IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v219y2012i3p773-783.html
   My bibliography  Save this article

Mathematical programming formulations for approximate simulation of multistage production systems

Author

Listed:
  • Alfieri, Arianna
  • Matta, Andrea

Abstract

Mathematical programming representation has been recently used to describe the behavior of discrete event systems as well as their formal properties. This new way of representing discrete event systems paves the way to the creation of simpler mathematical programming models that reduce the complexity of the system analysis. The paper proposes an approximate representation for a class of production systems characterized by several stages, limited buffer capacities and stochastic production times. The approximation exploits the concept of a time buffer, modeled as a constraint that put into a temporal relationship the completion times of two customers in a sample path. The main advantage of the proposed formulation is that it preserves its linearity even when used for optimization and, for such a reason, it can be adopted in simulation–optimization problems to reduce the initial solution space. The approximate formulation is applied to relevant problems such as buffer capacity allocation in manufacturing systems and control parameters setting in pull systems.

Suggested Citation

  • Alfieri, Arianna & Matta, Andrea, 2012. "Mathematical programming formulations for approximate simulation of multistage production systems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 773-783.
    • Handle: RePEc:eee:ejores:v:219:y:2012:i:3:p:773-783
    DOI: 10.1016/j.ejor.2011.12.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712000306
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2011.12.044?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jensen, Paul A. & Pakath, Ramakrishnan & Wilson, James R., 1991. "Optimal buffer inventories for multistage production systems with failures," European Journal of Operational Research, Elsevier, vol. 51(3), pages 313-326, April.
    2. L. Jeff Hong & Barry L. Nelson, 2006. "Discrete Optimization via Simulation Using COMPASS," Operations Research, INFORMS, vol. 54(1), pages 115-129, February.
    3. Stanley Gershwin & James Schor, 2000. "Efficient algorithms for buffer space allocation," Annals of Operations Research, Springer, vol. 93(1), pages 117-144, January.
    4. Jean-Luc Deleersnyder & Thom J. Hodgson & Henri Muller-Malek & Peter J. O'Grady, 1989. "Kanban Controlled Pull Systems: An Analytic Approach," Management Science, INFORMS, vol. 35(9), pages 1079-1091, September.
    5. N. Maggio & A. Matta & S. Gershwin & T. Tolio, 2009. "A decomposition approximation for three-machine closed-loop production systems with unreliable machines, finite buffers and a fixed population," IISE Transactions, Taylor & Francis Journals, vol. 41(6), pages 562-574.
    6. Lutz, Christian M. & Roscoe Davis, K. & Sun, Minghe, 1998. "Determining buffer location and size in production lines using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 301-316, April.
    7. Wai Kin (Victor) Chan & Lee Schruben, 2008. "Optimization Models of Discrete-Event System Dynamics," Operations Research, INFORMS, vol. 56(5), pages 1218-1237, October.
    8. Stephen M. Robinson, 1996. "Analysis of Sample-Path Optimization," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 513-528, August.
    9. Jack P.C. Kleijnen, 2015. "Design and Analysis of Simulation Experiments," International Series in Operations Research and Management Science, Springer, edition 2, number 978-3-319-18087-8, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wai Kin Victor Chan, 2016. "Linear Programming Formulation of Idle Times for Single-Server Discrete-Event Simulation Models," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-17, October.
    2. Kolb, Oliver & Göttlich, Simone, 2015. "A continuous buffer allocation model using stochastic processes," European Journal of Operational Research, Elsevier, vol. 242(3), pages 865-874.
    3. Arianna Alfieri & Andrea Matta & Giulia Pedrielli, 2015. "Mathematical programming models for joint simulation–optimization applied to closed queueing networks," Annals of Operations Research, Springer, vol. 231(1), pages 105-127, August.
    4. Alfieri, Arianna & Matta, Andrea, 2013. "Mathematical programming time-based decomposition algorithm for discrete event simulation," European Journal of Operational Research, Elsevier, vol. 231(3), pages 557-566.
    5. Khayyati, Siamak & Tan, Barış, 2020. "Data-driven control of a production system by using marking-dependent threshold policy," International Journal of Production Economics, Elsevier, vol. 226(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arianna Alfieri & Andrea Matta & Giulia Pedrielli, 2015. "Mathematical programming models for joint simulation–optimization applied to closed queueing networks," Annals of Operations Research, Springer, vol. 231(1), pages 105-127, August.
    2. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
    3. Qi Fan & Jiaqiao Hu, 2018. "Surrogate-Based Promising Area Search for Lipschitz Continuous Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 677-693, November.
    4. George Liberopoulos, 2020. "Comparison of optimal buffer allocation in flow lines under installation buffer, echelon buffer, and CONWIP policies," Flexible Services and Manufacturing Journal, Springer, vol. 32(2), pages 297-365, June.
    5. Hachicha, Wafik & Ammeri, Ahmed & Masmoudi, Faouzi & Chachoub, Habib, 2010. "A comprehensive literature classification of simulation optimisation methods," MPRA Paper 27652, University Library of Munich, Germany.
    6. Elisa Gebennini & Andrea Grassi & Cesare Fantuzzi & Stanley Gershwin & Irvin Schick, 2013. "Discrete time model for two-machine one-buffer transfer lines with restart policy," Annals of Operations Research, Springer, vol. 209(1), pages 41-65, October.
    7. Liujia Hu & Sigrún Andradóttir, 2019. "An Asymptotically Optimal Set Approach for Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 21-39, February.
    8. Elisa Gebennini & Andrea Grassi & Cesare Fantuzzi, 2015. "The two-machine one-buffer continuous time model with restart policy," Annals of Operations Research, Springer, vol. 231(1), pages 33-64, August.
    9. Yongchao Liu & Huifu Xu & Jane J. Ye, 2011. "Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 670-694, November.
    10. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    11. Tian, Wei & Song, Jitian & Li, Zhanyong & de Wilde, Pieter, 2014. "Bootstrap techniques for sensitivity analysis and model selection in building thermal performance analysis," Applied Energy, Elsevier, vol. 135(C), pages 320-328.
    12. Wilhelm, W. E. & Som, Pradip, 1998. "Analysis of a single-stage, single-product, stochastic, MRP-controlled assembly system," European Journal of Operational Research, Elsevier, vol. 108(1), pages 74-93, July.
    13. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    14. S. Göttlich & S. Kühn & J. A. Schwarz & R. Stolletz, 2016. "Approximations of time-dependent unreliable flow lines with finite buffers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 295-323, June.
    15. Kim, Ilhyung & Tang, Christopher S., 1997. "Lead time and response time in a pull production control system," European Journal of Operational Research, Elsevier, vol. 101(3), pages 474-485, September.
    16. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    17. Dellino, Gabriella & Kleijnen, Jack P.C. & Meloni, Carlo, 2010. "Robust optimization in simulation: Taguchi and Response Surface Methodology," International Journal of Production Economics, Elsevier, vol. 125(1), pages 52-59, May.
    18. Angun, M.E. & Kleijnen, Jack P.C., 2012. "An asymptotic test of optimality conditions in multiresponse simulation optimization," Other publications TiSEM a69dfa59-b0e1-45bd-8cd6-a, Tilburg University, School of Economics and Management.
    19. Flam, Sjur Didrik & Mirman, Leonard J., 1998. "Groping for optimal growth," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 191-207, September.
    20. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:219:y:2012:i:3:p:773-783. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.