Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services

Wei Chen, Liang Chen, Xiaoxiao Shen (), Yutao Zhang and Xiulai Wang
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Wei Chen: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
Liang Chen: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
Xiaoxiao Shen: School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Yutao Zhang: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
Xiulai Wang: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

Mathematics, 2025, vol. 13, issue 16, 1-17

Abstract: Patient unpunctuality substantially complicates appointment scheduling in integrated telemedicine–traditional outpatient systems. The current research frequently ignores behavioral distinctions between telemedicine patients and outpatients, while neglecting to measure the intangible burden on physicians from service mode switches. To address these gaps, this study incorporates patient heterogeneity and introduces two novel cost metrics. Specifically, we implement penalties for service-mode switching and penalties for consecutive telemedicine sessions. We develop a Stochastic Mixed-Integer Programming (SMIP) model. This stochastic model is transformed into a deterministic Mixed-Integer Linear Programming (MILP) formulation via Sample Average Approximation (SAA). Linearization techniques enhance computational efficiency. In numerical experiments, the dual-penalty model yields balanced schedules with moderate patient mix, reducing physician overtime by 62.5% and service mode switches by 55% compared to baseline approaches. Sensitivity analysis confirms that narrowing outpatient unpunctuality ranges significantly reduces patient waiting and overtime, while raising telemedicine patient proportions bolsters system stability at the cost of increased physician idle time. These insights offer actionable guidance for healthcare institutions managing integrated online–offline services.

Keywords: telemedicine; outpatient appointment scheduling; stochastic optimization; service switching (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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