articles

A multifactor probabilistic model of product sales on an electronic trading platform (marketplace) is proposed, allowing to calculate the dependence of such key performance indicators as sales volume and sellers’ revenue on the time characteristics of product reliability: actual lifespan, guaranteed (established by the manufacturer) lifespan and expected (desired by the consumer) lifespan of the product. It was assumed that there is an unlimited amount of goods on the marketplace and, in addition, each consumer purchases only one unit of the product, choosing a seller within the window of their purchasing power at the minimum price. It is shown that the sales volume and revenue from the sale of goods are random variables, the expected values of which, as well as their distribution laws, can be represented as functionals of the probability distributions of the above-mentioned characteristics of product reliability. Within the framework of the proposed probabilistic model of product sales, formulas for these functionals are derived. In a particular case, when the lifespan of the product does not depend on the price, and the price itself is described by one- or two-parameter exponential distribution laws, mathematical expressions are obtained for the distribution laws and raw moments of the amount of goods sold and sellers’ revenue. The dependence of expected values of sales volume and revenue on the average actual, average guaranteed and average expected lifespan of the product is analysed. As an example of taking into account the effect of the price dependence of the product lifespan on sales volume, revenue and profit, the sale of smartphones on the Yandex Market marketplace is considered. Based on empirical data, the dependence of the guaranteed lifespan to the actual lifespan ratio on the price is established. With its help, numerical modelling is carried out, revealing the effect of the parameters included in the lifespan distribution laws on the average sales volume of smartphones and the average profit from their sale.