Mathematical models and methods of objects’ location with area zoning in emergency logistics


  • Koriashkina Larysa
  • Dziuba Serhii



emergency logistics, multiplex partitioning of sets, multiple circle coverage, modeling, optimization


The mathematical models for distribution processes related to organizing precautionary measures in the event of threats or occurrences of man-made emergencies are presented. The tasks include optimal zoning of territories with the fixing of zones by objects of social purpose for service provision. Provision is made for: the possibility of overlapping zones in case the nearest center cannot provide the service; optimal placement of a certain number of new cen-ters of emergency logistics systems with simultaneous redistribution of the load on all their structural elements; the selection of locations of structural subdivisions based on existing fa-cilities. The optimality criteria involve minimizing either the time to provide the service even to the most remote object in the given territory, or the total distance to the nearest centers from consumers that are densely distributed in the given territory, and/or the organizational costs associated with the arrangement of new centers. Mathematical models are proposed in the form of continuous problems of optimal multiplex partitioning of sets with a linear or minimax functional of quality. The latter provides such placement of centers that provides op-timal multiple coverage of the territory (with a minimum radius of multiple coverage). Meth-ods for solving the formulated problems were developed using LP-relaxation of linear prob-lems with Boolean variables, duality theory to reduce the initial problems of infinite-dimensional programming to problems of conditional optimization of a non-smooth function of several variables, and modern methods of non-differentiated optimization.


Koriashkina, L.S., Dziuba, S.V. (2023). Pererozpodil navantazhennia v systemi ekstrenoi lohistyky za rakhunok optymalnoho rozmishchennia yii novykh pidrozdiliv. International sci-entific-practical conference “Modern trends and prospects for the development of science, education and society”: conference proceedings (Aarhus, Denmark, August 10, 2023). Aarhus, Denmark: Scholarly Publisher ICSSH, 2023. – С. 42 – 43.

Hezam, I.M., Nayeem, Mk., Lee, G.M. (2021). A Systematic Literature Review on Mathematical Models of Humanitarian Logistics. Symmetry; 13(1):11.

Seraji H., Tavakkoli-Moghaddam R., Asian S., Kaur H. (2022). An integrative location-allocation model for humanitarian logistics with distributive injustice and dissatisfaction un-der uncertainty. Annals of Operations Research, Springer, vol. 319(1), p. 211-257, December. DOI: 10.1007/s10479-021-04003-5

Weng, X., Duan, S., Zhang, J., Fan, H. (2024). A Material Allocation Model for Public Health Emergency under a Multimodal Transportation Network by Considering the Demand Priority and Psychological Pain. Mathematics, 12(3):489.

Tlili, T., Abidi, S., Krichen, S. (2018). A mathematical model for efficient emergency transportation in a disaster situation. American Journal of Emergency Medicine, 36, 1585–1590. DOI:10.1016/j.ajem.2018.01.039

Safaei, A.S., Farsad, S., Paydar, M.M. (2018). Emergency logistics planning under supply risk and demand uncertainty. Oper Res Int J.

Ehsani, B., Karimi, H., Bakhshi, A., Aghsami, A., Rabbani, M. (2023). Designing humani-tarian logistics network for managing epidemic outbreaks in disasters using Internet-of-Things. A case study. Computers and Industrial Engineering. 175:C. Online publication date: 1-Jan-2023.

Koriashkina, L., Us, S., Odnovol, M., Stanina, O., Dziuba, S.(2024). Two-stage problems of optimal location and distribution of the humanitarian logistics system’s structural subdivi-sions. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, 1.

Dziuba S., Koriashkina, L., Stanina, O., Lubenets, D. (2023). Mathematical models of optimization problems of partially two-stage population evacuation with territory segmentation. Information Technol-ogy: Computer Science, Software Engineering and Cyber Security, 3, 13–21, doi:

Mallozzi, L., Puerto, J., Rodríguez-Madrena, M. (2019). On Location-Allocation Prob-lems for Dimensional Facilities. Journal of Optimization Theory and Applications, Springer, vol. 182(2): 730-767, August. DOI: 10.1007/s10957-018-01470-y

Mohamadi, A., Yaghoubi, S., Pishvaee, M.S. (2019) Fuzzy multi-objective stochastic programming model for diaster relief logistics considering telecommunication infrastructures: a case study. Oper Res Int J, 19(1): 59-99

Koriashkina, L., Sazonova, M., Odnovol, M. (2023). Algorithms of territorial segmenta-tion for a facility network with overlapping service zones. Information Technology: Computer Science, Software Engineering and Cyber Security, 2, 12–25. doi:

Dziuba, S., Bulat, A., Koriashkina, L., Blyuss, B. (2023). Discrete-Continuous Model of the Optimal Location Problem for the Emergency Logistics System. Available at SSRN: