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Using linear programming to analyze and optimize stochastic flow lines

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  • Stefan Helber
  • Katja Schimmelpfeng
  • Raik Stolletz
  • Svenja Lagershausen

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 us 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. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Stefan Helber & Katja Schimmelpfeng & Raik Stolletz & Svenja Lagershausen, 2011. "Using linear programming to analyze and optimize stochastic flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 193-211, January.
    • Handle: RePEc:spr:annopr:v:182:y:2011:i:1:p:193-211:10.1007/s10479-010-0692-3
    DOI: 10.1007/s10479-010-0692-3
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.
    4. 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.
    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).
    6. 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.
    7. 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.

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    JEL classification:

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

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