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Optimal balanced chain decomposition of partially ordered sets with applications to operating cost minimization in aircraft routing problems

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Abstract

We consider the task of constructing a cost-effective daily flight schedule with a minimum number of required aircrafts and a maximum number of balanced flight routes, namely, routes with the same start and end spatial location. We suggest a solution strategy which is able to determine the problem’s hardness by estimating the number of all flight plans with a minimum number of required aircrafts. Provided that this number is not too large, the same algorithm is utilized for fully enumerating and detecting the set of solutions that have the maximum number of balanced routes. Our experimental study implies that the method is both effective and scalable in practice. For example, when applied to the Australian domestic flights timetable which is serviced by a total of eighty-eight aircrafts, our method manages to increase the number of balanced flight routes from nine to forty-two, while using only several minutes of computational time.

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Data availability

Software packages and the research data is available on the author’s website under: https://people.smp.uq.edu.au/RadislavVaisman/sw/scheduling/software.zip

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Acknowledgements

We are thoroughly grateful to the anonymous reviewers for their valuable and constructive remarks and suggestions. This paper is dedicated to the memory of Professor Ilya B. Gertsbakh (1933–2020). This work was supported by the Australian Research Council Centre of Excellence for Mathematical & Statistical Frontiers, under CE140100049 grant number.

Funding

Centre of Excellence for Electromaterials Science, Australian Research Council (AU) (Grant no. CE140100049).

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Authors and Affiliations

  1. School of Mathematics and Physics, The University of Queensland, St Lucia QLD, 4072, Brisbane, Australia

    Radislav Vaisman

  2. Department of Mathematics, Ben-Gurion University, Beer-Sheva, 84105, Israel

    Ilya B. Gertsbakh

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  1. Radislav Vaisman
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  2. Ilya B. Gertsbakh
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Correspondence to Radislav Vaisman.

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Appendices

Appendices

A The F30 timetable from Stern and Gertsbakh (2019)

Table 3 The F30 flight timetable with 30 passages. For each passage, the table displays the flight number, the departure and the arrival terminals, and the departure and the arrival times. Here, a fraction such as 4.5 in the first row, stands for the 4:30AM time
Full size table

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Vaisman, R., Gertsbakh, I.B. Optimal balanced chain decomposition of partially ordered sets with applications to operating cost minimization in aircraft routing problems. Public Transp 15, 199–225 (2023). https://doi.org/10.1007/s12469-022-00304-5

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