A location–allocation model for service providers with application to not-for-profit health care organizations

Abstract

In this paper, we develop and solve a model for the location and allocation of specialized health care services such as traumatic brain injury (TBI) treatment. The model is based on and applied to one of the Department of Veterans Affairs’ integrated service networks. A cost minimization model with service proportion requirements is solved using simulated annealing. Large instances of the model with 100 candidate medical center locations and 15 open treatment units are solved in about 1000 s. In order to test the real-world applicability of our model, an extensive managerial experiment is conducted using data derived from our health care setting. In this experiment, the effects of three critical factors: (1) degree of centralization of services, (2) the role of patient retention as a function of distance to a treatment unit, and (3) the geographic density of the patient population are investigated with respect to the important trade-off between the cost of providing service and the need to provide such service. Our analysis shows that all three factors of the experiment are both relevant and useful to decision-makers when selecting locations for their services.

Introduction

At the beginning of the 21st century, health care remains one of the areas of crucial concern for millions of Americans. As evidence, it may be noted that obtaining and paying for high-quality health care was a major topic of debate in both the 2004 and 2008 presidential elections. While the United States is fortunate in possessing the world's finest medical facilities and technologies, it is well-known that health care costs are rapidly spiraling upward, currently constituting some 15% of national spending [1].

Health care providers are pressured by two conflicting aspects of the public debate on health issues. On one hand, it is clear that Americans value the quality of their health care facilities, treatments, and options. On the other hand, much to the consternation of the American public, the continuously rising cost of health care is reflected in ever-increasing health care insurance premiums, which remain a significant expense for most households. At a time when medical procedures, new technologies, and drugs are highly developed and consequently very expensive, the pressure to control costs is affecting the operations of health care organizations in general and hospitals in particular. While the public debate about health care will not diminish, health care providers such as hospitals have no choice at present but to become as efficient as possible in all aspects of their operations [2], [3].

This study is motivated by the need for effective delivery of specialized health services at the Department of Veterans Affairs (VA), the primary service organization dedicated to the care and well-being of American veterans. In particular, this study is based upon a funded research project that investigated the optimal location of traumatic brain injury (TBI) treatment units for VA medical centers. As a not-for-profit service organization, the VA has to define optimality using a multi-objective approach where both controlling the cost of providing care and determining the level and extent of the care provided (i.e., access and availability) are equally important goals to pursue.

This paper is organized as follows. Section 2 provides the motivation and literature review germane to our research. Section 3 describes our optimization model and defines the relevant decision variables and model coefficients. Section 4 describes our solution methodology for the optimization model while Section 5 provides the results of a rigorous computational testing of the model. Section 6 applies our model in a real-world experimental setting based upon our work with the VA. Last, concluding remarks and future research directions are given in Section 7.