Minimal Total Weighted Tardiness in Tight-Tardy Single Machine Preemptive Idling-Free Scheduling


Two possibilities of obtaining the minimal total weighted tardiness in tight-tardy single machine preemptive idling-free scheduling are studied. The Boolean linear programming model, which allows obtaining the exactly minimal tardiness, becomes too time-consuming as either the number of jobs or numbers of job parts increase. Therefore, a heuristic based on remaining available and processing periods is used instead. The heuristic schedules 2 jobs always with the minimal tardiness. In scheduling 3 to 7 jobs, the risk of missing the minimal tardiness is just 1.5 % to 3.2 %. It is expected that scheduling 12 and more jobs has at the most the same risk or even lower. In scheduling 10 jobs without a timeout, the heuristic is almost 1 million times faster than the exact model. The exact model is still applicable for scheduling 3 to 5 jobs, where the averaged computation time varies from 0.1 s to 1.02 s. However, the maximal computation time for 6 jobs is close to 1 minute. Further increment of jobs may delay obtaining the minimal tardiness at least for a few minutes, but 7 jobs still can be scheduled at worst for 7 minutes. When scheduling 8 jobs and more, the exact model should be substituted with the heuristic.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] A. S. Uyar, E. Ozcan, and N. Urquhart, Eds. Automated Scheduling and Planning: From Theory to Practice. Springer-Verlag Berlin Heidelberg, 2013.

  • [2] J. M. Framinan, R. Leisten, and R. R. García, Manufacturing Scheduling Systems: An Integrated View on Models, Methods and Tools. Springer-Verlag London, 2014.

  • [3] F. Jaramillo and M. Erkoc, “Minimizing Total Weighted Tardiness and Overtime Costs for Single Machine Preemptive Scheduling,” Computers & Industrial Engineering, vol. 107, pp. 109–119, May 2017.

  • [4] B. Yang, J. Geunes, and W. J. O’Brien, “A Heuristic Approach for Minimizing Weighted Tardiness and Overtime Costs in Single Resource Scheduling,” Computers and Operations Research, vol. 31, pp. 1273–1301, Jul. 2004.

  • [5] J. M. van den Akker, G. Diepen, and J. A. Hoogeveen, “Minimizing Total Weighted Tardiness on a Single Machine With Release Dates and Equal-Length Jobs,” Journal of Scheduling, vol. 13, iss. 6, pp. 561–576, Dec. 2010.

  • [6] R. Panneerselvam, “Simple Heuristic to Minimize Total Tardiness in a Single Machine Scheduling Problem,” The International Journal of Advanced Manufacturing Technology, vol. 30, iss. 7–8, pp. 722–726, Oct. 2006.

  • [7] M. L. Pinedo, Scheduling: Theory, Algorithms, and Systems. Springer Inter. Publishing, 2016.

  • [8] P. Brucker, Scheduling Algorithms. Springer-Verlag Berlin Heidelberg, 2007.

  • [9] V. V. Romanuke, “Accuracy of a Heuristic for Total Weighted Completion Time Minimization in Preemptive Single Machine Scheduling Problem by no Idle Time Intervals,” KPI Science News, no. 3, pp. 52–62, 2019.

  • [10] S. Haruhiko and S. Hiroaki, Online Scheduling in Manufacturing: A Cumulative Delay Approach. Springer-Verlag London, 2013.

  • [11] V. V. Romanuke, “Decision Making Criteria Hybridization for Finding Optimal Decisions’ Subset Regarding Changes of the Decision Function,” Journal of Uncertain Systems, vol. 12, no. 4, pp. 279–291, 2018.

  • [12] J. O. Berger, Ed. Statistical Decision Theory and Bayesian Analysis. New York: Springer, 1985.


Journal + Issues