MODIFIED GENETIC ALGORITHM APPROACH FOR SOLVING THE TWO-STAGE LOCATION PROBLEM
Authors: Serhieiev O. S. , Us S. A. 
Published: October 2023

Context. Optimization of logistics processes is one of the important tasks of supply chain management in various fields, including medicine. Effective coordination in medical logistics is essential to ensure public health and prosperity. This is especially essential during global emergencies when the rapid and efficient distribution of medicines is critical. In addition, professional logistics management is critical to delivering humanitarian aid, where the timely transportation of medical supplies and resources can be lifesaving. The most advanced technologies and algorithms are being used to improve medical logistics processes. This paper considers modifying the genetic algorithm for solving the two-stage location problem in supply chain management in the distribution of medicines and medical equipment.
Objective. The work aims to build a model and develop an algorithm for solving a two-stage location problem in the context of the medical logistics problem with further analysis of their applications and performance.
Method. We propose to use a genetic algorithm to solve a two-stage logistics problem. The peculiarities of this algorithm are the modification of evaluation procedures and the use of mixed mutation, which allows for solving the problem effectively, considering irregularities in the statement regarding the subject – the limits on the centers’ location at several stages of the logistic process.
Results. The paper deals with a two-stage location problem with constraints on the maximum number of centers. Considering the specific requirements of medical logistics in the transportation context of medicines and medical equipment, a mathematical model and modification of the genetic algorithm are proposed. The developed algorithm is tested on model tasks and can produce effective solutions for problems ranging in size from 25 to 1000. The solution process takes longer for larger problems with dimensions from 1001 to 2035. Additionally, the influence of increasing the maximum generations number on the time of execution is investigated. When the maximum generation value increases from 50 to 100 and from 100 to 150 generations, the algorithm’s execution time increases by 45.69% and 51.68%, respectively. 73% of the total execution time is dedicated to the evaluation procedure. The algorithm is applied to the medical logistics problem in the Dnipropetrovsk region (Ukraine). An efficient solution is obtained within an acceptable execution time.
Conclusions. A mathematical model for a two-stage location problem in the context of medical logistics is introduced. It considers the peculiarities of the medical field. A solution algorithm based on a genetic approach is developed and applied to the medical logistics problem. The algorithm has been tested on model tasks of varying sizes, with a comprehensive analysis conducted on the correlation between the problem size and the algorithm’s running time. In addition, it is investigated how the maximum number of generations affects the algorithm’s execution time. The role of each stage in the genetic algorithm research towards the overall effectiveness of the algorithm is researched. The obtained results indicate high efficiency and wide application possibilities of the proposed mathematical model and algorithm. The developed method demonstrates high performance and reliability.