A robust survival model for emergency medical services in Delhi, India

Abstract

We propose a Double Standard Robust Survival Model (DSRSM) for efficient utilization of ambulances to maximize the survivability of high priority calls under uncertain travel times. The DSRSM provides dual coverage using primary and secondary ambulances to maximize the expected survival probability. A mixed-integer linear program equivalent of the quadratic DSRSM is proposed and solved using a combination of Variable Neighbourhood Search metaheuristic and Local Branching technique. The model was applied to the real-world conditions of Delhi, India, one of the largest metropolitan areas in the world. First, a survival probability function was estimated for emergency cases using empirical data from Delhi's public emergency medical services. Next, probability distributions of pre-trip delay, travel time to the demand site, and travel time to the nearest hospital were estimated using field data. The DSRSM utilized survival functions and the travel time distributions to locate ambulances optimally to maximize survivability. Results show that using multiple scenarios to capture varying travel times produces a more realistic performance evaluation for survival outcomes than a single scenario with average travel time. The model produces a single set of ambulance locations each for weekdays and weekends, which is more economically feasible than relocating ambulances across scenarios while providing survival outcomes comparable to the relocation approach.