A Benders Decomposition Approach for Appointment Scheduling of Unpunctual Patients in a Multi-Server Setting

Appointment patients usually arrive unpunctually, which significantly affects the daily operations of healthcare facilities. To mitigate the negative impact of unpunctuality, this paper attempts to optimize the appointment schedule by considering unpunctual arrivals and no-shows in a multi-server setting. A two-stage stochastic programming model is formulated with the objective of minimizing patient waiting cost and overtime cost. The appointment schedule is determined by a modified Benders decomposition with sample average approximation. The effectiveness of this algorithm is validated through the comparison with lower bounds. Extensive experiments show that the optimal appointment schedule exhibits a zigzag pattern rather than a dome pattern. The impacts of various factors are also explored by numerical experiments.