Using linear programming to analyze and optimize stochastic flow lines

Stefan Helber, Katja Schimmelpfeng, Raik Stolletz, Svenja Lagershausen

    Research output: Contribution to journalJournal articleResearchpeer-review

    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.
    Original languageEnglish
    JournalAnnals of Operations Research
    Volume182
    Issue number1
    Pages (from-to)193-211
    ISSN0254-5330
    DOIs
    Publication statusPublished - 2011

    Cite this

    Helber, Stefan ; Schimmelpfeng, Katja ; Stolletz, Raik ; Lagershausen, Svenja. / Using linear programming to analyze and optimize stochastic flow lines. In: Annals of Operations Research. 2011 ; Vol. 182, No. 1. pp. 193-211.
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    title = "Using linear programming to analyze and optimize stochastic flow lines",
    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.",
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    Helber, S, Schimmelpfeng, K, Stolletz, R & Lagershausen, S 2011, 'Using linear programming to analyze and optimize stochastic flow lines', Annals of Operations Research, vol. 182, no. 1, pp. 193-211. https://doi.org/10.1007/s10479-010-0692-3

    Using linear programming to analyze and optimize stochastic flow lines. / Helber, Stefan; Schimmelpfeng, Katja; Stolletz, Raik; Lagershausen, Svenja.

    In: Annals of Operations Research, Vol. 182, No. 1, 2011, p. 193-211.

    Research output: Contribution to journalJournal articleResearchpeer-review

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    T1 - Using linear programming to analyze and optimize stochastic flow lines

    AU - Helber, Stefan

    AU - Schimmelpfeng, Katja

    AU - Stolletz, Raik

    AU - Lagershausen, Svenja

    PY - 2011

    Y1 - 2011

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    AB - 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.

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