Mathematical modeling of combat operations with planning of target distribution coefficients for one of the opposing sides

Oleksandr Fursenko, Nataliia Chernovol, Olha Udodova, Yaroslav Savchuk

Abstract


The subject of the study is models of combat operations. The purpose of this study is to build mathematical and computer models to identify the optimal target distribution coefficients of the active side in order to inflict the greatest losses on the enemy at a given time for the case when the sides have several types of weapons and direct fire at each type of enemy combat units with some target distribution coefficients. Objectives: 1) to consider the case when the active side has one type of weapon, and the other side has two dissimilar types of weapons; 2) to generalize the problem to the case when the active side has n dissimilar types of weapons, and the other side has m dissimilar types of weapons; 3) to conduct a detailed study of the solution of the problem in the case when the sides have two dissimilar types of weapons. The following results were obtained: 1) a mathematical and computer models for the first case of the problem were built, the admissibility of the problem parameters was analyzed, and the corresponding numerical calculations were presented; 2) a mathematical model for the second case of the problem was created, the admissibility of the problem parameters was analyzed; 3) a mathematical and computer model for the third case was built and studied, the corresponding numerical calculations were presented, and the analysis was performed. Conclusions. The examples considered in this paper illustrate that, using a computer model, it is possible to predict how to allocate combat resources to fight the enemy to achieve success in combat at a given time if the enemy has two types of combat units. The problem has a solution in the general case, which requires maximizing a function of many variables at admissible lattice nodes, whose coordinates are the first side's objective coefficients. The paper shows how to find these admissible nodes. Numerical calculations before generalizing the problem demonstrate that it is possible by changing the time to predict the battle even in cases where the parties have several types of weapons.

Keywords


optimization mathematical model of combat dynamics; combat resources; velocity of impact; target distribution coefficient; intact combat units; striking potential

Full Text:

PDF

References


Cannon, Shaun. Alliance Concept for Multi-Domain Operations. An AIRCOM Perspective. Journal Edition 37, 2024. Available at: https://www.japcc.org/articles/the-alliances-transition-to-multi-domain-operations (accessed 12.12.2025).

Hercilla Heredia, L. G. Mathematical Models for Planning Combat Strategy and Decision Making. 22nd LACCEI International Multi-Conference for Engineering, Education, and Technology: Sustainable Engineering for a Diverse, Equitable, and Inclusive Future at the Service of Education, Research, and Industry for a Society 5.0. Hybrid Event, San Jose – Costa Rica, July 17 - 19, 2024, p. 1-8. DOI: 10.18687/LACCEI2024.1.1.1368

Kuikka, V. Probabilistic Modelling of System Capabilities in Operations. Systems, 2023, vol. 11, iss. 3, article no. 115. DOI: 10.3390/systems11030115.

Popken, D.A., & Cox Jr., L.A. Simulation-based planning for theatre air warfare. Proceedings of SPIE - The International Society for Optical Engineering, 2004, vol. 5423, pp. 54-65. DOI: 10.1117/12.541137.

Atkinson, M.P., Kress, M., & MacKay N.J. Targeting, deployment, and loss-tolerance in lanchester engagements. Operations Research, 2021. vol. 69, no. 1, pp. 71-81. DOI: 10.1287/opre.2020.2022.

Ji, X., Zhang, W.P., Xiang, F.T., Yuan, W., & Chen, J. A swarm confrontation method based on Lanchester law and Nash equilibrium. Electronics, 2022, vol. 11, no. 6, pp. 896–911. DOI: 10.3390/electronics11060896.

Kostić, M., & Jovanović, A. Modeling of Real Combat Operations. Journal of Process Management and New Technologies, 2023, vol. 11, iss. 3-4, pp. 39-56. DOI: 10.5937/jpmnt11-46482.

Kress, M., Caulkins, J. P., Feichtinger, G., Grass, D., & Seidl, A. Lanchester model for three-way combat. European Journal of Operational Research, 2018, vol. 264, no. 1., pp. 46-54. DOI: 10.1016/j.ejor.2017.07.026.

Zhang, L. Combat modelling using Lanchester equations. International Journal of Mathematical Education in Science and Technology, 2024, vol. 55, iss. 2, pp. 224-234. DOI: 10.1080/0020739X.2023.2242863.

Cangiotti, N., Capelli, M., & Mattia, S. A generalization of unaimed fire Lanchester’s model in multi-battle warfare. Operational Research, 2023, vol. 23, no. 2, pp. 38–57. DOI: 10.1007/s12351-023-00776-8.

González, E, & Villena, M. Spatial Lanchester models. European Journal of Operational Research, 2011, vol. 210, no. 3, pp. 706-715. DOI: 10.1016/j.ejor.2010.11.009.

Kostić Mladen, S., AcaJovanović, D., & Mitar Kovač, V. Modeling of combat operations. Vojnotehnicki glasnik/Military Technical Courier, 2023, vol. 71, iss. 3, pp. 529-558. DOI: 10.5937/vojtehg71-43509.

Nowicki, T. Modelling and simulation of combat operations in SimCombCalculator application. Journal of Telecommunications and Information Technology, 2004, vol. 4, pp. 14-20.

Xi, Z. Kou, Y., Li, Y., Li, Z., & Lv, Y. A Dynamic Air Combat Situation Assessment Model Based on Situation Knowledge Extraction and Weight Optimization. Aerospace, 2023, vol. 10, iss. 12, article no. 994. DOI: 10.3390/aerospace10120994.

Li, Y., Lyu, Y., Shi, J., & Li, W. Autonomous Maneuver Decision of Air Combat Based on Simulated Operation Command and FRV-DDPG Algorithm. Aerospace, 2022, vol. 9, iss. 11, article no. 658. DOI: 10.3390/aerospace9110658.

Wu, J., Lu, Y., Li, D., Ren, Y., Zhou, W., & Yuan, S., Modeling and Solution for Course of Action Planning Driven by Operational Task Network. IEEE Access, 2025, vol. 13, pp. 41169-41193.

Fursenko О.К., & Chernovol N.М. Mathematical Modelling of Combat Operations with the Possibility of Redistributing Combat Resources between the Areas of Contact and Distributing Reserves. Radio Electronics, Computer Science, Control, 2025, no. 1, pp. 63–74. DOI: 10.15588/1607-3274-2025-1-6.

Fursenko О.К., Chernovol N.М., Udodova O.I., & Savchuk Ya. I. Optymalʹnyy rozpodil resursiv pry matematychnomu modelyuvanni boyovykh diy [Optimal Resource Allocation in Mathematical Modeling of Combat Operations]. Systemy obrobky informatsiyi ̶ Information processing systems, 2025, iss. 3 (182), pp. 85-90. DOI: 10.30748/soi.2025.182.09 (In Ukrainian).

Grabchak, V. I., Suprun, V. M., Vakal, A. O., & Petrenko, P. M. Uzahal'nennya analitychnoyi modeli boyu dlya rizno-ridnykh protydiyuchykh uhrupuvan' [Usage of analytical battle models for young anti-youth groups]. Zbirnyk naukovykh prats' Kharkivs'koho natsional'noho universytetu Povitryanykh Syl ̶ Collection of Science Practitioners Kharkiv National Air Force University, 2008, iss. 2(17), pp. 10-13. (In Ukrainian).

Fursenko, O. K., & Chernovol, N. M. Lanchesterovs'ki modeli boyovykh diy [Lanchester models of combat operations]. Zbirnyk naukovykh prats' Kharkivs'koho natsional'noho universytetu Povitryanykh Syl ̶ Collection of Science Practitioners Kharkiv National Air Force University, 2020, iss. 4(66), pp. 85-91. DOI: 10.30748/zhups.2020.66.12. (In Ukrainian).




DOI: https://doi.org/10.32620/reks.2026.1.16

Refbacks

  • There are currently no refbacks.