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Telemedicine has emerged as an effective means to connect health service providers with patients remotely. In the context of emergency care, telemedicine typically involves a telemedicine service hub (TSH) that matches remote physicians with patients in emergency wards. Effective operation of such systems requires careful and continuous coordination between physicians and local providers and as such, physician staffing and scheduling is a major managerial challenge that a TSH has to overcome. In this context, our paper studies a setting, where the TSH must respond to an arriving emergency case by assigning a physician within a considerably short time window. An emergency case at a facility can be matched only with a physician who is credentialed at that facility. Since care is urgent, queuing patients is not an option when there is no available on-shift physician. In such cases, the system must invoke the off-shift physicians, which is referred to as “blast.” The telemedicine company tries to avoid this option due to high costs. We propose a novel integer programming model for generating physician schedules with optimal mix of credentials and coverage across multiple hospitals. The proposed model aims to minimize total costs under a chance constraint that limits the blast probabilities and other tactical constraints that are unique to this setting. Two fast acting heuristic-based solution approaches are developed for real-life size problems and their computational performances were demonstrated  via  numerical analyses.

Physician scheduling for emergency telemedicine across multiple facilities