Scheduling two-stage healthcare appointment systems via a knowledge-based biased random-key genetic algorithm

To address the scheduling problem of two-stage healthcare appointment systems, previous studies always assume that a positive linear correlation is obeyed between the customer waiting time and service dissatisfaction, and an arrived customer is served immediately if the provider at the first stage becomes available, which usually leads to heavy congestion at the second stage and a rapid decline in service satisfaction. To tackle this problem further, this paper assumes that customer waiting time within different ranges impacts service dissatisfaction differently. Then, it develops an efficient real-time scheduling strategy to decide the exact starting time of each customer's service at the first stage. Considering no-shows and non-punctual appointments, a knowledge-based biased random-key genetic algorithm (K-BRKGA) is used to determine the number of customers at each appointment slot, such that the total weighted cost associated with customers’ waiting time, providers’ idle time, and overtime at two stages can be minimized. Based on the data sets used, K-BRKGA reduces the total cost by 2.01 % and 1.01 % compared to the other two famous algorithms.