ОПТИМІЗАЦІЯ ВИРОБНИЧИХ ТА ЛОГІСТИЧНИХ ЗАДАЧ У ФАРМАЦІЇ ЗАСОБАМИ МАТЕМАТИЧНОГО ТА КОМП’ЮТЕРНОГО МОДЕЛЮВАННЯ

This publication provides an analysis of the development of mathematical programming from the approaches of J. Lagrange to modern methods of lin- ear and nonlinear programming, which have found widespread application in the economy and the pharmaceutical industry. Special attention is given to mathematical modeling of optimal resource distribution and transport logistics in pharmacy. The role of computer mathematics systems (CMS), such as MathCad, in simplifying the process of solving optimization problems is considered. MathCad allows for quick formulation and computation of linear and nonlinear programming tasks, automating calculations and minimizing the risk of errors. Due to the ability to promptly adjust input pa- rameters, such as raw material stocks and production costs, various production and logistics scenarios can be effectively modeled. The study demon- strates the methodology for solving an optimization problem in drug production, where the objective function is maximizing the profit from sales. Ad- ditionally, a methodology for solving a typical transport problem, which involves minimizing transportation costs from several warehouses to several consumers with resource constraints, is proposed. The potential method, which ensures the adjustment of transport routes to reduce overall logistics costs, is applied. The educational aspect of applying mathematical models in the preparation of future pharmacy masters is also considered. The use of computer modeling in the educational process contributes to the development of analytical thinking and skills in working with optimization methods, which are essential for effective resource management in the pharmaceutical sector. This work proposes the implementation of real pharmaceutical in- dustry problems during practical lessons in the course «Computer Modeling in Pharmacy», which are crucial for the formation of professional compe- tencies for future pharmaceutical workers. Thus, the article presents a comprehensive study that combines theoretical and practical aspects of mathe- matical modeling in pharmacy. The prospects for its use to improve the efficiency of production processes, optimize logistical decisions, and enhance the educational process are identified. The results obtained indicate the effectiveness of using mathematical programming methods to solve optimiza- tion problems in pharmacy. The use of mathematical models allows for more accurate demand forecasting, planning of production capacities, and lo- gistics processes, which, in turn, reduces the risks of shortages or surpluses of products. Further development of mathematical methods and computer technologies opens up broad prospects for improving existing processes and implementing innovations.