An Optimal Allocation Algorithm for Reentrant Resources on Network Graphs
- Authors: Kosorukov O.A1,2, Lemtyuzhnikova D.V3,4
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Affiliations:
- Moscow State University
- The Presidential Academy (RANEPA)
- Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
- Moscow Aviation Institute (National Research University)
- Issue: No 2 (2024)
- Pages: 23-29
- Section: Mathematical Problems of Control
- URL: https://bakhtiniada.ru/1819-3161/article/view/273419
- DOI: https://doi.org/10.25728/pu.2024.2.2
- ID: 273419
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Abstract
This paper considers the problem of allocating reentrant resources when performing a set of interdependent works that are represented by a network graph. By assumption, the work completion time linearly depends on the resource amount used. We justify a solution algorithm in the case of a set of works with a predetermined sequence of events in the network graph. Also, we propose an algorithm for reducing the general problem to an auxiliary one with ordered event times and an algorithm for constructing an optimal solution of the original problem. The convergence of this algorithm is ensured by finite iterations at each stage. The overall computational complexity of the algorithm can be estimated as O(n2), where n denotes the number of vertices in the original network graph. It seems promising to apply this algorithm for planning the sets of interdependent works using reentrant resources.
Keywords
About the authors
O. A Kosorukov
Moscow State University; The Presidential Academy (RANEPA)
Email: kosorukovoa@mail.ru
Moscow, Russia
D. V Lemtyuzhnikova
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences; Moscow Aviation Institute (National Research University)
Email: darabbt@gmail.com
Moscow, Russia
References
- Давыдов Э.Г. Игры, графы, ресурсы. – М.: Радио и связь, 1981. – 113 c. [Davydov, E.G. Igry, grafy, resursy. – M.: Radio I svyaz’, 1981. – 113 s. (In Russian)] ]
- Бурков В.Н., Горгидзе И.А., Ловецкий С.Е. Прикладные задачи теории графов. – Тбилиси: Мецнииреба, 1974. – 234 с. [Burkov, V.N., Gorgidze ,I.A., Loveckij, S.E. Prikladnye zadachi teorii grafov. – Tbilisi: Mecniireba, 1974. – 234 s. (In Russian)]
- Косоруков О.А., Лемтюжникова Д.В., Мищенко А.В. Методы и модели управления ресурсами проекта в условиях неопределенности // Известия РАН. Теория и системы управления. – 2023. – № 3. – С. 38–56. [Kosorukov, O.A., Lemtyuzhnikova, D.V., Mishchenko, A.V. Metody i modeli upravleniya resursami proekta v usloviyah neopredelennosti // Izvestiya RAN. Teoriya i sistemy upravleniya. – 2023. – No. 3. – P. 38–56. (In Russian)]
- Mironov, A.A., Tsurkov, V.I. Transport-Type Problems with a Minimax Criterion // Automation and Remote Control. – 1995. – No. 12. – P. 109–118.
- Ляхов О.А. Ресурсы в сетевом планировании сложных комплексов работ // Проблемы информатики. – 2013. – № 1 (18). – С. 27–36. [Lyahov, O.A. Resursy v setevom planirovanii slozhnyh kompleksov rabot // Problemy informatiki. – 2013. – No. 1 (18). – P. 27–36. (In Russian)]
- Разумихин Б.С. Задача об оптимальном распределении ресурсов // Автоматика и телемеханика. – 1965. – Т. 26. – Вып. 3. – С. 1227–1247. [Razumikhin, B.S. The Problem on Optimal Resources Distribution // Automation and Remote Control. – 1965. – Vol. 26, no. 7. – P. 1227–1246. (In Russian)]
- Mishenko, А., Kosorukov, О., Sviridova, О. Optimization of Works Management of the Investment Project // The 2-nd International & European Conference «Modelling and Simulation of Social-Behavioural Phenomena in Creative Societies» (MSBC-2022). – Vilnius, 2022. – P. 201–217.
- Gehring, М., Volk, R., Schultmann, F. On the Integration of Diverging Material Flows into Resource‐Constrained Project Scheduling // European Journal of Operational Research. – 2022. – Vol. 303, iss. 3. – P. 1071–1087.
- Bianco, L., Caramia, M., Giordani, S. Project Scheduling with Generalized Precedence Relations: A New Method to Analyze Criticalities and Flexibilities // European Journal of Operational Research. – 2022. – Vol. 298, iss. 2. – P. 451–462.
- de Lima, V.L., Alves, C., Clautiaux, F., et al. Arc Flow Formulations Based on Dynamic Programming: Theoretical Foundations and Applications // European Journal of Operational Research. – 2022. – Vol. 296, iss. 1. – P. 3–21.
- Майника Э. Алгоритмы оптимизации на сетях и графах. – М.: Изд-во «Мир», 1981. – 319 с. [Minieka, E. Optimization Algorithms for Networks and Graphs. – New York: M. Dekker, 1978.]
- Филиппова А.С., Поречный С. С., Рамазанова Р.Р. Основы комбинаторных алгоритмов. – Уфа: Изд-во БГПУ, 2018. – 131 с. [Filippova, A.S., Porechnyj, S.S., Ramazanova, R.R. Osnovy kombinatornyh algoritmov. – Ufa: Izd-vo BGPU, 2018. – 131 s. [(In Russian)]
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