Deterring the Gray Market: Product Diversion Detection via Learning Disentangled Representations of Multivariate Time Series

A gray market emerges when some distributors divert products to unauthorized distributors/retailers to make sneaky profits from the manufacturers’ differential channel incentives, such as quantity discounts. Traditionally, manufacturers rely heavily on internal audits to periodically investigate the flows of products and funds so as to deter the gray market; however, this is too costly given the large number of distributors and their huge volumes of orders. Owing to the advances in data analytics techniques, the ordering quantities of a distributor over time, which form multivariate time series, can help reveal suspicious product diversion behaviors and narrow the audit scope drastically. To that end, in this paper, we build on the recent advancement of representation learning for time series and adopt a sequence autoencoder to automatically characterize the overall demand patterns. To cope with the underlying entangled factors and interfering information in the multivariate time series of ordering quantities, we develop a disentangled learning scheme to construct more effective sequence representations. An interdistributor correlation regularization is also proposed to ensure more reliable representations. Finally, given the highly scarce anomaly labels for the detection task, an unsupervised deep generative model based on the learned representations of the distributors is developed to estimate the densities of distributions, which enables the anomaly scores generated through end-to-end learning. Extensive experiments on a real-world distribution channel data set and a larger simulated data set empirically validate our model’s superior and robust performances compared with several state-of-the-art baselines. Additionally, our illustrative economic analysis demonstrates that the manufacturers can launch more targeted and cost-effective audits toward the suspected distributors recommended by our model so as to deter the gray market. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72031001, 72301017, 72371011, and 72242101]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0155 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0155 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .