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Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes

Author

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  • Nima Manafzadeh Dizbin

    (Koç University)

  • Barış Tan

    (Koç University)

Abstract

Empirical studies show that the inter-event times of a production system are correlated. However, most of the analytical studies for the analysis and control of production systems ignore correlation. In this study, we show that real-time data collected from a manufacturing system can be used to build a Markovian arrival processes (MAP) model that captures correlation in inter-event times. The obtained MAP model can then be used to control production in an effective way. We first present a comprehensive review on MAP modeling and MAP fitting methods applicable to manufacturing systems. Then we present results on the effectiveness of these fitting methods and discuss how the collected inter-event data can be used to represent the flow dynamics of a production system accurately. In order to study the impact of capturing the flow dynamics accurately on the performance of a production control system, we analyze a manufacturing system that is controlled by using a base-stock policy. We study the impact of correlation in inter-event times on the optimal base-stock level of the system numerically by employing the structural properties of the MAP. We show that ignoring correlated arrival or service process can lead to overestimation of the optimal base-stock level for negatively correlated processes, and underestimation for the positively correlated processes. We conclude that MAPs can be used to develop data-driven models and control manufacturing systems more effectively by using shop-floor inter-event data.

Suggested Citation

  • Nima Manafzadeh Dizbin & Barış Tan, 2019. "Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 1042-1076, December.
    • Handle: RePEc:spr:flsman:v:31:y:2019:i:4:d:10.1007_s10696-018-9329-7
    DOI: 10.1007/s10696-018-9329-7
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    References listed on IDEAS

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    Cited by:

    1. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    2. Petra Tomanová & Vladimír Holý, 2021. "Clustering of arrivals in queueing systems: autoregressive conditional duration approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 859-874, September.
    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. Tan, Barış & Karabağ, Oktay & Khayyati, Siamak, 2023. "Production and energy mode control of a production-inventory system," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1176-1187.

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