🤖 AI Summary
In omnichannel retail, demand uncertainty is time-varying and distributionally unknown, complicating inventory allocation across physical stores and e-commerce fulfillment channels.
Method: This paper proposes a data-driven optimistic-robust bimodal inventory allocation framework that jointly optimizes in-store stockout costs and e-commerce fulfillment costs. Unlike conventional robust optimization—which guarantees performance only under worst-case scenarios—our approach introduces a tunable trade-off mechanism, enhancing average profitability while preserving risk resilience. Technically, it integrates distributionally robust optimization, bi-objective modeling, and empirical parameter calibration—without requiring prior knowledge of demand distributions.
Results: Experiments on real peak-demand data from a major U.S. retailer demonstrate that our method improves average profit by 27% over a pure robust baseline and outperforms mainstream benchmarks by over 10%, validating its dual advantages of robustness and profitability.
📝 Abstract
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.
