Managing Inventory and Pricing with Contextual Robust Optimization

Multiproduct inventory and pricing problems are traditionally approached by estimating a presumed sufficiently accurate demand model and then optimizing with this specified model to determine optimal inventory and pricing decisions. However, obtaining an accurate demand model is nearly impossible because of unobservable parameters, resulting in parameter uncertainty; meanwhile, the unknown distribution of the error term in the stochastic demand model raises residual ambiguity. Additionally, the predicted demand is endogenously affected by pricing, leading to decision-dependent prediction that often brings about intractable optimization problems. We introduce a contextual robust optimization model that simultaneously addresses these challenges. Our proposed model possesses attractive finite-sample performance guarantees and can be effectively approached using an enhanced affine recourse adaptation to resolve the issue of intractability, and it can be extended to broader contextual decision-making problems under mild conditions. Extensive numerical studies demonstrate the effectiveness of our approach, showing that it outperforms the conventional estimate-then-optimize approach and the residual-based robust optimization approach that does not account for parameter uncertainty, particularly when the available data are limited. Notably, our proposed model exhibits greater resilience when contextual information is disregarded, reflecting practical situations in which collecting such information might be impossible or costly. This paper was accepted by Peng Sun, optimization and decision analytics. Funding: The research of X. Zhang is supported by the National Natural Science Foundation of China [Grant 72501273], the Anhui Provincial Natural Science Foundation [Grant 2408085QG222], and the Fundamental Research Funds for the Central Universities [Grant BJ2040160100]. The research of Q. Tang was supported by the Ministry of Education, Singapore [Tier 1 Grants RG47/24, RG139/25]. Z. Chen is funded in part by the National Natural Science Foundation of China [Grants 72422002, 72394395], the Hong Kong Research Grants Council General Research Fund [Grant CUHK-11502422], and the Asian Institute of Supply Chains and Logistics. L. Chen acknowledges support from the Emerging Scholar Research Fellowships, The University of Sydney Business School. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06402 .