M.N. Belozerov1, E.A. Kalashnikov2, A.N. Smirnov3

1-2 MISIS National Research Technological University (Moscow, Russia) 3 PJSC SberBank of Russia (Moscow, Russia)

1 mnbelozyorov@gmail.com, 2 e.a.kalashnikov@mail.ru, 3 asmirnov889@yandex.ru

The problem of calculating possible technological options for the production of aluminum alloys (charges) lies in the combinatorial complexity that arises as a result of the fact that the number of possible options for charges significantly exceeds the number of initial elements (charge materials), which leads to high dimensional constraints of the linear programming problem and creates computational and analytical difficulties.

The purpose of the study is to develop and test an algorithm for finding a suboptimal solution to the charge calculation problem for optimizing the production of secondary aluminum alloys.

The authors propose the use of a new method based on the combined application of the theory of linear programming and the theory of duality.

The proposed approach can be applied both to calculate rational production options for cutting and mixing tasks. The results of the work are necessary to increase production efficiency and ensure the competitiveness of metallurgical enterprises' products.

Belozerov M.N., Kalashnikov E.A., Smirnov A.N. Iterative optimization procedure of production of secondary alu minium alloys. Nonlinear World. 2026. V. 24. № 1. P. 62–70. DOI: https:// doi.org/10.18127/ j20700970-202601-05 (In Russian)

1. Harchenko A.V. i dr. Razrabotka informacionno-tekhnologicheskoj sistemy «For vard» dlyaupravleniya metallurgicheskimi processami vreal'nom masshtabe vremeni. Izv. vuzov. Ser.: CHernaya metallurgiya. 1991. № 12. S. 89–91 (In Russian).
2. Arhangel'skij A.B. i dr. Opyt ispol'zovaniyakomp'yuternojprogrammy raschetashihty. Lit'eimetallurgiya. 2000. № 2. S. 37 (In Russian).
3. Bogushevskij V.S., Suhenko V.Yu. Avtomatizirovannaya sistemaupravleniya konverternoj plavkoj. Sovremennye innovacionnye tekhnologii podgotovki inzhenernyh kadrovdlya gornoj promyshlennosti itransporta. 2014. № 1. S. 339–345 (In Russian).
4. Belozerov M.N., Kalashnikov E.A. Dialogovaya procedura rascheta potrebnosti viskhodnyh materia lah iupravlenie syr'evymizapasami pri proizvodstve vtorichnyh alyuminievyh splavov. Cvetnye metally. 2009. № 10. S. 75–78 (In Russian).
5. Belozerov M.N., Kalashnikov E.A. Raschet grafikaispol'zovaniyakonechnogo naboravariantov shi htovok iformirovanie planadozakupki iskhodnyh materialov. Cvetnye metally. 2010. № 3. S. 102–106 (In Russian).
6. Pikul' V.V., Eroshenko A.E. Snizhenie zatrat na legirovanie iraskislenie staliferrosplav ami putemoptimizacii tekhnologii dvojstvennym simpleks-metodomsispol'zovaniemprogrammnyh sredstvvusloviyah RUP «BMZ». Lit'eimetallurgiya. 2008. № 2 (46). S. 93–96 (In Russian).
7. Andrianov N.V. i dr. Opredelenie optimal'nogosostava metalloshihty dlyarazlichnogo marochnogo sortamenta stalej, vyplavlyaemyh v DSP-100№ 3 RUP «Belorusskij metallurgicheskij zavod». 2004 (In Russian).
8. Rogozhin P.I., Brusov A.L. Raschet shihtydlya vyplavkimednogo splava iz mednogoloma. M etallurgiya XXI stoletiya glazami molodyh. 2017. S. 77–78 (In Russian).
9. Belkovskij A.G. Issledovanie irazrabotka parametrov tekhnologii vyplavki stal isprimeneniem DSP srednejvmestimosti dlyapovysheniya effektivnosti proizvodstva sortovojzagotovki: Dis. Nacional'nyj issledovatel'skij tekhnologicheskij universitet «MISiS». 2013 (In Russian). 1
10. Karashaev M.M. i dr. Tekhnologicheskie osnovysozdaniya metallicheskih kompozicionnyh materialov, armirovannyh oksidnymi iintermetallidnymi chasticami. Aviacionnye materialy itekhnologii. 2020. № 3 (60). S. 29–36 (In Russian). 1
11. Kolesnikova E.V., Prokopovich I.V., Lopakov A.S. Ocenka effektivnosti reshenij po upravleniyu processom vyplavkistali. Trudy Odesskogo politekhnicheskogo universiteta. 2010. № 1–2. S. 155–157 (In Russian).