# An Optimistic-Robust Approach for Dynamic Positioning of Omnichannel Inventories

arXiv: https://arxiv.org/abs/2310.12183 · HTML: https://mlsanity.com/paper/2310.12183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 6 of 6)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Robust Sample Average Approximation](https://mlsanity.com/paper/1408.4445/) (2014)
- [A data-driven approach to beating SAA out-of-sample](https://mlsanity.com/paper/2105.12342/) (2021)
- [A Scalable Algorithm for Two-Stage Adaptive Linear Optimization](https://mlsanity.com/paper/1807.02812/) (2018)
- [Sustainable Inventory with Robust Periodic-Affine Policies and Application to Medical Supply Chains](https://mlsanity.com/paper/1806.06744/) (2018)

## Abstract (arXiv)

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.