A multi-objective optimisation approach for the location of a public primary health facility

Abstract

The location allocation decisions for hospitals and clinics are essential to communities. Ensuring that these facilities are rstly, accessible to patient populations and secondly, equitably distributed such that each patient population travels equal or similar distances to their nearest facility is important to urban planning and development. This study thus developed a multi-objective optimisation approach to locate public primary care facilities such that the objectives of accessibility and equity are achieved. The rst model formulated the accessibility objective using the p-median location problem and the equity objective using the p-center problem. The second model formulated the accessibility objective using the p-median problem and the coverage objective using the maximal coverage location problem. The trade-o s between the accessibility and equity objectives were investigated and mapped on a Pareto frontier. In the rst model it was found that there was a possible trade-o between accessibility and equity, because as equity increased, accessibility decreased. In the second model it was found that there was a trade-o between accessibility and equity until a speci c maximum allowable distance value between a facility and the demand points it serves, thereafter a trade-o no longer existed, because as equity increased, access increased for those demand points covered at the expense of those demand points not covered