Geographic Pooling of Hospital Resources: Data-Driven Trade-off between Waiting and Traveling

Abstract

(1) Problem definition: Using patient-level data from 72 MRI hospitals in Ontario, Canada from 2013 to 2017, we find that over 60% of patients exceeded their wait time targets. We conduct a data-driven analysis to quantify the reduction in the Fraction Exceeding Target (FET) for MRI services through geographic resource sharing while controlling for the cost of patient driving. (2) Academic/Practical Relevance: Grouping hospitals in the same geographic region into resource-sharing pools can reduce waiting time but increase travel costs. We prove analytically that partial pooling typically dominates complete pooling and no pooling for a simple linear city model with homogeneous patients. We present a data-driven method to solve the generalized (practical but more difficult) geographic pooling problem of 72 hospitals with heterogeneous patients with different wait time targets located in a two-dimensional region. (3) Methodology: We propose a geographic resource sharing model that groups hospitals into clusters to reduce the FET while controlling for patient driving distance. For any given geographic cluster, using forecasted data generated by a neural network, we propose an advance scheduling mechanism that informs the patient of her service time when she requests an MRI scan, an ``augmented-priority queuing that ranks the patient based on her priority and waiting time target, and a routing algorithm that determines at which hospital she will receive the MRI scan. We then optimize clusters using modified K-means clustering and Genetic Algorithms. Lastly, we conduct a counterfactual analysis to determine the minimal capacity expansions needed to achieve the desired 10% FET. (4) Results: Our resource pooling model lowers the FET to 34% while limiting patients' driving time to maximally two hours. In addition, our model and method show that only eight additional scanners are needed to achieve 10% FET while 50 additional scanners would be needed without resource sharing. (5) Managerial Implication: Our paper provides a practical, data-driven geographical resource-sharing model that hospitals can readily implement. Our solution method achieves a near-optimal solution with low computational complexity. Using smart data-driven scheduling and routing, a little extra capacity placed at the right location is all we need to achieve the desired FET under geographic resource sharing.