Refined Wasserstein Distributionally Robust Optimization for Contract Pricing: The Value of Optimality Conditions in Transactions

This paper introduces a refined Wasserstein distributionally robust optimization (RWDRO) model to address contract pricing under information asymmetry. Our RWDRO model improves on traditional Wasserstein DRO (WDRO) models that rely solely on pure demand data by refining the Wasserstein ambiguity set through inverse optimization techniques applied to the buyer’s historical order data. To address the computational challenges arising from semi-infinite programming in determining the new center distribution of the Wasserstein ball with dual-source data, we propose an equivalent linear programming approach leveraging Lagrange duality and set partitioning techniques. Then, we establish bounds for the buyer’s worst-case order quantity and the seller’s worst-case profit using first-order conditions. For dependent multiproduct cases, we propose a partition-based cutting-plane algorithm to obtain an σ-optimal solution. For single-product and independent multiproduct cases, we develop a tractable second-order cone programming model. Numerical experiments highlight the superior out-of-sample performance of RWDRO over traditional WDRO models, especially in small-data regimes, and the computational efficiency of our proposed solution methods. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72271145, 72134004, and 92367202]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0547 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0547 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .