АЛГОРИТМ ОПТИМАЛЬНОГО УПРАВЛЕНИЯ ЗАМКНУТОЙ СИСТЕМОЙ РЫНКА ТРУДА НА ЗАДАННОМ ВРЕМЕННОМ ИНТЕРВАЛЕ

The ratio of supply and demand in the labor market is an important criteria for the effectiveness of the functioning of the economic system at the macro level. Improving the effectiveness of employers' personnel policy requires the development of new control tools and forecasting of dynamic labor market processes at the macro and micro levels. The problem of optimal control of the previously proposed closed labor market system is considered. The problem of optimal control of a system described by a system of nonlinear differential equations is formulated in general form. Aim. Finding piecewise constant control values at which the price-quality ratio in the labor market will be maximum over the next three years. Materials and methods. According to the concept of the model, the subjects of the labor market are divided into three categories depending on the amount of demand for their labor: subjects of high, low and medium qualifications. A hypothesis has been adopted according to which vacant places in the labor market are considered to be occupied by low-skilled subjects. Due to the previously proven uniqueness of solving the problem of optimal control of a closed labor market, a greedy algorithm for finding the maximum value of the price-quality ratio in the labor market is justified. Using Wolfram Mathematica, according to the method found earlier, the formulated optimal control problem was solved at each time half-interval. Results. Control values have been obtained at which the price-quality ratio in the labor market of the village of Sylva in the Perm Territory will be maximum over the next three years. The results substantiate the recommendation to introduce stricter requirements for applicants for vacant positions at the city-forming enterprise of the village of Sylva in the Perm Territory.Соотношение спроса и предложения на рынке труда – один из важнейших критериев эффективности функционирования экономической системы на макроуровне. Решение вопросов управления и прогнозирования динамики кадров на рынке труда является важным в силу того, что качество продукции напрямую зависит от уровня квалифицированности рабочей силы. Повышение эффективности кадровой политики работодателей требует разработки новых инструментов управления и прогнозирования динамических процессов рынка труда на макро- и микроуровнях. Рассматривается задача оптимального управления предложенной ранее замкнутой системой рынка труда. Сформулирована в общем виде задача оптимального управления системой, описываемой системой нелинейных дифференциальных уравнений. Цель исследования: нахождение кусочно-постоянных значений управления, при которых соотношение «цена – качество» на рынке труда будет максимальным в течение ближайших трёх лет. Материалы и методы. Согласно концепции модели, субъекты рынка труда делятся на три категории в зависимости от величины спроса на их труд: субъекты высокой, низкой и средней квалификации. Принята гипотеза, согласно которой вакантные места на рынке труда считаются занятыми субъектами низкой квалификации. В силу доказанной ранее единственности решения задачи оптимального управления замкнутым рынком труда обоснован жадный алгоритм нахождения максимального значения соотношения «цена – качество» на рынке труда. С помощью Wolfram Mathematica по найденному ранее способу сформулированная задача оптимального управления решена на каждом временном полуинтервале. Результаты. Получены значения управления, при которых соотношение «цена – качество» на рынке труда посёлка Сылва Пермского края в течение ближайших трёх лет будет максимальным. Результаты обосновывают рекомендацию ввести более строгие требования к соискателям вакантных должностей на градообразующем предприятии посёлка Сылва Пермского края

Comparativo entre a estratégia gulosa e a programação dinâmica para o problema do troco com sistemas de moedas canônicos

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade UnB Gama, 2018.O problema do troco é uma especialização do problema da mochila, sendo possível resolvêlo com um algoritmo de programação dinâmica. É possível, também, resolver o problema utilizando um algoritmo guloso quando o sistema de moedas do problema é canônico. Este trabalho analisa e compara os tempos de execução dos algoritmos de programação dinâmica, guloso e de um algoritmo de determinação da canonicidade em cima de sistemas de moedas gerados pseudo-aleatoriamente. Os algoritmos foram implementados e seus tempos mensurados na linguagem de programação C++, seguindo o padrão C++14. Foi verificado que, apenas para sistemas de moedas com tamanhos pequenos (até 76 moedas), o algoritmo de programação dinâmica se mostra mais eficiente que os algoritmos guloso e de determinação de canonicidade, este necessário para garantir a canonicidade do sistema e assegurar a correção do algoritmo guloso.The coin change problem is a specialization of the knapsack problem, being possible to solve it with a dynamic programming algorithm. It is also possible to solve the problem using a greedy algorithm when the coin system is canonical. This work analyzes and compares the execution times of dynamic programming, greedy and canonicity determination algorithms on top of pseudo-randomly generated coin systems. The algorithms were implemented in the C++ programming language, following the C++ 14 standard. It was verified that, solely for coin systems with small sizes (up to 76 coins), the dynamic programming algorithm is more efficient than the greedy one, along with the canonicity determination algorithm, which is used to guarantee the canonicity of the system and enable the use of the greedy algorithm

Greedy and dynamic programming by calculation

Dissertação mestrado integrado em Informatics EngineeringThe mathematical study of the greedy algorithm provides a blueprint for the study of Dynamic Programming (DP), whose body of knowledge is largely unorganized, remaining obscure to a large part of the software engineering community. This study aims to structure this body of knowledge, narrowing the gap between a purely examplebased approach to DP and its scientific foundations. To that effect, matroid theory is leveraged through a pointfree relation algebra, which is applied to greedy and DP problems. A catalogue of such problems is compiled, and a broad characterization of DP algorithms is given. Alongside, the theory underlying the thinning relational operator is explored.O estudo matemático do algoritmo ganancioso («greedy») serve como guia para o estudo da programação dinâmica, cujo corpo de conhecimento permanece desorganizado e obscuro a uma grande parte da comunidade de engenharia de software. Este estudo visa estruturar esse corpo de conhecimento, fazendo a ponte entre a abordagem popular baseada em exemplos e os métodos mais teóricos da literatura científica. Para esse efeito, a teoria dos matroides é explorada pelo uso de uma álgebra de relações pointfree, e aplicada a problemas «greedy» e de programação dinâmica. Um catálogo de tais problemas é compilado, e é feita uma caraterização geral de algoritmos de programação dinâmica. Em paralelo, é explorada a teoria do combinador relacional de «thinning».This work is financed by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project UIDB/50014/202