Two-stage appointment scheduling considering patient foldback under a stochastic approximation approach

Patient foldback frequently disrupts clinical operations, reduces productivity, and leads to patient congestion. To mitigate these negative impacts, this study aims to optimize appointment scheduling for a series of patients within service systems. These systems are defined by a two-stage service process, the occurrence of patient foldback behavior, and stochastic service durations. To achieve this objective, we propose a stochastic programming model to minimize the expected weighted sum of costs associated with physician idle time and patient wait times. We examine the characteristics of the sample path function and propose a stochastic approximation (SA) algorithm to address the problem effectively. Numerical experiments indicate that the proposed SA algorithm significantly decreases the solution time compared to the sample average approximation (SAA)-based algorithm, thereby confirming the efficiency and effectiveness of the proposed algorithm. Moreover, the analysis of the optimal appointment schedule characteristics, while considering patient foldback, reveals that the optimal job allowances retain a 'dome' shape; however, there is a marked steep increase at the start of the curve.