Refining Data-driven Upfront Reservation Discount Pricing Via Inverse Inferring Newsvendor Transactions

This paper investigates the supplier’s pricing problem under upfront reservation discount (URD) contracts where the buyer reserves products in advance and then adjusts the purchase quantity based on realized end-market demand. A key challenge is that the supplier typically has limited data to estimate the demand distribution and possesses inferior information compared to the buyer. To address the challenges of distributional ambiguity and information asymmetry, we develop a refined distributionally robust optimization model for the supplier’s URD pricing to maximize her worst-case profit. To better infer true demand patterns, beyond the conventional reliance on historical demand data, our approach leverages past transaction records involving supplier–buyer interactions through the inverse optimization underlying the first-order conditions of the buyer’s newsvendor behavior. Then, a general Wasserstein <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>p</mml:mi> </mml:math> -distance minimization problem for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>p</mml:mi> <mml:mo>≥</mml:mo> <mml:mspace width=".1em"/> <mml:mn>1</mml:mn> </mml:math> is developed to generate a Refined Empirical Distribution (RED) in the enhanced set. We prove that the RED provides a superior estimation of the true demand distribution compared to the classical empirical distribution when the buyer holds an informational advantage. Although identifying the RED leads to an intractable semi-infinite program, we show that the RED admits a closed-form solution. To obtain the supplier’s worst-case profit involving a nonconvex distributionally optimistic optimization problem with a decision-dependent uncertainty set, we exploit the monotone transport structure between univariate distributions to truncate the distributions and convert the decision-dependent quantile constraints, which results in a finite-dimensional convex model that can be efficiently solved. Moreover, we extend the model to accommodate data noise, volatile market prices, evolving market conditions, and multi-item settings. Numerical experiments based on a virtual machine reservation problem in the cloud service market demonstrate the effectiveness and robustness of the proposed approach.