Min-max optimal public service system design

This paper deals with designing a fair public service system. To achieve fairness, various schemes are be applied. The strongest criterion in the process is minimization of disutility of the worst situated users and then optimization of disutility of the better situated users under the condition that disutility of the worst situated users does not worsen, otherwise called lexicographical minimization. Focusing on the first step, this paper endeavours to find an effective solution to the weighted p-median problem based on radial formulation. Attempts at solving real instances when using a location-allocation model often fail due to enormous computational time or huge memory demands. Radial formulation can be implemented using commercial optimisation software. The main goal of this study is to show that the suitability solving of the minmax optimal public service system design can save computational time.