Machine Learning and MILP for Capacity Optimization and Educational Workload in Academic Endodontics

Appointment scheduling in endodontic clinics is challenging due to heterogeneous treatment durations and varying practitioner competencies. Conventional scheduling methods frequently overlook these complexities, leading to underutilized unit capacity, extended patient wait times, and uneven workloads. This study sought to develop a machine learning-assisted optimization framework to enhance operational efficiency and patient access within an academic endodontic clinic.

Daily treatment demand distributions were estimated by modelling historical data from seven endodontic procedures using a Poisson Generalized Linear Model, which accounted for count data characteristics, and Softmax (multinomial logistic) Regression to characterize the operational treatment mix. The predicted ratios were integrated into a mixed-integer linear programming (MILP) model, implemented in Python and solved with the CPLEX optimizer. The primary objective was to maximize daily patient throughput while maintaining balanced workloads across practitioner groups and preserving clinically realistic treatment distributions.

The proposed framework significantly improved scheduling efficiency compared with current practice, yielding a simulation-based estimate of daily treatment capacity of up to 113 patients compared with the current baseline of 36 patients. Predicted treatment distributions were closely aligned with optimized scheduling outputs, and workload allocation among students, residents, and specialists remained balanced, supporting equitable resource utilization.

The integration of machine learning-based demand forecasting with mathematical optimization offers a practical decision-support framework for appointment scheduling in academic endodontic clinics. This approach enhances resource utilization, improves patient access to care, and promotes sustainable workload distribution while maintaining clinical standards.