Wasserstein Risk-Sensitive Appointment Scheduling Under Delay Constraints

Abstract

We consider a risk-averse appointment scheduling problem for a healthcare service delivery system with discrete appointment times and service-duration ambiguity, focusing on the tradeoff between overtime work and patient delays. We employ conditional value-at-risk (CVaR) to measure the risk, and to address the ambiguity, we develop a distributionally robust optimization (DRO) model over a type-1 Wasserstein ball centered at an empirical service-duration distribution. We show that the Wasserstein DRO model enjoys a regularized reformulation, which captures an empirical-risk effect and a position-differentiated effect on synthesized aversion to risk and ambiguity. The regularized reformulation provides an important operational insight of position-differentiated robustness for delay management under service-duration ambiguity, without incurring additional complexity. Leveraging the regularized reformulations, the optimal schedule can be determined efficiently by evaluating the empirical CVaRs with binary search for each position sequentially. We then perform sensitivity analysis and derive finite-sample and asymptotic performance guarantees for the obtained optimal schedule. Furthermore, we extend our model to incorporate sequencing decisions for multiple types of patients, which also exploits the regularization structure and can be solved as one instance of mixed-integer linear program. Finally, numerical experiments demonstrate the insights and performance of the proposed approach. History: Accepted by J. Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Funding: S. Wang is supported by the National Natural Science Foundation of China [Grants 72471224, 72171221, 71922020, and 71988101], the Fundamental Research Funds for the Central Universities [Grant UCAS-E2ET0808X2], and a grant from the Ministry of Education (MOE) Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at University of Chinese Academy of Sciences. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0782 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0782 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .