  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.
