Productivity–efficiency-driven physician scheduling in emergency telemedicine

Emergency telemedicine networks require timely, reliable, and coordinated specialist coverage across geographically distributed hospitals. Scheduling physicians in such settings is challenging due to heterogeneous productivity, facility-dependent inefficiency, and nonuniform credentialing portfolios, which together create highly variable service capacity across time and location. This study develops a productivity–efficiency-driven scheduling (PEDS) framework that integrates these operational factors into both a mixed-integer linear programming (MILP) model and a scalable Hybrid Genetic Algorithm (HGA). Numerical experiments across a broad range of demand, coverage, and network configurations demonstrate that explicitly incorporating physician productivity and hospital inefficiency leads to substantial reductions in shortage relative to conventional scheduling approaches that ignore these factors. The HGA produces near-MILP-quality solutions for small and medium-sized instances and remains highly competitive on large-scale networks under fixed runtime limits, particularly on computationally difficult instances where the MILP retains substantial optimality gaps. Results further indicate that productivity- and efficiency-driven scheduling is most valuable when demand is moderate and credentialing flexibility is limited, whereas extreme demand conditions shift the primary bottleneck from scheduling quality to overall system capacity. A real-world case study based on operational emergency telemedicine data further demonstrates the practical applicability of the proposed framework. The approach can be adapted to other distributed emergency care environments with heterogeneous provider performance and facility-level workflow variation.