Abstract
In this paper we present algorithms for the solution of two server (machine) allocation problems that occur in manufacturing networks. The manufacturing network is modelled as an open network of queues with general interarrival time and service time distributions. The queueing network is analyzed by using the parametric decomposition method: a two-moment approximation scheme. The server allocation problems are solved by means of a marginal analysis scheme. Numerical results on two manufacturing networks are presented.
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References
Bitran, G. R. and Tirupati, D. (1988a) Multiproduct queueing networks with deterministic routing: decomposition approach and the notion of interference.Management Science,34, 75–100.
Bitran, G. R. and Tirupati, D. (1988b) Capacity planning in manufacturing networks with discrete options.Working paper 87/88-04-03, University of Texas at Austin, USA.
Bitran, G. R. and Tirupati, D. (1989) Trade-off curves, targeting, and balancing in manufacturing networks.Operations Research,37, 547–64.
Boxma, O. J., Rinnooy Kan, A. H. G. and van Vliet, M. (1990) Machine allocation problems in manufacturing networks.European Journal of Operational Research,45, 47–54.
Buzacott, J. A. and Yao, D. D. (1986) Flexible manufacturing systems: a review of analytical models.Management Science,32, 890–907.
Dallery, Y. and Frein, Y. (1986) An efficient method to determine the optimal configuration of a flexible manufacturing system, inProceedings of the Second ORSA/TIMS Conference on Flexible Manufacturing Systems: Operations Research Models and Applications, Stecke, K. and Suri, R. (eds.), North-Holland, Amsterdam.
Dyer, M. E. and Proll, L. G. (1977) On the validity of marginal analysis for allocating servers in M/M/c queues.Management Science,23, 1019–22.
Fox, B. (1966) Discrete optimization via marginal analysis.Management Science,13, 210–6.
Gerla, M. and Kleinrock, L. (1977) On the topological design of distributed computer networks.IEEE Transactions on Communications,COM-25 48–60.
Kleinrock, L. (1976)Queueing Systems Volume II: Computer Applications. John Wiley, New York, USA.
Kuehn, P. J. (1976) Analysis of complex queueing networks by decomposition inProceedings of the 8th ITC, Melbourne, Australia, Section 236, 1–236.8.
Kuehn, P. J. (1979) Approximate analysis of general networks by decomposition.IEEE Transactions on Communications,COM-27, 113.
Little, J. D. C. (1961) A proof for the queueing formula:L=λW.Operations Research,9, 383–9.
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1987)Numerical Recipes The Art of Scientific Computing. Cambridge University Press, Cambridge, UK.
Reiser, M. and Kobayashi, H. (1974) Accuracy of diffusion approximation for some queueing systems.IBM Journal of Research and Development,18, 110–24.
Segal, M. and Whitt, W. (1989) A queueing network analyzer for manufacturing inProceedings of the 12th ITC, Benatti, M. (ed.), North-Holland, Amsterdam.
Sevcik, K. C., Levy, A. I., Tripathi, S. K. and Zahorjan, J. L., (1977) Improving approximations of aggregated queueing network systems inProceedings Computer Performance, Modelling, Measurement, and Evaluation, Beilner, H. and Gelenbe, E. (eds), North-Holland, Amsterdam.
Shanthikumar, J. G. and Buzacott, J. A. (1981) Open Queueing Network Models of Dynamic Job Shops.International Journal of Production Research,19, 255–66.
Shanthikumar, J. G. and Yao, D. D. (1987) Optimal server allocation in a system of multi-server stations,Management Science,33, 1173–80.
Shanthikumar, J. G. and Yao, D. D. (1988) On server allocation in multiple center manufacturing systems.Operations Research,36, 333–42.
Tijms, H. C. (1986)Stochastic Modelling and Analysis, John Wiley, New York, USA, pp. 365–76.
Vinod, B. and Solberg, J. J. (1985) The optimal design of flexible manufacturing systems.International Journal of Production Research.23, 1141–51.
Weber, R. W. (1980) On the marginal benefit of adding servers toGI/G/m queues.Management Science,26, 946–51.
Whitt, W. (1983) The queueing network analyzer.The Bell System Technical Journal,62, 2779–815.
Whitt, W. (1985) Approximations for theGI/G/m queue, working paper AT&T Bell Labs., USA.
Whitt, W. (1987) A light traffic approximation for single-class departure processes from multi-class queues.Working paper, AT&T Bell Labs, USA.
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van Vliet, M., Rinnooy Kan, A.H.G. Machine allocation algorithms for job shop manufacturing. J Intell Manuf 2, 83–94 (1991). https://doi.org/10.1007/BF01471221
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DOI: https://doi.org/10.1007/BF01471221