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 the main plac healthcare managers to make an effective assignment plan for the patients and telemedical doctors when providing telemedicine services. Motivated by this, we present the first comprehensive study of a two-stage robust telemedicine assignment problem when three different sources of uncertainty are incorporated, including uncertain service duration, no-show behaviours of both patients and telemedical doctors. From an algorithmic viewpoint, we propose an efficient nested column-and-constraint generation (C&CG) solution scheme that decomposes the model into an outer level problem and an inner level problem. Our results show that we can solve the problems of realistic sizes within a reasonable time (e.g., up to 100 patients, 10 telemedical doctors, and 200 scenarios within two hours). On the empirical side, we demonstrate how the hyper-parameters make a balance between cost management and the coverage level of the served patients in the presence of three different sources of uncertainty. Our comparison with a two-stage stochastic programming model implies that our model is not overly conservative and seems to provide a relatively cheaper modeling alternative that requires much less information support when hedging against three different sources of uncertainty under a worst-case situation.