Individual and Group Dynamics in Purchasing Activity

TL;DR

This paper analyzes the timing of purchase orders at individual and group levels, revealing distinct power-law and mixed distribution patterns, and introduces a product life cycle model to explain these dynamics.

Contribution

It uncovers the different distribution patterns of purchase order timings for individuals and groups, and proposes a model based on product life cycle to explain the observed heterogeneity.

Findings

Individual purchase times follow a power-law distribution with exponent ~2.0.

Group purchase times fit a mixture distribution with power-law and exponential features.

The proposed model aligns well with empirical data, explaining heterogeneity in purchase behaviors.

Abstract

As a major part of the daily operation in an enterprise, purchasing frequency is of constant change. Recent approaches on the human dynamics can provide some new insights into the economic behaviors of companies in the supply chain. This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plot. It's found that the former displays a power-law distribution with approximate exponent 2.0, while the latter is fitted by a mixture distribution with both power-law and exponential characteristics. Obviously, two distinctive characteristics are presented for the interval time distribution from the perspective of individual dynamics and group dynamics. Actually, this mixing feature can be attributed to the fitting deviations as they are negligible for individual dynamics, but those of different vendors are cumulated and then lead to an exponential factor for group dynamics. To better describe the mechanism generating the heterogeneity of purchase order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good line with the empirical data.