Use of uncertain additional information in newsvendor models

The newsvendor problem is a popular inventory management problem in supply chain management and logistics. Solutions to the newsvendor problem determine optimal inventory levels. This model is typically fully determined by a purchase and sale prices and a distribution of random market demand. From a statistical point of view, this problem is often considered as a quantile estimation of a critical fractile which maximizes anticipated profit. The distribution of demand is a random variable and is often estimated on historic data. In an ideal situation, when the probability distribution of demand is known, one can determine the quantile of a critical fractile minimizing a particular loss function. When a parametric family is known, maximum likelihood estimation is asymptotically efficient under certain regularity assumptions and the maximum likelihood estimators (MLEs) are used for estimating quantiles. Then, the Cramer-Rao lower bound determines the lowest possible asymptotic variance for the MLEs. Can one find a quantile estimator with a smaller variance then the Cramer-Rao lower bound? If a relevant additional information is available then the answer is yes. This manuscript considers minimum variance and mean squared error estimation which incorporate additional information for estimating optimal inventory levels

Use of uncertain external information in statistical estimation

A product’s life cycle hinges on its sales. Product sales are determined by a combination of market demand, industrial production, logistics, supply chains, labor hours, and countless other factors. Business-specific questions about sales are often formalized into questions relating to specific quantities in sales data. Statistical estimation of these quantities of interest is crucial but restricted availability of empirical data reduces the accuracy of such estimation. For example, under certain regularity conditions the variance of maximum likelihood estimators cannot be asymptotically lower than the Cramer-Rao lower bound. The presence of additional information from external sources therefore allows the improvement of statistical estimation. Two types of additional information are considered in this work: unbiased and possibly biased. In order to incorporate these two types of additional information in statistical estimation, this manuscript minimizes mean squared error and variance. Publicly available Walmart sales data from 45 stores across 2010-2012 is used to illustrate how these statistical methods can be applied to use additional information for estimating weekly sales. The holiday effect (sales spikes during holiday weeks) adjusted for overtime trends is estimated with the use of relevant external information

Accounting for deficit in ABC-XYZ analysis

This work proposes an ABC-XYZ-type analysis modified with observed merchandise deficit. The deficit is determined by right censoring. This manuscript proposes to account for right censoring in the ABC-XYZ analysis. The modified ABC-XYZ analysis updates many important quantities including projected income, the coefficient of variation, and the Kaplan-Meier estimator. An illustrative example shows that the classical ABC-XYZ algorithm underestimates a merchandise value when deficit was observed; magnitude of the coefficient of variation is also underestimated. The new method corrects this bias and recalculates overall profit and the coefficient of variation

Regional risks of artificial forestation in the steppe zone of Kazakhstan (case study of the green belt of Astana)

This article deals with results of research on artificial forest in a green zone around the city of Astana. The authors of the article established temporary sample plots where condition, capacity for survival, and growth of trees were observed by standard techniques adapted to conditions of the forest-steppe subzone of Northern Kazakhstan. The reasons for the unsatisfactory condition of the planted forest were found and recommendations on improvement were made. The conclusion was drawn that to establish forest plantations it is necessary to select such species of trees and shrubs that will be resistant in specific conditions to the negative factors of urban lands. A possibility of replanting adult trees to intensify reforestation was also studied. The authors analyzed the dynamics of Silver birch preservation in 2011-2017. The Mann-Whitney-Wilcoxon U test was used to prove the presence of differences between the types of trees' average preservations. Based on the data thus obtained, it was concluded that the forest plantations created by the different methods differed significantly in terms of the preservation rate, as well as in the heights and diameters of the trees. Forecasts of tree preservations in 2018 were made using moving average and linear regression methods. The best forecasts were chosen in terms of the mean relative absolute error of approximation. The results confirmed an initial hypothesis predicting significant differences between the methods used for artificial reforestation: the non-replanted trees are expected to have the highest rate of preservation, whereas the trees replanted to a low location, the lowest preservation rate. The prediction of the preservation rate of forest plantations of Silver birch created by the different methods will allow reducing the risks when conducting forestry activities on artificial reforestation. Regional features must be taken into account in the development of recommendations for a comprehensive system of measures which are based on the scientific forestry techniques to ensure optimum reforestation

Wind speed prediction performance based on modal decomposition method

As wind energy and other renewable energy sources are valued by various countries, it is very important to estimate and predict the wind energy level. The accuracy of wind energy prediction mainly depends on the accuracy of wind speed prediction. Therefore, to seek ways of improvement the accuracy of wind speed prediction has become the most important issue. In this paper, three different decomposition methods and commonly used wind speed prediction methods are used to compose the corresponding combined models, and to study which combined prediction model has higher accuracy. According to data research conducted by the National Meteorological Science Center, experiments show that the prediction accuracy of the combined prediction model using the Variational mode decomposition (VMD) method is higher than that of the combined prediction model using empirical mode decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD)

The ABC-XYZ analysis modified for data with outliers

The ABC-XYZ analysis is widespread in moder

The ABC-XYZ analysis modified for data with outliers

The ABC-XYZ analysis is widespread in moder