Two-Stage Robust Telemedicine Assignment Problem with Uncertain Service Duration and No-Show Behaviours

The current pandemic of COVID-19 has caused significant strain on medical center resources, which are now the main places to provide the rapid response to COVID-19 through the adoption of telemedicine, especially for the health care delivery, in order to meet patients' needs and reduce the transmission of the virus and protect medical practitioners from infection while minimizing their exposure to the public and in-person visits. Thus it is crucial for the healthcare managers to make an effective assignment plan for the patients and telemedical doctors when providing telemedicine services in a highly uncertain environment. In this regard, this paper presents the first comprehensive study of a two-stage robust optimization telemedicine assignment problem when different sources of uncertainty are incorporated in practice, including uncertain service duration, no-show behaviours of both patients and telemedical doctors. To overcome the difficulty of resolution for such a model with a max-min based mixed-integer linear programming recourse problem, from the algorithmic viewpoint we propose an efficient nested column-and-constraint generation (CCG) solution scheme that decomposes the model into the outer level problem and inner level problem, which both can be solved by CCG algorithm. Our computational results show that our method can solve the problems of realistic sizes within a reasonable time (e.g., up to 100 patients, 10 telemedical doctors, and 200 empirical scenarios within one and a half hours). On the empirical side, this paper has also demonstrated how to choose the optimal hyper-parameters to make an optimal trade-off between cost management and the coverage level of the served patients in the presence of different sources of uncertainty, and what's the added value of our robust policy when compared with its two-stage stochastic programming counterpart model