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Sequencing with uncertain numerical data for makespan minimisation

Author

Listed:
  • T-C Lai

    (National Taiwan University)

  • Y N Sotskov

    (Belarusian Academy of Sciences)

Abstract

We consider a scheduling problem with the objective of minimising the makespan under uncertain numerical input data (for example, the processing time of an operation, the job release time and due date) and fixed structural input data (for example the precedence and capacity constraints). We assume that at (before) the scheduling stage the structural input data are known and fixed but all we know about the numerical input data are their upper and lower bounds, where the uncertain numerical data become realised at the control stage as the scheduled process evolves. After improving the mixed graph model, we present an approach for dealing with our scheduling problem under uncertain numerical data based on a stability analysis of an optimal makespan schedule. In particular, we investigate the candidate set of the critical paths in a circuit-free digraph, characterise a minimal set of the optimal schedules, and develop an optimal and a heuristic algorithm. We also report computational results for randomly generated as well as well-known test problems.

Suggested Citation

  • T-C Lai & Y N Sotskov, 1999. "Sequencing with uncertain numerical data for makespan minimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(3), pages 230-243, March.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:3:d:10.1057_palgrave.jors.2600690
    DOI: 10.1057/palgrave.jors.2600690
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    Citations

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    Cited by:

    1. Carlo Meloni & Marco Pranzo, 2020. "Expected shortfall for the makespan in activity networks under imperfect information," Flexible Services and Manufacturing Journal, Springer, vol. 32(3), pages 668-692, September.
    2. Yuri N. Sotskov & Natalja M. Matsveichuk & Vadzim D. Hatsura, 2020. "Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times," Mathematics, MDPI, vol. 8(8), pages 1-51, August.
    3. Levorato, Mario & Figueiredo, Rosa & Frota, Yuri, 2022. "Exact solutions for the two-machine robust flow shop with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 300(1), pages 46-57.
    4. Meloni, Carlo & Pranzo, Marco & Samà, Marcella, 2022. "Evaluation of VaR and CVaR for the makespan in interval valued blocking job shops," International Journal of Production Economics, Elsevier, vol. 247(C).
    5. Theodor Freiheit & Wei Li, 2017. "The effect of work content imbalance and its interaction with scheduling method on sequential flow line performance," International Journal of Production Research, Taylor & Francis Journals, vol. 55(10), pages 2791-2805, May.
    6. Meloni, Carlo & Pranzo, Marco & Samà, Marcella, 2021. "Risk of delay evaluation in real-time train scheduling with uncertain dwell times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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