Abstract—
The problem of optimal flow production planning at the operational scheduling stage is being studied, using the example of the out-of-furnace department of a converter-based steel-making production in the iron metallurgy industry. To solve this problem, a linear integer programming model is proposed, which fully describes the specifics of the investigated technological processes. A major advantage of this approach is its scalability for solving related optimization problems in the industry of plant logistics, as well as flexibility in adapting to changes and fine-tuning the system of constraints and objective function. The software implementation of the developed model forms the basis of the operational scheduling module of the optimal flow production planning system, which is used for a large-scale computational experiment on real-world data.
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REFERENCES
Lazarev, A.A. and Musatova, E.G., Integer Formulations of the Problem of Forming Railway Trains and Scheduling Their Movement, Control of Large Systems, 2012, no. 38, pp. 161–169.
Gainanov, D.N., Ignatov, A.N., Naumov, A.V., and Rasskazova, V.A., On Track Procession Assignment Problem at the Railway Network Sections, Autom. Remote Control, 2020, vol. 81, no. 6, pp. 967–977. https://doi.org/10.1134/S0005117920060028
Khoo, T., Tselochislennoe programmirovanie i potoki v setyakh (Integer Programming and Network Flows), Moscow: Mir, 1974.
Ryan, D.M. and Foster, B.A., An Integer Programming Approach to Scheduling, in Computer Scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling, Wren, A., Еd., Amsterdam: North-Holland, 1981, pp. 269–280.
Wagner, H.M., An Integer Linear-Programming Model for Machine Scheduling, Naval Research Logistics Quarterly, 1959, vol. 6, no. 2, pp. 131–140.
Pochet, Y. andWolsey, L.A., Production Planning by Mixed Integer Programming, Springer Series in Operations Research & Financial Engineering, Cham: Springer, 2006.
Shevchenko, V.N. and Zolotykh, N.Y., Lineinoe i tselochislennoe lineinoe programmirovanie (Linear and Integer Linear Programming), Nizhny Novgorod: Nizhny Novgorod State University named after N.I. Lobachevsky, 2004.
Schrijver, A., Teoriya lineinogo i tselochislennogo programmirovaniya (Theory of Linear and Integer Programming), Moscow: Mir, 1991.
Sigal, I.Kh. and 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.
Appa, G.M., Pitsoulis, L.S., and Paul, W.H., Handbook on Modeling for Discrete Optimization, Springer Series in Operations Research & Management Science, Cham: Springer, 2006.
Wolsey, L.A., Integer Programming, Hoboken, N.J.: John Wiley & Sons, 2020.
Hu, T.C. and Kahng, A.B., Linear and Integer Programming Made Easy, Cham: Springer, 2016.
Kabulova, E.G., Intelligent Control of Multistage Systems in Metallurgical Production, Modeling, Optimization, and Information Technology, 2019, vol. 7, no. 1(24), pp. 341–351. https://doi.org/10.26102/2310-6018/2019.24.1.022
Stolbov, V.Yu., Gitman, M.B., and Fedoseev, S.A., Management of the Process of Forming the Quality of Products of an Industrial Enterprise, Applied Mathematics and Control, 2016, no. 3, pp. 79–98.
Gainanov, D.N. and Berenov, D.A., Algorithm for Predicting the Quality of the Product of Metallurgical Production, CEUR Workshop Proceedings, 2017, vol. 1987, pp. 194–200.
Qiu, Y., Wang, L., Xu, X., Fang, X., and Pardalos, P.M., Scheduling a Realistic Hybrid Flow Shop with Stage Skipping and Adjustable Processing Time in Steel Plants, Applied Soft Computing, 2018, vol. 64, pp. 536–549.
Kong, M., Pei, J., Xu, J., Liu, X., and Pardalos, P.M., A Robust Optimization Approach for Integrated Steel Production and Batch Delivery Scheduling with Uncertain Rolling Times and Deterioration Effect, International Journal of Production Research, 2020, vol. 58, no. 17, pp. 5132–5154. https://doi.org/10.1080/00207543.2019.1693659
Long, J., Sun, Z., et al., A Robust Dynamic Scheduling Approach Based on Release Time Series Forecasting for the Steelmaking Continuous Casting Production, Applied Soft Computing, 2020, vol. 92, p. 106271.
Lazarev, A.A. and Gafarov, A.A., Teoriya raspisanii. Zadachi i algoritmy (Scheduling Theory. Problems and Algorithms), Moscow: Nauka, 2011.
Brucker, P. and Knust, S., Complex Scheduling, Berlin: Springer, 2006.
Mingozzi, A., Maniezzo, V., Ricciardelli, S., and Bianco, L., An Exact Algorithm for Project Scheduling with Resource Constraints Based on a New Mathematical Formulation, Management Science, 1998, vol. 44, pp. 714–729.
Burkov, V.N., Problems of Optimum Distribution of Resources, Control Cybernetics, 1972, vol. 1, no. 2, pp. 27–41.
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The paper was supported by the Russian Science Foundation (project no. 23-21-00293).
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This paper was recommended for publication A.A. Lazarev, a member of the Editorial Board
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Kibzun, A.I., Rasskazova, V.A. Linear Integer Programming Model as Mathematical Ware for an Optimal Flow Production Planning System at Operational Scheduling Stage. Autom Remote Control 84, 529–542 (2023). https://doi.org/10.1134/S0005117923050065
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DOI: https://doi.org/10.1134/S0005117923050065