Vadim V. Romanuke


Background. In setting a problem of minimizing total tardiness by the heuristic based on remaining available and processing periods, there are two opposite ways to input the data: the job release dates are given in either ascending or descending order. It was recently ascertained that scheduling a few equal-length jobs is expectedly faster by ascending order, whereas scheduling 30 to 70 equal-length jobs is 1.5 % to 2.5 % faster by descending order. For the number of equal-length jobs between roughly 90 and 250, the ascending job order again results in shorter computation times.

Objective. The goal is to ascertain whether the job order input is significant in scheduling by using the heuristic for the case when the jobs have different lengths. Job order efficiency will be studied on tight-tardy progressive idling-free 1-machine preemptive scheduling.

Methods. To achieve the said goal, a computational study is carried out with a purpose to estimate the averaged computation time for both ascending and descending orders of job release dates. Instances of the job scheduling problem are generated so that schedules which can be obtained trivially, without the heuristic, are excluded.

Results. On average, the descending job order input gives a tiny advantage in computation time. This advantage decreases as the number of jobs increases. The decrement resembles a steep exponential decrease. The factual advantage is so insignificant that even after solving long series of job scheduling problems the saved computational time cannot be counted in minutes, not speaking about hours as it was for the case of equal-length jobs.

Conclusions. The significance of the job order input is much lower than that for the case of equal-length jobs. Theoretically, the heuristic’s efficient job order input does exist but its efficiency can be practically used only by working on extremely long series of scheduling problems where the number of jobs should not exceed 300.


preemptive single machine job scheduling; total tardiness; heuristic; ascending/descending job order; computation time; efficient job order.Preemptive single machine job scheduling; Total tardiness; Heuristic; Ascending job order; Descending job order; Computation time; Efficient job order

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V.V. Romanuke, “Efficient exact minimization of total tardiness in tight-tardy progressive single machine scheduling with idling-free preemptions of equal-length jobs”, KPI Sci. News, no. 1, pp. 27–39, 2020. doi: 10.20535/kpi-sn.2020.1.180877

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