Simultaneous Location of Trauma Centers and Helicopters for Emergency Medical Service Planning

Abstract:     
This paper studies the problem of simultaneously locating trauma centers and helicopters. The standard approach involves the use of a busy fraction to model helicopter availability. However, a busy fraction cannot be estimated a priori in our problem because the demand for a helicopter at a certain location cannot be determined until the locations of trauma centers are determined. To overcome this challenge, we endogenize the computation of a busy fraction within an optimization problem. Unfortunately, our formulation has a non-convex bilinear term, which introduces computational difficulties. To establish bounds on our model's objective, we develop an integrated method that iteratively solves a sequence of problem relaxations and restrictions. Specifically, we devise a specialized algorithm, called the Shifting Quadratic Envelopes algorithm, that 1) generates tighter outer-approximations than linear McCormick envelopes, and 2) outperforms a Benders-like cut generation scheme. We apply our integrated method to the design of a nationwide trauma care system in Korea. By running a trace-based simulation on a full year of patient data, we find that the solutions generated by our model outperform several benchmark heuristics by up to 20%-30%, as measured by an industry-standard metric: the proportion of patients successfully transported to a care facility within one hour. Our results have helped the Korean government to plan its nationwide trauma care system, and can be applied broadly to joint hospital-helicopter system designs anywhere in the world.

Number of Pages in PDF File: 39

working papers series