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.