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Discrete scheduling and critical utilization

Author

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  • Pianykh, Oleg S.
  • Perez, Sebastian
  • Zhang, Chengzhao “Richard”

Abstract

Efficient scheduling is essential for optimizing resource allocation and robust system performance in a wide range of real-life applications. In most of these cases, the success of scheduling largely depends on one's ability to ensure that system resources can be utilized to their maximum capacity, yet without overloading the system. In this work, we study the problem of critical utilization and efficient scheduling by considering systems with discrete schedules, widely used in real-life workflows. Using an implementation-based approach, we introduce discrete scheduling by developing its analytic equations, which enables us to express the behavior of the scheduling metrics with respect to system utilization. Using this result, we define critical resource utilization and solve for its exact value as a function of schedule length. Finally, we compare our results with the equations from the classical queueing theory, and discuss their applicability. Our findings have immediate practical implications in developing robust schedules and controlling for optimal system performance.

Suggested Citation

  • Pianykh, Oleg S. & Perez, Sebastian & Zhang, Chengzhao “Richard”, 2024. "Discrete scheduling and critical utilization," European Journal of Operational Research, Elsevier, vol. 312(2), pages 445-455.
    • Handle: RePEc:eee:ejores:v:312:y:2024:i:2:p:445-455
    DOI: 10.1016/j.ejor.2023.06.010
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    References listed on IDEAS

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    1. Mehmet A. Begen & Maurice Queyranne, 2011. "Appointment Scheduling with Discrete Random Durations," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 240-257, May.
    2. Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis I," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 297-304, June.
    3. Eugene M. Klimko & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis II," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 305-319, June.
    4. Diwas S. Kc & Christian Terwiesch, 2009. "Impact of Workload on Service Time and Patient Safety: An Econometric Analysis of Hospital Operations," Management Science, INFORMS, vol. 55(9), pages 1486-1498, September.
    5. David Heimann & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis IV," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(4), pages 753-766, December.
    6. Marcel F. Neuts & Eugene Klimko, 1973. "The single server queue in discrete time‐numerical analysis III," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(3), pages 557-567, September.
    7. Sudarshan K. Dhall & C. L. Liu, 1978. "On a Real-Time Scheduling Problem," Operations Research, INFORMS, vol. 26(1), pages 127-140, February.
    8. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
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