Do we need optimization models to locate health service facilities?

The rapid growth of population in cities and major regional areas, shorter length of stays in hospitals, ageing (and the desire of the elderly to stay longer in their homes), and traffic poses a challenge to health departments in meeting the demand for preventive, emergency and health center services. The changes in factors such as urbanization, demography and the rate of service utilization may affect the optimal distances or cost between patients and healthcare facilities. However, there is limited information about the impact of such changes on the effectiveness of the existing facilities. The interest in facility locations spans a wide range of academic disciplines and industrial activity. Mathematicians, geographers, economists, urban planners, retailers, engineers, hospital administrators, and even politicians campaigning for an election all deal with facility location problems. The increasing interest in location theory is attributed to several factors such as: its widespread applicability at all levels of human activities with beneficial economic effects; the computational complexity of location models; and the variation of location models from problem to problem. The primary objectives of locating facilities can be summarized into three categories. The first category known as the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP) are designed to cover demand within a specified time or distance. The LSCP seeks to locate the minimum number of facilities required to ‘cover’ all demand or population in an area. The MCLP is to locate a predetermined number of facilities to maximize the demand or population that is covered. The second category known as the p-center are designed to minimize maximum distance. The p-center addresses the difficulty of minimizing the maximum distance that a demand or population is from its closet facility given that p facilities are to be located. The third category known as the p-median problem are designed to minimize the average weighted distance or time. The p-median problem finds the location of p facilities to minimize the demand weighted average or total distance between demand or population and their closest facility. The objective of this study is to discuss the importance of the application of optimization models (covering, p-center and the p-median models) to locate emergency healthcare stations. We discuss the history of facility location models to the location of emergency facilities. We present the real application of location models to the location of public facilities such as ambulance and fire station in various parts of the world. We outline the models that are used with the methodology and present the outcomes of the application of the models. We finally apply three discrete location models to real data from Mackay region in Queensland, Australia. We compare existing emergency health care sites with the optimal solutions proposed by the location models. We also discuss the policy implication in terms of cost of using existing facilities as compare to the proposed sites by the location models.