Data-Driven Shelf Stocking: Robustness and Vertical-Location Effect

In this article, we study a shelf-stock allocation problem in a data-driven setting where the demand distribution is unknown. The retailer needs to decide which commodities to place on each level of the shelf (location decision), and determine the stock level for each selected commodity at the shelf (stock decision) that can be adjusted based on updated demand prediction, under constraints on allocation and capacity, so as to maximize total expected profit. Key issues of the problem include demand endogeneity on vertical-location effect and the demand ambiguity that may arise from the ever shorter life cycles of commodities and other complicated determinants. We address the problem in a rolling-horizon fashion and develop a two-phase data-driven robust optimization model leveraging a decision-dependent Wasserstein metric that incorporates time-series demand forecasts and captures vertical-location effect under demand ambiguity. We derive tractable solution schemes for the model, in which the phase-I model determines the optimal location decision by solving one instance of mixed-integer linear program, while the phase-II model admits an analytical solution for updating the optimal stock. Furthermore, we discuss the sensitivity implications on how the ambiguity aversion impacts the optimal stock, and prove the consistency of the model solution under regularity condition on the underlying demand process that well justifies the asymptotic performance of the proposed data-driven approach. Finally, we extend our model to incorporate substitution effect, and conduct sufficient numerical experiments with real-life data that demonstrate the performance of our model.