Appointment scheduling optimization with chance constraints in a single-server consultation system
With the development of modern society,appointment scheduling management which facilitates the improvement of healthcare service quality has been gaining increased attention from healthcare service providers.This paper considers the appointment scheduling of a healthcare consultation system in a single-server setting.In this consultation server,the service duration for patients is random and the overtime is restricted to a reasonable level with a chance constraint.Therefore,the appointment scheduling model with the chance constraint is formulated.To solve the model under large-scale scenarios,we analyze and reformulate the original model.Then the following two reformulations are proposed.The first reformulation is developed based on the assumption that the service duration follows the Gaussian distribution,and the gradient-based method is implemented to obtain the global optimal solution.In the second reformulation,an approximation is designed based on the conditional value-at-risk,and Benders decomposition is tailored to tackle the resulting model.Simulation experiments demonstrate the feasibility of the two reformulations and the effectiveness of the algorithms under large-scale scenarios.Through analysis of the numerical results,appointment scheduling decisions are provided for healthcare service providers.