The issues of optimal organization of the functioning of complex organized systems are within the competence of management subjects who need a problem-oriented tool in the form of models of analysis and synthesis of organization structures. The article considers the approach to the synthesis of the optimal composition of the mobile complex, as a sub-system of a complex organized critical system. The task of completing a mobile complex with the optimal composition of telecommunication equipment for servicing and repairing facilities is formulated. A mathematical model of the problem is proposed. The model is classified as a multi-index open assignment task with invalid assignments. This type of task relates to linear programming transport problems. Methods of bringing the problem to a closed type are considered, equivalent transformations of the assignment matrix are proposed, reducing the problem to a linear model. By entering additional constraints on the model, the effect of invalid assignments is taken into account. To implement a mathematical model, a solution method based on "greedy" algorithms has been proposed. The mathematical model is implemented in the form of a software application that showed the reliability of the results obtained, versatility and high resistance to changes in input data.
Complex organized systems, assignment problem, multi-index problem, open problem, problem with invalid assignments, optimization problems, transport problem, linear programming, assignment matrix, objective function, Hungarian method, Mack method, "greedy" algorithms.
1. Lavlinskaya, O.Yu. Napravleniya povysheniya effektivnosti upravlencheskoy deyatel'nosti organov gosudarstvennoy vlasti i mestnogo samoupravleniya / O.Yu. Lavlinskaya, Yu.S. Sova // Cbornik materialov V Mezhdunarodnoy nauchno-prakticheskoy konferencii. - Alchevsk: GOU VO LNR «LGU im. V. Dalya», 2023. - C. 408-416.
2. The Comparison of the Metaheuristic Algorithms Performances on Airport Gate Assignmnet Problem / A. Aktel, B. Yagmahan, T. Özcan [et al.] // Transportation Research Procedia. - 2017. - Vol. 22. -Pp. 469-478. - DOI:https://doi.org/10.1016/j.trpro.2017.03.061.
3. Probability Model of Situational Decision-Making under the Influence of Subjective Factors / O.Y. Lavlinskaya [et al.] // Proceedings of the 2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering, ElConRus. - 2021. - Pp. 502-506. - DOI:https://doi.org/10.1109/ElConRus51938.2021.9396589.
4. Liles, J.M. Improving defensive air battle management by solving a stochastic dynamic assignment problem via approximate dynamic programming / J.M. Liles, M.J. Robbins, B.J. Lunday // European Journal of Operational Research. - 2023. - Vol. 305, I. 3. - Pp. 1435-1449. - DOI:https://doi.org/10.1016/j.ejor.2022.06.031.
5. Balashova, I.Yu. Modeli i algoritmy resheniya obobschennyh zadach o naznacheniyah / magisterskaya dissertaciya. - URL: https://habr.com/ru/post/63982/ (data obrascheniya 13.02.2023).
6. Korkishko, N.M. Priblizhennye algoritmy resheniya nekotoryh mnogoindeksnyh zadach o naznacheniyah : avtoreferat dis. kand. fiz.-mat. nauk.: 01.01.09 - Novosibirsk, 2003. - 20 s.
7. Bouzekri, H. An integrated Decision Support System for planning production, storage and bulk port operations in a fertilizer supply chain / H. Bouzekri, N. Bara, G. Alpan, V. Giard // International Journal of Production Economics. - 2022. - Pp. 108561. - DOI:https://doi.org/10.1016/j.ijpe.2022.108561.
8. Hydyrova, G.D. Matematicheskaya model' zadachi o naznacheniyah i vozmozhnosti ee ispol'zovaniya pri prinyatii upravlencheskih resheniy / G.D. Hydyrova, A.Yu. Dushkina, A.G. Savina // Nauchnye zapiski OrelGIET. - 2014. - № 1 (7). - S. 305-310.
9. Fontes, D.B.M.M. Joint production and transportation scheduling in flexible manufacturing systems / D.B.M.M. Fontes, S.M. Homayouni // Journal of Global Optimization. - 2019. - Vol.784. - Pp. 879-908. - DOI:https://doi.org/10.1007/s10898-018-0681-7.
10. Malyugina, O.A. Ispol'zovanie zadachi o naznacheniyah pri reshenii problemy formirovaniya shtatov / O.A. Malyugina, G.D. Chernyshova // Vestnik Fakul'teta prikladnoy matematiki, informatiki i mehaniki. - 2010. - № 8.- S. 141-148.
11. Kogan, D.I. Koncepcii i algoritmy resheniya mnogokriterial'nyh modifikaciy zadachi o naznacheniyah / D.I. Kogan, Yu.S. Fedosenko, D.A. Handurin // Vestnik Volzhskoy gosudarstvennoy akademii vodnogo transporta. - 2018. - № 53. - S. 25-36.
12. Model' i algoritmizaciya optimizacionnoy zadachi o naznacheniyah v usloviyah dopolnitel'nyh ogranicheniy / R.Yu. Kordyukov, R.V. Dopira, A.V. Ivanova [et al.] // Programmnye produkty i sistemy. - 2016. - № 2 (114). - S. 16-22.
13. Goyala, S. An evaluation of the productivity change in public transport sector using DEA-based model / S. Goyala, Sh. Agarwala, T. Mathura // Management Science Letters. - 2022. - Vol. 12. - Pp. 125-136. - DOI:https://doi.org/10.5267/j.msl.2021.10.001.
14. Srinivasan, S A Heuristic Approach to Obtain an Optimal Solution for Transportation Problem Using Assignment / S. Srinivasan, N. Srinivasan // Taga Journal. - 2018. - Vol. 14. - Pp. 1862-1870.
15. Frieze, A. Efficient Algorithms For Three-Dimensional Axial and Planar Random Assignment Problems / A. Frieze , G. Sorkin // Random Struct. Algorithms. - 2015. - № 46/1. - Pp. 160-196. - DOI:https://doi.org/10.48550/arXiv.1008.0390.
16. Reyes, J.J.R. The Storage Location Assignment Problem: A Literature Review / J.J.R. Reyes, E.L. Solano-Charris, J.R. Montoya-Torres // International Journal of Industrial Engineering Computations. - 2019. - Vol. 10. - Pp. 199-224. - DOI:https://doi.org/10.5267/j.ijiec.2018.8.001.
17. Salehi, K. An approach for solving multi-objective assignment problemwith interval parameters / K. Salehi // Management Science Letters. - 2017. - Vol. 4. - Pp. 2155 -2160.
18. Arjomandia, M.A. Selecting maintenance strategy in a combined cycle power plant: An AHP model utilizing BOCR technique / M.A. Arjomandia, B. Mosallanezhadb // Management Science Letters. - 2022. - Vol. 12. - Pp. 153-164. - DOI:https://doi.org/10.5267/j.msl.2022.2.004.
19. Kammerdiner, A. Multidimensional Assignment Problem for Multipartite Entity Resolution / A. Kammerdiner, A. Semenov, E.L. Pasiliao // Journal of Global Optimization. - 2022. - Vol. 84. - Pp. 491-523. - DOI:https://doi.org/10.48550/arXiv.2112.03346.
20. An interleaved depth-first search method for the linear optimization problem with disjunctive constraints / Yi. Lyu, L. Chen, Ch. Zhang [et al.] // Journal of Global Optimization. - 2018. - Vol. 70. - Pp. 737-756. - DOI:https://doi.org/10.1007/s10898-017-0602-1.
21. Medvedeva, O.A. Modeli i algoritmy resheniya mnogokriterial'nyh zadach o naznacheniyah s dopolnitel'nymi ogranicheniyami : dissertaciya ... kand. fiz.-mat. nauk : 05.13.18 - Voronezh, 2013. - 159 s.
22. Balashova, I.Yu. Model' i algoritm resheniya zadachi o naznacheniyah s prioritetami / I.Yu. Balashova // Informacionnye tehnologii v nauke i obrazovanii : tr. VII Vseros. nauch.-prakt. konf. - Penza: Izd-vo PGU, 2020. - S. 80-82.
23. Li, J. A dual approach to multi-dimensional assignment problems / J. Li, T. Kirubarajan, R. Tharmarasa [et al.] // Journal of Global Optimization. - 2021. - Vol. 81. - Pp. 691-716. - DOI:https://doi.org/10.1007/s10898-020-00988-8.
24. Lelyakova, L. V. Prikladnye zadachi o naznacheniyah (modeli, algoritmy resheniya) / L. V. Lelyakova, A. G. Haritonova, G. D. Chernyshova // Vestnik Voronezhskogo gosudarstvennogo universiteta. - 2019. - № 2. - S. 22-27.
25. Homayouni, S.M. Production and transport scheduling in flexible job shop manufacturing systems / S.M. Homayouni, D.B.M.M. Fontes // Journal of Global Optimization. - 2021. - Vol. 79. - Pp. 463-502. - DOI:https://doi.org/10.1007/s10898-021-00992-6.
