The Problem of Allocation of Production Resources with a System of Constraints

76

Abstract

The problem of optimizing production and resource allocation have been always relevant. The paper deals with the problem of allocation of production resources with a system of constraints. As an example, the problem of optimizing the process of pouring raw aluminum into vacuum buckets in the electrolysis department of the foundry is considered. To solve this problem, a model of integer linear programming is proposed. The advantage of this approach is the ability to flexibly configure the system of constraints and minimized of objective in accordance with production priorities. The paper discusses the software implementation of the developed model and presents the results of a numerical experiment based on test samples. Based on the obtained solution, a conclusion is made about the effectiveness of the integer linear programming model in this optimization problem.

General Information

Keywords: linear programming, optimization problem, production optimization, metallurgy

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2023130208

Received: 17.04.2023

Accepted:

For citation: Rasskazova V.A., Skuridin A.A. The Problem of Allocation of Production Resources with a System of Constraints. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2023. Vol. 13, no. 2, pp. 142–150. DOI: 10.17759/mda.2023130208. (In Russ., аbstr. in Engl.)

References

  1. Kabulova E. G. Intellektual'noe upravlenie mnogostadiinymi sistemami metallurgicheskogo proizvodstva [Intelligent management of multi-stage systems of metallurgical production]. Modelirovanie, optimizatsiya i informatsionnye tekhnologii. [Modeling, optimization and information technology.] – 2019. – T. 7. – № 1(24). – S. 341-351. – DOI 10.26102/2310- 6018/2019.24.1.022
  2. O zadache naznacheniya “tekhnologicheskogo okna” na uchastkakh zheleznodorozhnoi seti [About the task of assigning a “technological window” on sections of the railway network]. Gainanov D. N., Ignatov A. N., Naumov A. V., Rasskazova V. A. Avtomatika i telemekhanika. [Automation and telemechanics.] – 2020. – № 6. – S. 3-16. – DOI 10.31857/S0005231020060013
  3. Lazarev A. A., Musatova E. G. Tselochislennye postanovki zadachi formirovaniya zheleznodorozhnykh sostavov i raspisaniya ikh dvizheniya [Integer statements of the problem of forming railway trains and their schedules]. Upravlenie bol'shimi sistemami: sbornik trudov. [Managing large systems: a collection of works.] – 2012. – № 38. – S. 161-169
  4. Shevchenko V. N., Zolotykh N. Yu. Lineinoe i tselochislennoe lineinoe programmirovanie. [Linear and integer linear programming.] Nizhnii Novgorod: Izdatel'stvo Nizhegorodskogo gosuniversiteta im. N. I. Lobachevskogo [Nizhni Novgorod University Press (NNUP)], 2004
  5. Skhreiver A. Teoriya lineinogo i tselochislennogo programmirovaniya. [Theory of linear and integer programming.] Moscow: Mir, 1991
  6. Sigal I. Kh., Ivanova A. P. Vvedenie v prikladnoe diskretnoe programmirovanie. Modeli i vychislitel'nye algoritmy. [Introduction to applied discrete programming. Models and computational algorithms.] Moscow: Fizmatlit, 2007
  7. Appa G. M., Pitsoulis L. S., Paul, W. H. (Eds.) Handbook on modeling for discrete optimization. Springer Series, Int. Series in Operations Research & Management Science, vol. 88, XXII, 2006
  8. Pochet Y., Wolsey L. A. Production planning by mixed integer programming. In: Springer Series in Operations Research & Financial Engineering (Eds. Mikosh, T. V., Resnick, S. I., Robinson, S. M.). 2006
  9. Integer Linear Programming in Solving an Optimization Problem at the Mixing Department of the Metallurgical Production. Gainanov N., Berenov D. A., Nikolaev E. A., Rasskazova V. A. Lecture Notes in Computer Science (2023), vol. 13621, pp. 145-161. doi: https://doi.org/10.1007/978-3-031-24866-5_12

Information About the Authors

Varvara A. Rasskazova, PhD in Physics and Matematics, Associate Professor of Department 804 "Probability Theory and Computer Modeling", Moscow Aviation Institute, (NRU MAI), Moscow, Russia, ORCID: https://orcid.org/0000-0003-4943-3133, e-mail: varvara.rasskazova@mail.ru

Alexey A. Skuridin, Graduate Student, Department of the Institute of Computer Science and Applied Mathematics, Moscow Aviation Institute (National Research University) (MAI), Moscow, Russia, ORCID: https://orcid.org/0009-0002-6466-2110, e-mail: aas-allex@gmail.com

Metrics

Views

Total: 229
Previous month: 16
Current month: 0

Downloads

Total: 76
Previous month: 3
Current month: 1