Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services
Abstract
1. Introduction
2. Literature Review
2.1. Traditional Outpatient Appointment Scheduling
2.2. Appointment Scheduling Incorporating Telemedicine
2.3. Appointment Scheduling with Mathematical Programming Methods
3. Problem Formulation
4. Solution Approach
5. Numerical Studies
5.1. Data Settings
5.2. Ablation Study
5.3. Sensitivity Analysis
5.3.1. Impact of Time Slot Length
5.3.2. Impact of Unpunctuality Range
5.3.3. Impact of Telemedicine Patient Proportion
5.3.4. Impact of Weighting Coefficients
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Stochastic Mixed-Integer Programming | |
Mixed-Integer Linear Programming | |
Sample Average Approximation | |
Standard Deviation | |
PHA | Progressive Hedging Algorithm |
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Sets and Parameters | Description |
Set of time slots | |
Set of scenarios | |
Fixed length of a time slot | |
Planned start time of the -th time slot | |
Proportion of telemedicine patients scheduled | |
Proportion of outpatients scheduled | |
Service time for telemedicine patient assigned to slot in scenario | |
Service time for outpatient assigned to slot in scenario | |
Unpunctuality of outpatient assigned to slot in scenario | |
Weight coefficients | |
Decision Variables | Description |
Binary variable, 1 if slot assigned to telemedicine patient, else 0 | |
Binary variable, 1 if slot assigned to outpatient, else 0 | |
Continuous variable, actual service start time for patient in slot , scenario | |
Continuous variable, waiting time of telemedicine patient in slot , scenario | |
Continuous variable, waiting time of outpatient in slot , scenario | |
Continuous variable, physician idle time in slot , scenario | |
Continuous variable, physician overtime in scenario | |
Binary variable, 1 if the service status switches between time slots and , else 0 | |
Binary variable, 1 if both slots and are assigned to telemedicine patients, else 0 |
Sample Size (K) | Objective Value | Solution Time |
---|---|---|
20 | 67.15 | 1.6 |
30 | 68.03 | 4.4 |
40 | 69.60 | 7.3 |
50 | 70.79 | 14.7 |
60 | 70.30 | 21.8 |
70 | 71.72 | 35.7 |
80 | 70.33 | 23.8 |
90 | 72.11 | 76.4 |
100 | 71.32 | 41.6 |
110 | 71.49 | 151.4 |
120 | 71.75 | 158.7 |
130 | 71.09 | 179.8 |
140 | 71.45 | 299.2 |
150 | 71.92 | 300.9 |
160 | 71.13 | 317.1 |
170 | 71.55 | 398.9 |
180 | 71.45 | 416.9 |
Weighting Coefficients | Objective Value | ||||
---|---|---|---|---|---|
72.44 | 21.2 | 21.7 | 13.0 | 0.6 | |
44.07 | 32.2 | 24.9 | 0.0 | 0.5 | |
105.73 | 15.1 | 17.7 | 19.7 | 2.5 | |
62.24 | 14.0 | 19.7 | 20.2 | 2.5 | |
72.52 | 32.0 | 23.4 | 0.0 | 1.1 | |
71.42 | 17.1 | 22.3 | 14.4 | 3.1 | |
73.30 | 22.1 | 21.3 | 12.1 | 0.4 | |
66.01 | 22.9 | 19.8 | 11.3 | 0.6 | |
78.32 | 16.3 | 25.4 | 15.2 | 3.4 | |
68.39 | 18.4 | 22.5 | 14.4 | 2.6 | |
77.74 | 23.1 | 20.4 | 11.6 | 0.6 | |
43.80 | 21.3 | 22.7 | 13.0 | 0.5 | |
128.20 | 19.6 | 19.1 | 14.0 | 2.5 |
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Chen, W.; Chen, L.; Shen, X.; Zhang, Y.; Wang, X. Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services. Mathematics 2025, 13, 2591. https://doi.org/10.3390/math13162591
Chen W, Chen L, Shen X, Zhang Y, Wang X. Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services. Mathematics. 2025; 13(16):2591. https://doi.org/10.3390/math13162591
Chicago/Turabian StyleChen, Wei, Liang Chen, Xiaoxiao Shen, Yutao Zhang, and Xiulai Wang. 2025. "Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services" Mathematics 13, no. 16: 2591. https://doi.org/10.3390/math13162591
APA StyleChen, W., Chen, L., Shen, X., Zhang, Y., & Wang, X. (2025). Appointment Scheduling Considering Outpatient Unpunctuality Under Telemedicine Services. Mathematics, 13(16), 2591. https://doi.org/10.3390/math13162591