ОЦЕНКА ЭФФЕКТИВНОСТИ РАВНОВЕСНОЙ СТРАТЕГИИ ДЛЯ ПЕРЕРАБОТКИ САХАРНОЙ СВЕКЛЫ
Ключевые слова:
математическая модель, переработка сахарной свеклы, венгерский алгоритм, квазиоптимальная стратегия, равновесная стратегия
Аннотация
В статье рассматривается математическая модель управления процессом переработки
скоропортящегося продукта ‒ сахарной свеклы. Решается вопрос о смешивании нескольких партий во
время обработки для достижения наивысшего выхода конечного продукта. В статье показано, что
стратегия смешивания в любых пропорциях ни при каких обстоятельствах не увеличит оптимальную
целевую функцию, полученную без смешивания различных партий. Однако, теоретически, даже
смешанная стратегия может претендовать на роль квазиоптимальной. В статье предложены оценки потери
целевой функции для равновесной стратегии, которая получается, если свекла из всех партий подается на
вход каждый раз в равных долях
Литература
1. Balandin D.V., Kuzenkov O.A., Vildanov V.K. «A software module for constructing an optimal schedule for processing raw materials» // Modern information technologies and IT education. 2021. 17(2). P. 442‒452. (In Russ.)
2. Balandin D.V., Vildanov V.K., Kuzenkov O.A., Egamov A.I. «Optimal schedule of sugar beet processing in conditions of uncertainty». In Actual problems of applied mathematics, computer science and mechanics: Proceedings of the International Scientific Conference, Voronezh. 2022. P. 328‒334. (In Russ.)
3. Balandin D.V., Vildanov V.K., Kuzenkov O.A., Zakharova I.V., Egamov A.I.. «Strategy of processing sugar beet batches with close parameters of its withering», [Digests of the second All-Russian scientific and practical seminar "Mathematical and computer modeling and business analysis in the conditions of digitalization of the economy" Proceedings. Nizhny Novgorod. UNN, N.Novgorod, 2022. P.10‒18. (In Russ.)
4. Sapronov A.R. Technology of sugar production. 2nd ed., corrected and additional. 1999. M.: Kolos. (In Russ.)
5. Jiao Z., Higgins A.J., Prestwidge D.B. An integrated statistical and optimization approach to increasing sugar production within a mill region. // Computers and Electronics in Agriculture. 2005. 48. P. 170-181.
6. Ionitsa Y.S., «Change in sugar yield during storage of sugar beet of various selection». 2007. Sugar. №1. PP. 31‒33. (In Russ.) Kulneva N.G., Putilina L.N., Sveshnikov I.Y.,
7. Kazakevich S.Y. «Storage and processing of sugar beet of low technological quality». In the proceedings of scientific articles and reports of the II International
Scientific and Practical Conference Innovative solutions in the production of food from vegetable raw materials. Voronezh, October 26-27, 2016. P. 380‒384. (In Russ.)
8. Kulneva N.G., Putilina L.N. Selection of optimal parameters of sugar beet processing before storage. Proceedings of the XIX International scientific conference «The priorities of the world science: experiments and scientific debate». North Charleston, SC, USA 28-29 November, 2018. P. 8‒11.
9. Kukhar V.N., Chernyavsky A.P., Chernyavskaya L.I. and Mokanyuk Yu.A., Methods for assessing the technological qualities of sugar beet using indicators of the content of potassium, sodium and α-amine nitrogen determined in beet and its processed products // 2019. Sugar. 1. P. 18‒36. [In Russian]
10. Brusenkov A.V., Strukov I.A. and Myakotin V.O. «Factors affecting the storage of sugar beet». In the proceedings of the conference 2nd All-Russian (national) Scientific and Practical Conference "Modern Science: theory, methodology, practice". Tambov, May 28-29, 2020. P. 234‒237. (In Russ.)
11. Junqueira R., Morabito R. Modeling and solving a sugarcane harvest front scheduling problem // International Journal of Production Economics. 2019. 231 (1). P.150-160.
12. Emelichev V.A., Kovalev M.M., Kravtsov M.K. Polyhedra, Graphs, Optimization. M.: Nauka, 1981. 344c (In Russ.)
13. Bunday B., Basic linear programming. 1984. London.
14. Sigal I.H., Ivanova A.P. Introduction to applied discrete programming: models and computational algorithms. Textbook. Moscow. 2002. (In Russ.)
15. Rainer B., Mauro D., Silvano M. «Assignment problems». Printed in the USA. Philadelphia: Society for Industrial and Applied Mathematics. 2009.
16. Malyugina O.A., Chernyshova G.D. The use of the assignment problem in solving the problem of staff formation // Bulletin of the Voronezh State University
(Faculty of Adj. mathematics, computer science and mechanics). 2010. 8. P. 141‒148. (In Russ.)
17. Lelyakova L.V., Kharitonova A.G., Chernyshova G.D. Applied assignment problems (models, solution algorithms) // Bulletin of the Voronezh State University. 2017. 2. P. 22‒27. (In Russ.)
18. Kuhn H. The Hungarian Method for the assignment problem // Naval Research Logistics Quarterly. 1955. 2. P. 83‒97
19. Hopcroft J., Karp R. An n 5/2 algorithm for maximum matchings in bipartite graphs // SIAM J. on Computing. 1973. 2 (4). P. 225‒231.
20. Radzivilovsky L.V. Generalization of permutation inequality and Mongolian inequality // Mathematical Enlightenment. 2006. 10. (In Russ.)
2. Balandin D.V., Vildanov V.K., Kuzenkov O.A., Egamov A.I. «Optimal schedule of sugar beet processing in conditions of uncertainty». In Actual problems of applied mathematics, computer science and mechanics: Proceedings of the International Scientific Conference, Voronezh. 2022. P. 328‒334. (In Russ.)
3. Balandin D.V., Vildanov V.K., Kuzenkov O.A., Zakharova I.V., Egamov A.I.. «Strategy of processing sugar beet batches with close parameters of its withering», [Digests of the second All-Russian scientific and practical seminar "Mathematical and computer modeling and business analysis in the conditions of digitalization of the economy" Proceedings. Nizhny Novgorod. UNN, N.Novgorod, 2022. P.10‒18. (In Russ.)
4. Sapronov A.R. Technology of sugar production. 2nd ed., corrected and additional. 1999. M.: Kolos. (In Russ.)
5. Jiao Z., Higgins A.J., Prestwidge D.B. An integrated statistical and optimization approach to increasing sugar production within a mill region. // Computers and Electronics in Agriculture. 2005. 48. P. 170-181.
6. Ionitsa Y.S., «Change in sugar yield during storage of sugar beet of various selection». 2007. Sugar. №1. PP. 31‒33. (In Russ.) Kulneva N.G., Putilina L.N., Sveshnikov I.Y.,
7. Kazakevich S.Y. «Storage and processing of sugar beet of low technological quality». In the proceedings of scientific articles and reports of the II International
Scientific and Practical Conference Innovative solutions in the production of food from vegetable raw materials. Voronezh, October 26-27, 2016. P. 380‒384. (In Russ.)
8. Kulneva N.G., Putilina L.N. Selection of optimal parameters of sugar beet processing before storage. Proceedings of the XIX International scientific conference «The priorities of the world science: experiments and scientific debate». North Charleston, SC, USA 28-29 November, 2018. P. 8‒11.
9. Kukhar V.N., Chernyavsky A.P., Chernyavskaya L.I. and Mokanyuk Yu.A., Methods for assessing the technological qualities of sugar beet using indicators of the content of potassium, sodium and α-amine nitrogen determined in beet and its processed products // 2019. Sugar. 1. P. 18‒36. [In Russian]
10. Brusenkov A.V., Strukov I.A. and Myakotin V.O. «Factors affecting the storage of sugar beet». In the proceedings of the conference 2nd All-Russian (national) Scientific and Practical Conference "Modern Science: theory, methodology, practice". Tambov, May 28-29, 2020. P. 234‒237. (In Russ.)
11. Junqueira R., Morabito R. Modeling and solving a sugarcane harvest front scheduling problem // International Journal of Production Economics. 2019. 231 (1). P.150-160.
12. Emelichev V.A., Kovalev M.M., Kravtsov M.K. Polyhedra, Graphs, Optimization. M.: Nauka, 1981. 344c (In Russ.)
13. Bunday B., Basic linear programming. 1984. London.
14. Sigal I.H., Ivanova A.P. Introduction to applied discrete programming: models and computational algorithms. Textbook. Moscow. 2002. (In Russ.)
15. Rainer B., Mauro D., Silvano M. «Assignment problems». Printed in the USA. Philadelphia: Society for Industrial and Applied Mathematics. 2009.
16. Malyugina O.A., Chernyshova G.D. The use of the assignment problem in solving the problem of staff formation // Bulletin of the Voronezh State University
(Faculty of Adj. mathematics, computer science and mechanics). 2010. 8. P. 141‒148. (In Russ.)
17. Lelyakova L.V., Kharitonova A.G., Chernyshova G.D. Applied assignment problems (models, solution algorithms) // Bulletin of the Voronezh State University. 2017. 2. P. 22‒27. (In Russ.)
18. Kuhn H. The Hungarian Method for the assignment problem // Naval Research Logistics Quarterly. 1955. 2. P. 83‒97
19. Hopcroft J., Karp R. An n 5/2 algorithm for maximum matchings in bipartite graphs // SIAM J. on Computing. 1973. 2 (4). P. 225‒231.
20. Radzivilovsky L.V. Generalization of permutation inequality and Mongolian inequality // Mathematical Enlightenment. 2006. 10. (In Russ.)
Опубликован
2023-01-06
Как цитировать
Эгамов, Альберт Исмаилович, Арина Олеговна Гертель, и Оксана Викторовна Приставченко. 2023. «ОЦЕНКА ЭФФЕКТИВНОСТИ РАВНОВЕСНОЙ СТРАТЕГИИ ДЛЯ ПЕРЕРАБОТКИ САХАРНОЙ СВЕКЛЫ». EurasianUnionScientists, январь, 13-18. https://fizmat-tech.euroasia-science.ru/index.php/Euroasia/article/view/843.
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