Data-driven inventory policy: Learning from sequentially observed non-stationary data

Abstract

This paper aims to find dynamic inventory policies for retailers that have limited knowledge about future demand and sequentially observe the unprecedented demand data. We assume the demand is non-stationary; it follows different distributions for different time periods, and the data distributions and the transition behavior are unknown. Two solution approaches are presented to tackle this problem. Integrated-Bayesian (IB) approach is a parametric approach and is introduced for the case when an uncertainty set of possible demand distributions is available. A non-parametric approach, separate-lasso (SL), is proposed for the case that the uncertainty set possible demand distributions is not known. Both methods are theoretically analyzed and empirically benchmarked against several state-of-the-art heuristics. The theoretical analyses provide easy-to-implement algorithms for both approaches, while performance guarantees are derived for the separate-lasso approach. Computational studies show that the proposed methods outperform state-of-the-art heuristics–namely, sample average approximation, rolling horizon, and exponential smoothing–in nine different data environments. The optimal dynamic policy is not obtainable in this dynamic setting as reliable demand forecasts are not available. Therefore, we derive an approximated optimal policy, OPT, assuming the complete knowledge of the demand data in advance. The empirical results reveal that the cost of the proposed approaches is only 12% higher than that of OPT on average. Furthermore, we show that the proposed methods capture the hidden patterns inside the highly non-stationary real-world demand data of one of the largest e-commerce websites.