Decision-Focused Bias Correction for Fluid Approximation

Abstract: Fluid approximation is a widely used approach for solving two-stage stochastic optimization problems, with broad applications in service system design such as call centers and healthcare operations. However, replacing the underlying random distribution (e.g., 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, which is not necessarily the mean, such that substituting this statistic into the two-stage optimization problem yields the optimal decision. We refer to this statistic as the decision-corrected point estimate (time-varying arrival rate). For a general service network with customer abandonment costs, we establish necessary and sufficient conditions for the existence of such a corrected point estimate and propose an algorithm for its computation. Under a decomposable network structure, we further show that the resulting decision-corrected point estimate is closely related to the classical newsvendor solution. Numerical experiments demonstrate the superiority of our decision-focused correction method compared to the traditional fluid approximation.