IDEAS home Printed from https://ideas.repec.org/p/han/dpaper/dp-389.html
   My bibliography  Save this paper

Using linear programming to analyze and optimize stochastic flow lines

Author

Listed:
  • Helber, Stefan
  • Schimmelpfeng, Katja
  • Stolletz, Raik
  • Lagershausen, Svenja

Abstract

This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time, to determine a production rate estimate. As our methodology is purely numerical, it offers the full modeling flexibility of stochastic simulation with respect to the probability distribution of processing times. However, unlike discrete-event simulation models, it also offers the optimization power of linear programming and hence allows to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines.

Suggested Citation

  • Helber, Stefan & Schimmelpfeng, Katja & Stolletz, Raik & Lagershausen, Svenja, 2008. "Using linear programming to analyze and optimize stochastic flow lines," Hannover Economic Papers (HEP) dp-389, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    • Handle: RePEc:han:dpaper:dp-389
    as

    Download full text from publisher

    File URL: http://diskussionspapiere.wiwi.uni-hannover.de/pdf_bib/dp-389.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stanley Gershwin & James Schor, 2000. "Efficient algorithms for buffer space allocation," Annals of Operations Research, Springer, vol. 93(1), pages 117-144, January.
    2. Helber, Stefan & Henken, Kirsten, 2007. "Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials," Hannover Economic Papers (HEP) dp-379, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    3. Stanley B. Gershwin & Irvin C. Schick, 1983. "Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers," Operations Research, INFORMS, vol. 31(2), pages 354-380, April.
    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. Ziwei Lin & Nicla Frigerio & Andrea Matta & Shichang Du, 2021. "Multi-fidelity surrogate-based optimization for decomposed buffer allocation problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 223-253, March.
    3. 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).
    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. Helber, Stefan & Schimmelpfeng, Katja & Stolletz, Raik, 2009. "Setting inventory levels of CONWIP flow lines via linear programming," Hannover Economic Papers (HEP) dp-436, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. 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.
    7. 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.

    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. 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.
    2. Shi, Chuan & Gershwin, Stanley B., 2009. "An efficient buffer design algorithm for production line profit maximization," International Journal of Production Economics, Elsevier, vol. 122(2), pages 725-740, December.
    3. Chang, Ping-Chen & Lin, Yi-Kuei & Chiang, Yu-Min, 2019. "System reliability estimation and sensitivity analysis for multi-state manufacturing network with joint buffers––A simulation approach," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 103-109.
    4. Chame, Anna & Tsallis, Constantino, 1990. "Criticality of the discrete N-vector ferromagnet in a cubic lattice with a free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(1), pages 41-63.
    5. 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.
    6. Benjamin Legros & Sihan Ding & Rob Mei & Oualid Jouini, 2017. "Call centers with a postponed callback offer," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1097-1125, October.
    7. 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.
    8. Juliane Müller & Christine Shoemaker & Robert Piché, 2014. "SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications," Journal of Global Optimization, Springer, vol. 59(4), pages 865-889, August.
    9. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    10. Adrien Wartelle & Farah Mourad-Chehade & Farouk Yalaoui & David Laplanche & Stéphane Sanchez, 2024. "Changing the perspective of system crowding evaluation using a new congestion measure: application to the Emergency Department," Operational Research, Springer, vol. 24(4), pages 1-35, December.
    11. Federico Nuñez-Piña & Joselito Medina-Marin & Juan Carlos Seck-Tuoh-Mora & Norberto Hernandez-Romero & Eva Selene Hernandez-Gress, 2018. "Modeling of Throughput in Production Lines Using Response Surface Methodology and Artificial Neural Networks," Complexity, Hindawi, vol. 2018, pages 1-10, January.
    12. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Discussion Paper 1997-97, Tilburg University, Center for Economic Research.
    13. Guan Wang & Yang Woo Shin & Dug Hee Moon, 2016. "Comparison of three flow line layouts with unreliable machines and profit maximization," Flexible Services and Manufacturing Journal, Springer, vol. 28(4), pages 669-693, December.
    14. Hołyst, R. & Poniewierski, A., 1988. "Quasi-wetting on a sphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(3), pages 622-630.
    15. Colledani, Marcello & Tolio, Tullio, 2009. "Performance evaluation of production systems monitored by statistical process control and off-line inspections," International Journal of Production Economics, Elsevier, vol. 120(2), pages 348-367, August.
    16. Mehmet Savsar, 2016. "Reliability and availability analysis of a manufacturing line system," Journal of Applied and Physical Sciences, Prof. Vakhrushev Alexander, vol. 2(3), pages 96-106.
    17. Widom, B. & Clarke, A.S., 1990. "Line tension at the wetting transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 149-159.
    18. Ziwei Lin & Nicla Frigerio & Andrea Matta & Shichang Du, 2021. "Multi-fidelity surrogate-based optimization for decomposed buffer allocation problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 223-253, March.
    19. 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.
    20. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Other publications TiSEM 77da022b-635b-46fd-bf4a-f, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Flow lines; random processing times; performance evaluation; buffer allocation; linear programming; simulation.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:han:dpaper:dp-389. 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: Heidrich, Christian (email available below). General contact details of provider: https://edirc.repec.org/data/fwhande.html .

    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.