• Us Svitlana
  • Serhieiev Oleksii



continuous-discrete two-stage location problem, optimal set partitioning, genetic algorithm, medical logistics


The research paper focuses on logistics optimization, a critical component in supply chain management across various sectors, including healthcare. Efficient coordination of medical logistics is essential for maintaining public health and welfare, particularly during global emergencies where quick and effective distribution of medicine is crucial. This study aims to create and analyze a model and algorithm for a two-stage continuous-discrete location problem within medical logistics applications. We present a mathematical model tailored for a two-stage continuous-discrete location problem in medical logistics, considering the unique aspects of this field. The solution algorithm combines genetic methods with the optimal partition of sets theory. Additionally, we demonstrate the algorithm's effectiveness through a software application, using it to solve a representative model problem.


Antony Arokia Durai Raj K., Rajendran C. A genetic algorithm for solving the fixed-charge transportation model: two-stage problem. Computers & operations research. 2012. Vol. 39, no. 9. P. 2016–2032. DOI: 10.1016/j.cor.2011.09.020.

Cosma O., Pop P., Sabo C. An efficient solution approach for solving the two-stage supply chain problem with fixed costs associated to the routes. Procedia com-puter science. 2019. Vol. 162. P. 900–907. DOI: 10.1016/j.procs.2019.12.066 (date of access: 15.11.2023).

Lee J.-E., Gen M., Rhee K.-G. Network model and optimization of reverse logistics by hybrid genetic algorithm. Computers & industrial engineering. 2009. Vol. 56, no. 3. P. 951–964. DOI: 10.1016/j.cie.2008.09.021 (date of access: 15.11.2023).

Location-Allocation and accessibility models for improving the spatial planning of public health services / G. Polo et al. Plos one. 2015. Vol. 10, no. 3. P. e0119190. DOI: 10.1371/journal.pone.0119190 (date of access: 15.11.2023).

Gen M., Altiparmak F., Lin L. A genetic algorithm for two-stage transportation prob-lem using priority-based encoding. OR spectrum. 2006. Vol. 28, no. 3. P. 337–354. DOI: 10.1007/s00291-005-0029-9 (date of access: 15.11.2023).

Two-stage multi-objective optimization for ICU bed allocation under multiple sources of uncertainty / F. Wan et al. Scientific reports. 2023. Vol. 13, no. 1. DOI: 10.1038/s41598-023-45777-x (date of access: 22.11.2023).

Lalmazloumian M., Baki M. F., Ahmadi M. A two-stage stochastic optimization framework to allocate operating room capacity in publicly-funded hospitals under un-certainty. Health care management science. 2023. DOI: 10.1007/s10729-023-09644-5 (date of access: 22.11.2023).

Salami A., Afshar-Nadjafi B., Amiri M. A two-stage optimization approach for healthcare facility location-allocation problems with service delivering based on ge-netic algorithm. International journal of public health. 2023. Vol. 68. DOI: 10.3389/ijph.2023.1605015 (date of access: 22.11.2023).

An empirical evaluation of a two-stage healthcare facility location approach using simulation optimization and mathematical optimization / S. Mohd et al. SSRN elec-tronic journal. 2022. DOI: 10.2139/ssrn.4246268 (date of access: 22.11.2023).

Capacity allocation and scheduling in two-stage service systems with multi-class customers / Z. Zhong et al. SSRN electronic journal. 2023. DOI: 10.2139/ssrn.4431264 (date of access: 22.11.2023).

Akıncılar A., Akıncılar E. A new idea for ambulance location problem in an envi-ronment under uncertainty in both path and average speed: absolutely robust plan-ning. Computers & industrial engineering. 2019. Vol. 137. P. 106053. DOI: 10.1016/j.cie.2019.106053 (date of access: 22.11.2023).

A two-stage stochastic optimization for disaster rescue resource distribution con-sidering multiple disasters / B. Wang et al. Engineering optimization. 2022. P. 1–17. DOI: 10.1080/0305215x.2022.2144277 (date of access: 22.11.2023).

Islam S., Hassanzadeh Amin S., Wardley L. J. Supplier selection and order allo-cation planning using predictive analytics and multi-objective programming. Com-puters & industrial engineering. 2022. P. 108825. DOI: 10.1016/j.cie.2022.108825 (date of access: 22.11.2023).

Islam M. T., Miah M. M. Optimization of interval cost multi-objective transportation problem in uncertain parameters: a modified least-cost method. Journal of bangla-desh academy of sciences. 2022. Vol. 46, no. 2. P. 155–164. DOI: 10.3329/jbas.v46i2.62168 (date of access: 23.11.2023).

The forecasting of dangerous goods transport by railin poland in terms of envi-ronmental security / M. Stajniak et al. European research studies journal. 2022. Vol. XXV, Issue 2B. P. 359–368. DOI: 10.35808/ersj/2968 (date of access: 23.11.2023).

Wang X., Song J., Qunqi W. A novel bi-level programming model for structure sustainability optimization of passenger transport corridor. PLoS ONE. 2022. Vol. 17, no. 7. P. 1–21.

Serhieiev O., Us S. Analysis of modern approaches to solving discrete and con-tinuous multi-stage allocation problems. Information technology: computer science, software engineering and cyber security. 2023. No. 2. P. 50–58. DOI: 10.32782/it/2023-2-7.

Us S. A., Koriashkina L. S., Stanina O. D. An optimal two-stage allocation of ma-terial flows in a transport-logistic system with continuously distributed resource. Radio electronics, computer science, control. 2019. No. 1. P. 256–271. DOI: 10.15588/1607-3274-2019-1-24 (date of access: 17.11.2023).

Kiselova O., Koriashkina L. Nepervni zadachi optymalnoho rozbyttia mnozhyn ta r-alhorytmy : monohrafiia. Dnipro : Naukova dumka, 2015. 400 p.

Serhieiev O. S., Us S. A. Modified genetic algorithm approach for solving the two-stage location problem. Radio electronics, computer science, control. 2023. No. 3. P. 159–170. DOI: 10.15588/1607-3274-2023-3-16 (date of access: 16.11.2023).