Optimization models to locate health care 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, health center and emergency 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 health care facilities. In addition, rapid population growth, increasing manmade and natural disasters seem to put increasing pressure on demands for timely health care. There is a challenge in optimally locating health care facilities to enable the community to have good access to preventive, health center and emergency services. The location of health care facilities is an important aspect in health service delivery. It is therefore crucial for health care facilities to be located optimally to serve the community well. Facility location models have a greater importance when applied to the location of health care facilities because improper location will have a serious impact on the community. The fundamental objectives of locating facilities can be summarized into three categories. The first category refers to those designed to cover demand within a specified time or distance. This objective gives rise to location problems which are known as the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). 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 refers to those designed to minimize maximum distance. This results in a location problem known as the p-center problem which 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 refers to those designed to minimize the average weighted distance or time. This objective leads to a location problem known as the p-median problem. 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 (maximal covering location and the p-median models) to locate health care facilities. We apply the p-median models and the maximal covering location models to real data from Mackay metropolitan area in Queensland, Australia. We compare the two models using the real data and with existing ambulance stations. The study shows that the p-median model gives a better solution than the maximal covering location model. We also noted that the results of the maximal covering location model depend on the pre-determined weighted coverage distance.