An Optimistic-Robust Approach for Dynamic Positioning of Omnichannel Inventories

We introduce a new class of data-driven and distribution-free optimistic-robust bimodal inventory optimization (BIO) strategy to effectively allocate inventory across a retail chain to meet time-varying, uncertain omnichannel demand. While prior Robust optimization (RO) methods emphasize the downside, i.e., worst-case adversarial demand, BIO also considers the upside to remain resilient like RO while also reaping the rewards of improved average-case performance by overcoming the presence of endogenous outliers. This bimodal strategy is particularly valuable for balancing the tradeoff between lost sales at the store and the costs of cross-channel e-commerce fulfillment, which is at the core of our inventory optimization model. These factors are asymmetric due to the heterogenous behavior of the channels, with a bias towards the former in terms of lost-sales cost and a dependence on network effects for the latter. We provide structural insights about the BIO solution and how it can be tuned to achieve a preferred tradeoff between robustness and the average-case. Our experiments show that significant benefits can be achieved by rethinking traditional approaches to inventory management, which are siloed by channel and location. Using a real-world dataset from a large American omnichannel retail chain, a business value assessment during a peak period indicates over a 15% profitability gain for BIO over RO and other baselines while also preserving the (practical) worst case performance.

Hierarchy-guided Model Selection for Time Series Forecasting

Generalizability of time series forecasting models depends on the quality of model selection. Temporal cross validation (TCV) is a standard technique to perform model selection in forecasting tasks. TCV sequentially partitions the training time series into train and validation windows, and performs hyperparameter optmization (HPO) of the forecast model to select the model with the best validation performance. Model selection with TCV often leads to poor test performance when the test data distribution differs from that of the validation data. We propose a novel model selection method, H-Pro that exploits the data hierarchy often associated with a time series dataset. Generally, the aggregated data at the higher levels of the hierarchy show better predictability and more consistency compared to the bottom-level data which is more sparse and (sometimes) intermittent. H-Pro performs the HPO of the lowest-level student model based on the test proxy forecasts obtained from a set of teacher models at higher levels in the hierarchy. The consistency of the teachers' proxy forecasts help select better student models at the lowest-level. We perform extensive empirical studies on multiple datasets to validate the efficacy of the proposed method. H-Pro along with off-the-shelf forecasting models outperform existing state-of-the-art forecasting methods including the winning models of the M5 point-forecasting competition.