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Building the mathematical model of the decision support system in the field of pricing for e-commerce

This work is devoted to the study of pricing issues for obtaining maximum profit when selling consumer goods at a constant purchase price. The said goods come in from either manufacturers or warehouses where the retail companies buy the goods in order to sell them directly to the consumers. The dependence of the selling rate per unit of time on the level of the added price in relation to the purchase price of the item is established by the means of sales price variation. The object of the research is the specific case of a linear approximation of said dependence, which is usually actualized in the event of either more elastic or less elastic demand for goods, when they are sold through Internet platforms. The proposed approach to determining prices of all the goods which are being sold for maximizing the total profit from the sales of all consumer goods or maximizing the total revenue throughout the whole period of sales time, based on the search of extremum points of the profit and revenue functions for each item of goods remains valid in the case of more complex approximations by quadratic and cubic functions of demand function. The type of the function of maximum value added revenue and the type of the function of maximum profit can be both found per unit of time depending on the variable level of the added price included into the sales price of the item. The type of maximum revenue function can be found per unit of time depending on the sales price of the item. The extremum points of the found functions are being determined. The theorems have been proved, that the extremum points which are being determined appear to be the maximum points of the researched functions for each item of goods, when the maximum profit or the maximum revenues are reached by selling goods to consumers. All common variables of said functions are found by summing up these functions among the multitude of goods on the interval of the whole sales time. The received data is used for the practical implementation of an effective sales strategy that ensures maximum profits for companies specializing in direct sales to consumers of the purchased goods. An applied methodicalэф approach to the sales of goods which ensures maximum profit from the sales in the field of elastic demand approximated by a linear function and under the condition of a constant purchase price for goods is proposed and theoretically substantiated. Read more...

Application of neural networks to reconstruct a continuous representation of a signal from discrete samples taken at random moments in time

Digital signal processing in cyber-physical technological systems is based on algorithms that operate with information presented in a discretized form both by level and by time. In the latter case, the constancy of the time quantization interval is assumed as one of the postulated conditions for the application of algorithms. At the same time, in practice, such constancy is not always ensured, which leads to the omission of individual samples or even to a random nature of the discretization. Therefore, an urgent research task is to develop methods and algorithms for signal processing under conditions of random discretization, in particular, for the restoration of continuous signals from their discrete samples taken with violation of the requirements of the Kotelnikov – Shannon theorem. If the discretization interval of a continuous signal is calculated taking into account its requirements (i. e. discretization is carried out with a frequency not lower than the Nyquist frequency), then its exact restoration from discrete samples is allowed, otherwise it is impossible. However, even for this situation, there are approaches to the restoration of continuous signals that take into account additional a priori information about the nature of the signal. Some of these approaches are based on complex mathematical apparatus, which makes them difficult to apply and not universal, while others use deep machine learning models that are expensive in terms of computational resources and demanding in terms of training data volumes. Under these conditions, a method is proposed for restoring a signal with a limited spectrum from discrete samples, the time interval between which is random, and its mathematical expectation is greater than the value determined by the Kotelnikov – Shannon theorem for regular discretization. The novelty of the research results lies in the proposed method and algorithm for restoring a continuous signal, as well as in the results of the analysis of a numerical experiment conducted with a software model executed in the MatLab environment and implementing the developed algorithm. Read more...