Математичне моделювання та розв’язання задачі оптимального управління діяльністю підприємства

Abstract

Запропоновано метод розв’язання управлінської задачі, зокрема під час прийняття рішень для складання оптимального плану діяльності підприємства, як комбінація математичних методів і економічних принципів. Здійснюється перехід від розв’язання економічної задачі до еквівалентної математичної. Для знаходження можливого варіанта розв’язку використовуються фрактали.

For the effective functioning of the enterprise, its owners and specialists must take optimal management decisions based on the processing of initial information (data) and include the determination of the means and ways to achieve them through a comparative assessment of alternative (possible) options and the adoption of the most acceptable of them in the expected conditions. The common methods for solving management problems include dynamic programming – a way to solve complex problems by breaking them down into simpler subtasks. One of the main conditions for using the dynamic programming method is the additivity of problems. Among the disadvantages, one can single out the complexity of use with a large number of task restrictions. The article proposes a method for solving a management problem, in particular when making decisions for drawing up an optimal plan for an enterprise's activities, as a combination of mathematical methods and economic principles. Having set the conditional density, each action (process) is represented in the form of an n-parallelepiped (rectangular n-dimensional parallelepiped). This made it possible to solve the economic problem: to draw up a possible version of the optimization plan for the production of products, provided that the resources available at the enterprise are limited, to go to the mathematical one: to arrange the n-parallelepipeds in a given n-parallelepiped in such a way as to minimize the area remaining empty after placement (or to maximize the coefficient filling it in). Fractals are used to find the initial possible placement of n-parallelepipeds. Thus, the work has developed an algorithm for sequential actions and mathematical calculations to solve the problem of optimal management of enterprise activities.