    Article  Google Scholar 

  • Schweitzer, P., “Approximate Analysis of Multiclass Closed Networks of Queues”, presented at the International Conference on Stochastic Control and Optimization, Free University, Amsterdam (1979).

  • Seidmann, A., Shalev-Oren, S., and Schweitzer, P.J., “An Analytical Review of Several Computerized Closed Queueing Network Models of FMS”, in Proceedings of the 2nd ORSA/TIMS Conference on FMS: Operations Research Models and Applications, Ann Arbor, MI, K.E., Stecke and R., Suri (Eds.), Elsevier Science Publishers, Amsterdam, pp 369–380 (1986).

    Google Scholar 

  • Shalev-Oren, S., Seidmann, A., and Schweitzer, P.J., “Analysis of Flexible Manufacturing Systems with Priority Scheduling: PMVA”, Annals of Operations Research, Vol. 3, pp 115–139 (1985).

    Google Scholar 

  • Solberg, J.J., “A Mathematical Model of Computerized Manufacturing Systems”, Proceedings of the 4th International Conference on Production Research, Tokyo, Japan (1977).

  • Suri, R., and Diehl, G.W., “A Variable Buffer-size Model and its Use in Analyzing Closed Queueing Networks with Blocking”, technical report, Division of Applied Sciences Harvard University, Cambridge, MA (1985).

    Google Scholar 

  • Takahashi, Y., Miyahara, H., and Hasegawa, T., “An Approximation Method for Open Restricted Queueing Networks”, Operations Research, Vol. 28, (1980).

  • Whitt, W., “The Queueing Network Analyzer”, Bell System Technical Journal, Vol. 62, No. 9 (1983).

  • Yao,D.D., and Buzacott,J.A., “Modeling the Performance of a Flexible Manufacturing System”, International Journal of Production Research, Vol. 23, No. 5, pp 945–959 (1985a).

    Google Scholar 

  • Yao,D.D., and Buzacott,J.A., “Queueing Models for a Flexible Machining Station Part II: The Method of Coxian Phases”, European Journal of Operational Research, Vol. 19, pp 241–252 (1985b).

    Google Scholar 

  • Yao,D.D., and Buzacott,J.A., “Modelling a Class of State-Dependent Routing in Flexible Manufacturing Systems”, Annals of Operations Research Vol. 3, pp 153–167 (1985c).

    Google Scholar 

  • Yao,D.D., and Buzacott,J.A., “The Exponentialization Approach to Flexible Manufacturing System Models with General Processing Times”, European Journal of Operational Research, Vol. 24, No. 3, pp 410–416 (1986a).

    Google Scholar 

  • Yao,D.D., and Buzacott,J.A., “Models of Flexible Manufacturing Systems with Limited Local Buffers”, International Journal of Production Research, Vol. 24, No. 1, pp 107–118 (1986b).

    Google Scholar 

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Jafari, M.A. Performance modeling of a manufacturing cell with a single material transporter: An approximation. Int J Flex Manuf Syst 2, 63–86 (1989). https://doi.org/10.1007/BF00227798

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