Mitigating concentrated and cascading delays in preference-based appointment systems: A cost and risk perspective

Our study is motivated by real-world observations indicating that preference-based appointment systems suffer from two concurrent types of service delays: concentrated delay and cascading delay. Concentrated delay refers to the physician-preference phenomenon in which patients opting for popular physicians experience significantly longer wait times compared to those selecting less popular providers. Cascading delay, on the other hand, denotes a time-preference pattern whereby, for any given physician, patients selecting later appointment slots tend to face longer delays than those with earlier slots. In a context with uncertain service duration, to mitigate both types of delays simultaneously, we propose a Cost-Risk model that incorporates delay-balancing constraints to mitigate their combined impact. The model robustly minimizes the weighted sum of patient rejection costs and service delay risks, based on the manager’s delay aversion level, by jointly optimizing decisions on service request rejection, patient-to-physician assignment, patient sequencing, and patient-to-slot assignment. Service delay risks are evaluated using the event-wise ambiguity set-based Delay Riskiness Index (DRI), a measure that captures both the probability and intensity of random delays. We propose a constraint generation-embedded branch-and-cut algorithm to exactly solve the model. We further extend the model to incorporate uncertain patient no-shows and unpunctuality, thereby enhancing its validity in practical applications. Numerical experiments validate that the proposed model and algorithm offer healthcare managers a practical tool for effectively and efficiently mitigating concentrated and cascading delays. We also provide insights into the impact of crucial parameters and model extensions on operational performance, particularly regarding profit and service punctuality.