Production of crushed stone from carbonate rocks intended for road construction produces а huge amount of screening fractions, which accumulate in landfills. To date, in the Leningrad region 70 million tons of waste from the production of crushed stone has been accumulated. Its use as an ameliorant can significantly reduce the severity of acid soil problems in the region and at the same time solve an important environmental problem – landfill disposal. In a 6-year 10-variant microfield experiment, a comparative study of the reclamation properties of the screening dolomite dropouts without separation into fractions and the particles of 5–7 and 7–10 mm in size used for liming in increasing doses was conducted on a medium-acid sod-podzolic light loamy soil. These dolomite screenings neutralized soil acidity already in the first year, while their positive aftereffect lasted for at least 6 experimental years. The use of a natural mixture of the screenings in high doses was not effective because of high losses of bases from soil. Clustering of individual experimental variables was carried out by their effect on the pH_KCl value over the entire experiment period.

This paper considers a model of opinion dynamics in a social network with two principals, in which the members may affect the opinions of each other and their opinions evolve according to a time-homogeneous Markov chain. We study the existence of a consensus in this network for two types of influence models, namely, when the principals may or may not affect the opinions of each other directly. In addition, we find the values of social network parameters under which a consensus is reached. For the cases without a consensus in its standard definition, we introduce the notion of a consensus of the majority and find the parameter values under which it is reached. Two numerical examples illustrate the obtained theoretical results.

Эдельгериев Р.С.Х., Иванов А.Л., Донник И.М., Багиров В.А., Кулик К.Н., Беляев А.И., Бедрицкий А.И., Козлов Д.Н., Савин И.Ю., Духанин Ю.А., Соломина О.Н., Куст Г.С., Юрова А.Ю., Вильфанд Р.М., Катцов В.М., Кулинцев В.В., Абдулаева А.С., Алымбаева Ж.Б., Андреев С.Г., Андреева О.В. и др.//2021

The hub location–allocation problem under uncertainty is a real-world task arising in the areas such as public and freight transportation and telecommunication systems. In many applications, the demand is considered as inexact because of the forecasting inaccuracies or human’s unpredictability. This study addresses the robust uncapacitated multiple allocation hub location problem with a set of demand scenarios. The problem is formulated as a nonlinear stochastic optimization problem to minimize the hub installation costs, expected transportation costs and expected absolute deviation of transportation costs. To eliminate the nonlinearity, the equivalent linear problem is introduced. The expected absolute deviation is the robustness measure to derive the solution close to each scenario. The robust hub location is assumed to deliver the least costs difference across the scenarios. The number of scenarios increases size and complexity of the task. Therefore, the classical and improved Benders decomposition algorithms are applied to achieve the best computational performance. The numerical experiment on CAB and AP dataset presents the difference of resulting hub networks in stochastic and robust formulations. Furthermore, performance of two Benders decomposition strategies in comparison with Gurobi solver is assessed and discussed.