Appointment scheduling optimization with two stages diagnosis for clinic outpatient

This paper attempts to compare the performance between a single-stage appointment scheduling system and two-stage appointment scheduling system. For this purpose, a queuing model is firstly formulated with the objective of maximizing the weighted hospitals benefit minus the cost of patient waiting and doctor overtime, for a two-stage appointment scheduling system considering no-shows. To facilitate the comparison, we can alter the number of diagnosis stages by adjusting the probabilities that patients need to do further examinations, e.g., X-rays or blood tests. The single-stage queuing model assumes that all patients will finish their treatment after their first diagnosis, and other assumptions are the same as that in a two-stage appointment scheduling system. The performances of two-stage appointment scheduling systems varying with no-show probabilities and probabilities that patients have a second-stage diagnosis are presented. Experimental results indicate that the optimal number of patients needs to be more than the capacity of doctors in the first few slots, and less than those in the last few slots. We need to weigh the probability of no-shows and the probability of doing further examinations (second-stage) when determining the total number of patients to be scheduled. Under a higher no-show probability, arranging more patients than the workload reduces the waste of doctors capacity; and on the contrary, under a higher probability of doing examinations, arranging fewer patients than the workload can reduce system congestion.