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Probabilistic model of goods sales dynamics on the marketplace: The influence of delivery duration

A probabilistic model of the dynamics of sales of goods on the marketplace, which takes into account the impact of delivery duration on the consumer’s decision to purchase this product, is proposed. It was assumed that the quantity of goods on the marketplace is unlimited, and consumers, all other things being equal, buy goods from sellers offering the shortest delivery time. In addition, it was assumed that each consumer purchases only one unit of the product. The cases of free and paid delivery of the product to the consumer are considered separately, as well as the general case where there are consumers choosing both free and paid delivery on the marketplace. The following economic factors were used as random variables determining the dynamics of goods sales: moments of consumers’ purchasing activity, duration of delivery and maximum possible duration of delivery for a consumer, purchasing power, price for goods, number of sellers and consumers of goods on the marketplace. It is shown that the quantity of goods sold on the marketplace by a certain moment of time is a random variable, the true value of which at a large number of consumers differs little from the expected value of this random variable. The analytical expression for time dependence of the expected value of the quantity of sold goods for the cases of free and paid delivery, as well as in the presence of both types of delivery on the marketplace is found. Numerical modeling of this dependence for all considered types of delivery has been carried out. In this case, we used partial laws of probability distributions of the above mentioned economic factors, simulating certain behavior of consumers and sellers on the marketplace. In addition, in the case of paid delivery the dependence of delivery cost on its duration found on the basis of empirical data was used in numerical modeling. We analyzed the influence of the parameters of the probability distribution law of delivery duration on such characteristics of sales volume dynamics as the maximum possible sales volume and the speed of approaching the expected value of the number of sold goods to the maximum sales volume. Read more...

Dependence of the efficiency of product sales on the electronic trading platform on the characteristics of its reliability: A probabilistic model

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. Read more...