Математичне моделювання задач оптимізації в економіці

Abstract

Адаптовано один із модифікованих методів розміщення багатовимірних об’єктів (п-вимірних паралелепіпедів) до розв’язання ряду оптимізаційних економічних задач на прикладі задачі оптимального планування діяльності підприємства (раціонального розподілу ресурсів), що дозволило звести розв’язок задачі до спрямованого перебору припустимих варіантів розподілу ресурсів. Наведено можливі типи вихідни х даних оптимізаційних задач та основні вимоги до них.

The impact of anthropogenic factor on decision-making, where by mathematical models developed in economics do not actually work or are adjusted during implementation that ultimately influences the work of specific companies and macroeconomic indicators is recognized as one of the problems of objective economic forecasting. One of the modified mathematical methods for solving a number of optimization economic problems is adapted in this article. The method is illustrated with the example of the problem regarding a company optimal planning. It is necessary to compile the production program of an optimal sequence of works’ execution at the enterprise, subject to the limited availability of the enterprise resources and minimize the completion time of a program (a set of specified work). The result is the optimal sequence of work and optimal deadline (determined by the optimal start and end times of execution of each work). When solving a problem, each job is considered as n-parallelepiped with the dimensions corresponding to the resources of the relevant work. Among the main types of resources transient (among the n gauges there is measuring “time” – watch type) and resource types (among the n meter there is no meter “time” – resource type) can be distinguished in economic objectives. Note that “meter” can be considered as a number of products of a certain type, the amount of a certain type of resources, the number of workers, profits (funds), etc. The following are among the main requirements for the establishment of baselines: the possibility of priority, simultaneity, or indifference of works; delay of work for a certain time; independence of resources, etc. Computational experiments confirm the efficiency of the method described from the point of view of forming the program, optimal sequence of works’ execution close to the optimum.