Outpatient appointment scheduling with decision‐dependent unpunctual arrivals

Abstract

This article investigates appointment scheduling with stochastic service times (exogenous uncertainty) and schedule‐dependent unpunctual arrivals (endogenous uncertainty). First, our empirical study confirms that patients exhibit unpunctual behavior that varies across different age categories, visit types, and departments. More importantly, the empirical results document a statistically significant association between appointment time and patient unpunctuality. Second, we develop a mathematical formulation of the problem within a stochastic‐optimization framework considering schedule‐dependent uncertainties. The empirically observed appointment‐time‐specific arrival pattern is incorporated as a planning input. We confirm the differentiability property of the objective function and that its derivative is uniformly bounded. Building upon this result, we obtain an unbiased estimator of the gradient for the objective function, enabling us to design a gradient‐based optimization approach. To further enhance optimization performance and avoid local optima, we integrate gradient‐based local refinement with a curvature‐informed Variable Neighborhood Search (VNS) procedure, resulting in a hybrid solution method. Finally, numerical experiments demonstrate the computational efficiency of the proposed method and show that appointment‐time‐dependent unpunctuality can materially affect optimal schedule structures. In particular, different unpunctuality profiles can lead to distinct scheduling arrangements.