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Using linear programming to analyze and optimize stochastic flow lines


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


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

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    References listed on IDEAS

    1. 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.
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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. 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.
    3. 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.
    4. 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.

    More about this item


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

    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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