Estimating substitution for optimised replenishment with slow movers products

Overview & Synopsis

In retail, inventory optimization is a common problem that involves balancing the risk of stockouts with the risk of overstocking to achieve optimal overall profit. This inventory optimization task is particularly challenging for products sold in small quantities due to their discrete nature. Nevertheless, slow movers are abundant in companies like ADEO (a French holding company selling consumer goods for DIY and home decoration). As a result, even a small improvement can have a significant impact.To address this challenge, this thesis reformulates the optimal replenishment problem for slow movers into a problem of estimating the probability of substitution between items. When a product is out of stock, a customer may choose another item as an alternative (a so-called substitute product), thereby avoiding a permanent loss of the initially intended sale. Consequently, instead of selecting the optimal replenishment quantity separately for each item (the classical approach), we leverage the additional information that a group of items can be substituted for one another. This allows for more efficient estimation of the optimal replenishment quantity for the entire group of items. Obviously, such a substitution process only occurs with a certain probability, which (1) we need to estimate and (2) we must then use appropriately when calculating the optimal replenishment. It is important to note that the discrete nature of stock quantity is expected to provide a relatively better improvement in terms of profit for slow movers compared to fast movers (the opposite of slow movers), which justifies the specific focus of our approach on slow movers.To estimate substitution probabilities within a group of substitutable products, we reformulate an existing specific model. However, this model relies only on limited observed data, as it is restricted to in-store sales and inventory transactions. In particular, the customer's initial demand, as well as lost sales, are unobservable. We overcome this missing data problem by adapting an EM algorithm to estimate substitution probabilities. We also address the identifiability of such a model to correctly apply the maximum likelihood paradigm by establishing certain strict theoretical constraints on the size of the group of substitutable products. Experiments on both synthetic and real datasets (from ADEO) measure the variability of substitution probability estimates (which is quite high in this case due to significant missing data) but nevertheless demonstrate that the quality of the estimates improves considerably when sales and inventory data from multiple stores are merged, leading to valuable and useful inferences regarding product substitution and replenishment.The final step of our work is to discover groups of substitutable products, ideally starting from a large raw list of products from the store. To do so, we propose a specific product grouping based on the light assumption that most products have zero substitution probability. We then adapt a hierarchical clustering algorithm, allowing us to quickly estimate the targeted groups, and apply it to a large dataset from the ADEO company.