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Mathematical programming models for joint simulation–optimization applied to closed queueing networks

Annals of Operations Research volume 231, pages 105–127 (2015)Cite this article

Abstract

The optimization of stochastic Discrete Event Systems (DESs) is a critical and difficult task. The search for the optimal system configuration (optimization problem) requires the assessment of the system performance (simulation problem), resulting in a simulation–optimization problem. In the past ten years, a noticeable research effort has been devoted to this area. Recently, mathematical programming has been proposed to integrate simulation and optimization for multi-stage open queueing networks. This paper proposes the application of this approach to closed queueing networks. In particular, the optimal pallet allocation problem is tackled through linear mathematical programming models for simulation–optimization.

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References

  • Alfieri, A., & Matta, A. (2012). Mathematical programming formulations for approximate simulation of multistage production systems. European Journal of Operational Research. doi:10.1016/j.ejor.2011.12.044.

    Google Scholar 

  • Birge, J., & Louveaux, F. (1997). Introduction to stochastic programming. Springer series in operations research and financial engineering series. Berlin: Springer.

    Google Scholar 

  • Boesel, J. N., Barry, L., & Kim, S. (2003). Using ranking and selection to “clean up” after simulation optimization. Operations Research, 51, 814–825. doi:10.1287/opre.51.5.814.16751.

    Article  Google Scholar 

  • Bouhchouch, A., Frein, Y., & Dallery, Y. (1993). Analysis of a closed-loop manufacturing system with finite buffers. Applied Stochastic Models and Data Analysis, 9(2), 111–125. doi:10.1002/asm.3150090205

    Article  Google Scholar 

  • Brodsky, A., Pedersen, J., & Wagner, A. (2003). On the complexity of buffer allocation in message passing systems. Journal of Parallel and Distributed Computing, 65(6), 692–713.

    Article  Google Scholar 

  • Chan, W., & Schruben, L. (2008a). Optimization models of discrete–event system dynamics. Operations Research, 56(5), 1218–1237.

    Article  Google Scholar 

  • Chan, W. K., & Schruben, L. W. (2008b). Mathematical programming models of closed tandem queueing networks. ACM Transactions on Modeling and Computer Simulation, 19(1). doi:10.1016/j.jpdc.2004.10.009.

  • Chick, S., Schmeiser, B., Sánchez, P. J., Ferrin, D., Morrice, D. J., & Jin, J. (2003). Simulation-based retrospective optimization of stochastic systems: a family of algorithms. In Proceedings of the 2003 winter: Vol. 1. Simulation conference, 2003 (pp. 543–547).

    Google Scholar 

  • Dallery, Y., & Frein, Y. (1989). A decomposition method for approximate analysis of closed queueing networks with blocking. In Queueing networks with blocking (pp. 193–216).

    Google Scholar 

  • Dallery, Y., & Liberopoulos, G. (2000). Extended kanban control system: combining kanban and base stock. IIE Transactions, 32, 369–386.

    Google Scholar 

  • Dolgui, A., Eremeev, A., & Sygaev, V. (2010). A problem of buffer allocation in production lines: complexity analysis and algorithms. In 3rd international conference on metaheuristics and nature inspired computing, Djerba, Tunisia.

    Google Scholar 

  • Fu, M., Glover, F., & April, J. (2005). In Simulation optimization: a review, new developments, and applications (pp. 83–95).

    Google Scholar 

  • Garey, M., & Johnson, D. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: Freeman

    Google Scholar 

  • Gershwin, S. B., & Werner, L. (2007). An approximate analytical method for evaluating the performance of closed-loop flow systems with unreliable machines and finite buffers. International Journal of Production Research, 45, 3085–3111.

    Article  Google Scholar 

  • Healy, K., & Schruben, L. W. (1991). Retrospective simulation response optimization. In Proceedings of the 23rd conference on winter simulation, WSC ’91 (pp. 901–906). Washington: IEEE Computer Society.

    Google Scholar 

  • Higle, J., & Sen, S. (1996). Stochastic decomposition: a statistical method for large scale stochastic linear programming. Nonconvex optimization and its applications. Norwell: Kluwer Academic.

    Book  Google Scholar 

  • Hong, L. J., & Nelson, B. L. (2006). Discrete optimization via simulation using compass. Operations Research, 54(1), 115–129.

    Article  Google Scholar 

  • Kleijnen, J. P. C. (2008). Design and analysis of simulation experiments. International series in operations research & management science: Vol. 111. Berlin: Springer.

    Google Scholar 

  • Kushner, H., & Yin, G. (1997). Stochastic approximation algorithms and applications. Berlin: Springer.

    Book  Google Scholar 

  • Law, A. (2007). Simulation modeling and analysis (4th ed.). New York: McGraw-Hill.

    Google Scholar 

  • Maggio, N., Matta, A., Gershwin, S., & Tolio, T. (2009a). A decomposition approximation for three-machine closed-loop production systems with unreliable machines, finite buffers and a fixed populatio. IIE Transactions, 41(6), 562–574.

    Article  Google Scholar 

  • Maggio, N., Matta, A., Gershwin, S. B., & Tolio, T. (2009b). A decomposition approximation for three-machine closed-loop production systems with unreliable machines, finite buffers and a fixed population. IIE Transactions, 41(6), 562–574.

    Article  Google Scholar 

  • Matta, A. (2008). Simulation optimization with mathematical programming representation of discrete event systems. In S. J. Mason, R. R. Hill, L. Monch, O. Rose, T. Jefferson, & J. W. Fowler (Eds.), Proceedings of the 2008 winter simulation conference Piscataway (pp. 1393–1400). New Jersey: Institute of Electrical and Electronics Engineers, Inc.

    Chapter  Google Scholar 

  • Matta, A., & Chefson, R. (2005). Formal properties of closed flow lines with limited buffer capacities and random processing times. In Proceedings of the European simulation and modelling conference, Porto, Portugal (pp. 190–194).

    Google Scholar 

  • Ming-Guang, H., Pao-Long, C., & Ying-Chyi, C. (2002). Buffer allocation in flow-shop-type production systems with general arrival and service patterns. Computers & Operations Research, 29(2), 103–121.

    Article  Google Scholar 

  • Montgomery, D. (2005). Progettazione e analisi degli esperimenti. Istruzione scientifica. New York: McGraw-Hill.

    Google Scholar 

  • Myers, R., Montgomery, D., & Anderson-Cook, C. (2009). Response surface methodology: process and product optimization using designed experiments. Wiley series in probability and statistics. New York: Wiley.

    Google Scholar 

  • Pedrielli, G. (2013). Discrete event systems simulation–optimization: time buffer framework. PhD thesis, Mechanical Engineering Department, Politecnico di Milano, Italy.

  • Robinson, S. (1996). Analysis of sample–path optimization. Mathematics of Operations Research, 21, 513–528.

    Article  Google Scholar 

  • Schruben, L. W. (2000). Mathematical programming models of discrete event system dynamics. In J. A. Joines, R. R. Bartona, K. Kang, & P. A. Fishwick (Eds.), Proceedings of the 2000 winter simulation conference Piscataway (pp. 381–385). New Jersey: Institute of Electrical and Electronics Engineers, Inc.

    Chapter  Google Scholar 

  • Spall, J. C. (2003). Introduction to stochastic search and optimization. New York: Wiley.

    Book  Google Scholar 

  • Zhang, Z. (2006). Analysis and design of manufacturing systems with multiple-loop structures. PhD thesis, Mechanical Engineering Department, Massachussetts Institute of Technology, Berkeley.

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Authors and Affiliations

  1. Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Arianna Alfieri

  2. Politecnico di Milano, via Giuseppe La Masa 1, 20156, Milano, Italy

    Andrea Matta & Giulia Pedrielli

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  1. Arianna Alfieri
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  2. Andrea Matta
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  3. Giulia Pedrielli
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Correspondence to Giulia Pedrielli.

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Alfieri, A., Matta, A. & Pedrielli, G. Mathematical programming models for joint simulation–optimization applied to closed queueing networks. Ann Oper Res 231, 105–127 (2015). https://doi.org/10.1007/s10479-013-1480-7

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  • DOI: https://doi.org/10.1007/s10479-013-1480-7

Keywords

  • Simulation–optimization
  • Mathematical programming
  • Loop manufacturing systems
  • Discrete event systems