Nan Kong, Ph.D.
Weldon School of Biomedical Engineering, Purdue University
Abstract: Optimizing the Regional Trauma Network via Bi-Level Integer Programming
Trauma continues to be the leading cause of mortality and morbidity among US citizens younger than 45 years of age. Evidence suggests that mal-distribution of high-level trauma centers and potentially too many low-level trauma centers and/or regular hospitals close to popular incident scenes can significantly contribute to pre-hospital mistriage errors (both under and over). Under-triage, transporting severely injured patients to a regular hospital, can lead to various health risks and even mortality. Over-triage, transporting less-severely injured patients to a hospital specializing in trauma care, leads to inappropriate use of trauma care resources, and higher healthcare spending, especially of publicly funded patients. Although the government (local or state) has little or no direct authority in promoting the location of trauma centers, they can influence the hospital system(s) who own these centers by offering financial subsidies.
In this talk, we consider the problem of optimizing a regional trauma network that minimizes the negative effects of UT (to improving social well-being) and OT (to reduce spending) errors in the presence of two decision-makers, the government and a hospital system. We present a novel bi-level subsidized network redesign problem, in which the government’s (upper-level) decision is to determine the total subsidy to support social well-being and minimize public spending; whereas the hospital system’s (lower-level) decision is to upgrade/downgrade facility status to maximize its revenue. We design a branch-and-bound based algorithm for the resultant bi-level integer programming model. Further, we add cuts to tighten lower bounds for subproblems whenever applicable. Through comprehensive numerical experiments with randomly generated instances, we are able to show the superiority of our algorithm in comparison with state-of-the-art algorithms for bi-level integer programming. If time allows, we will present case studies based on real incidence, geography, and cost data from the state of Ohio, and articulate the applicability of our work to other subsidized healthcare network design problems.