Small Extended Formulations for Cyclic Polytopes

We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} for the cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in [n]. First, we find an extended formulation of size log(n) for d= 2. Then, we use this as base case to construct small-rank nonnegative factorizations of the slack matrices of higher-dimensional cyclic polytopes, by iterated tensor products. Through Yannakakis's factorization theorem, these factorizations yield small-size extended formulations for cyclic polytopes of dimension d>2

Hotel business: customer loyalty management

The relevance of the chosen direction of the research is due to the need to develop modern marketing management technologies for the adaptation, survival and further development of hotel and restaurant industry, taking into account the fact that the current situation characterized by a socio-economic crisis, has been aggravated by the consequences of the COVID-19 coronavirus pandemic, which together led to new challenges in the hotel and restaurant industry. The hotel and restaurant product is presented as a combination of material product, services and atmosphere, which together form a unique selling proposition in the hotel and restaurant industry. With this in mind, it is reasonable that consumer loyalty to establishments of the hotel and restaurant industry is characterized by customer satisfaction, adherence, advocacy and impressions, which together reflect the perception of the establishment, attitude towards it and future intentions. The use of the proposed scientific and practical approach will make it possible to determine the level of customer loyalty in the hotel and restaurant industry as a whole and for each of its characteristics, to make justified management decisions in accordance with the stage of customer loyalty formation. In order to increase customer loyalty in the hotel and restaurant industry in today's changing situation and conditions of uncertainty, a number of practical recommendations are given to ensure the unique competitive advantages of the hotel product, the introduction of modern information technologies, and improvement of the service quality

Алгоритм ветвей и границ для задачи коммивояжера не является алгоритмом прямого типа

In this paper, we consider the notion of a direct type algorithm introduced by V. A. Bondarenko in 1983. A direct type algorithm is a linear decision tree with some special properties. the concept of a direct type algorithm is determined using the graph of solutions of a combinatorial optimization problem. e vertices of this graph are all feasible solutions of a problem. Two solutions are called adjacent if there are input data for which these and only these solutions are optimal. A key feature of direct type algorithms is that their complexity is bounded from below by the clique number of the solutions graph. In 2015-2018, there were five papers published, the main results of which are estimates of the clique numbers of polyhedron graphs associated with various combinatorial optimization problems. the main motivation in these works is the thesis that the class of direct type algorithms is wide and includes many classical combinatorial algorithms, including the branch and bound algorithm for the traveling salesman problem, proposed by J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel in 1963. We show that this algorithm is not a direct type algorithm. Earlier, in 2014, the author of this paper showed that the Hungarian algorithm for the assignment problem is not a direct type algorithm. us, the class of direct type algorithms is not so wide as previously assumed.В настоящей работе рассматривается понятие линейного разделяющего алгоритма прямого типа, введенное В. А. Бондаренко в 1983 г. Понятие алгоритма прямого типа определяется с помощью графа решений задачи комбинаторной оптимизации. Вершинами этого графа служат все допустимые решения задачи. Два решения называются смежными, если существуют входные данные, для которых эти решения и только они являются оптимальными. Ключевой особенностью алгоритмов прямого типа является то, что их трудоемкость оценивается снизу кликовым числом графа решений. В 2015–2018 гг. было опубликовано пять работ, основными результатами которых являются оценки кликовых чисел графов многогранников, ассоциированных с различными задачами комбинаторной оптимизации. В качестве основной мотивации в этих работах приводится тезис о том, что класс алгоритмов прямого типа является широким и включает в себя многие классические комбинаторные алгоритмы, в том числе алгоритм ветвей и границ для задачи коммивояжера, предложенный J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel в 1963 г. Мы покажем, что этот алгоритм не является алгоритмом прямого типа. Ранее, в 2014 г., автором настоящей работы было показано, что венгерский алгоритм для задачи о назначениях не является алгоритмом прямого типа. Таким образом, класс алгоритмов прямого типа не является настолько широким, как предполагалось ранее

An integrated approach to assessing the economic and ecological potential of the agricultural industry of the region

The article is devoted to topical issues of developing the economic and environmental potential of the region's agricultural industry. The opinions of domestic scientists regarding the formation of a system of indicators for assessing economic and environmental potential, as well as their main components, were studied. Based on the analysis, it is proposed to divide the indicators into four blocks. The first will include indicators of economic potential, the second will include aspects related to environmental potential, and when forming the third block, regional characteristics will be taken into account: climatic, social, natural, etc. The last, fourth block will include parameters reflecting the external impact on the economic and environmental potential of the region’s agricultural industry. An integrated approach to assessing the economic and environmental potential of the region’s agricultural industry has been formed, taking into account all possible external and internal factors

Green economy as a factor of sustainable development of the state

The problem of transition to a “green” economy based on sustainable technological changes is caused by global environmental pollution of the ecosystem, leading to warming and environmental change, insufficient natural resource potential to meet the vital needs of the planet’s population, does not contribute to its development. The practical content is determined by the fact that theoretical and methodological provisions, conclusions and scientific and practical recommendations form the scientific basis for the development of a new holistic concept for the development of a “green economy” in Russia. Conclusions are drawn that the “green” economy can become a driver of development of the Russian Federation, therefore the prospects for creating a “green” economy become dynamic and quite achievable