Optimal administrative geographies: an algorithmic approach

Centrally planned Beveridge healthcare systems typically rely heavily on local or regional "health authorities" as responsible organisations for the care of geographically defined populations. The frequency of reorganisations in the English NHS suggests that there is no compelling unitary definition of what constitutes a good healthcare geography. In this paper we propose a set of desirable objectives for an administrative healthcare geography, specifically: geographical compactness, co-extensiveness with current local authorities and size and population homogeneity, and we show how these might be operationally measured. Based on these objectives, we represent the problem of how to partition a territory into health authorities as a multi-objective optimisation problem. We use a state-of-the-art multi-objective genetic algorithm customised for the needs of our study to partition the territory of the East England into 14 Primary Care Trusts and 50 GP consortia and study the tradeoffs between objectives which this reveals.