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.