Decision-Focused Bias Correction for Fluid Approximation

We revisit the multi-period newsvendor network problem, in which demands from multiple customers are correlated and jointly time-varying. Due to the curse of dimensionality associated with estimating the full joint demand distribution, we consider fluid approximation, a widely used approach for solving two-stage stochastic optimization problems such as large-scale service-system design. However, replacing the underlying random distribution (e.g., the demand distribution) with its mean (e.g., the time-varying average arrival rate) introduces bias in performance estimation and can lead to suboptimal decisions. In this paper, we investigate how to identify an alternative point statistic, not necessarily the mean, such that substituting this statistic into the two-stage newsvendor network problem yields an optimal decision. We refer to this statistic as the decision-corrected point estimate (a time-varying arrival rate). Although the critical fractile is well known to be the decision-corrected point forecast for the single-item newsvendor problem, counterexamples show that such a point statistic may not exist for newsvendor networks. We establish necessary and sufficient conditions for the existence of such a corrected point estimate and propose an algorithm for computing it. Numerical experiments on real data demonstrate that using the proposed decision-corrected point forecast in fluid approximation achieves substantially lower cost than traditional fluid approximation and sample average approximation benchmarks.