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. The bimodal nature of BIO stems from its ability to balance downside risk, as in traditional Robust Optimization (RO), which focuses on worst-case adversarial demand, with upside potential to enhance average-case performance. This enables BIO to remain as resilient as RO while capturing benefits that would otherwise be lost due to endogenous outliers. Omnichannel inventory planning provides a suitable problem setting for analyzing the effectiveness of BIO's bimodal strategy in managing the tradeoff between lost sales at stores and cross-channel e-commerce fulfillment costs, factors that are inherently asymmetric due to channel-specific behaviors. 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 performance. Using a real-world dataset from a large American omnichannel retail chain, a business value assessment during a peak period indicates that BIO outperforms pure RO by 27% in terms of realized average profitability and surpasses other competitive baselines under imperfect distributional information by over 10%. This demonstrates that BIO provides a novel, data-driven, and distribution-free alternative to traditional RO that achieves strong average performance while carefully balancing robustness.

翻译：本文提出了一类新型的数据驱动、无分布乐观-鲁棒双模态库存优化（BIO）策略，以在零售链中有效分配库存，满足时变且不确定的全渠道需求。BIO的双模态特性源于其平衡下行风险（如传统鲁棒优化（RO）专注于最坏对抗性需求）与提升平均性能上行潜力的能力。这使得BIO在保持与RO同等韧性的同时，能够捕捉因内生异常值而可能损失的利益。全渠道库存规划为分析BIO双模态策略在管理门店缺货损失与跨渠道电子商务履约成本之间权衡的有效性提供了合适的问题场景，这些因素由于渠道特定行为而具有内在不对称性。我们提供了关于BIO解决方案的结构性见解，以及如何调整它以在鲁棒性与平均性能之间实现更优权衡。基于美国一家大型全渠道零售链的真实数据集，在高峰期的商业价值评估表明，BIO在实现平均利润率方面比纯RO高出27%，在分布信息不完善的情况下超越其他竞争基线超过10%。这证明BIO为传统RO提供了一种新颖的、数据驱动的、无分布的替代方案，在谨慎平衡鲁棒性的同时实现了强大的平均性能。