Accuracy Sensitivity of the Radial Approach to Large Public Service System Design

This paper deals with the optimal resource location problems used for large public service systems designing. Such problems have many practical applications in different areas of human life. To describe the problems, the weighted p-median problem is usually formulated. A standard objective in this formulation is to minimize the total disutility, like social costs. The social costs are often proportional to the distance travelled by all system users to the nearest located source of provided service. If a large instance of the problem is described by a location-allocation model, then the model size often exceeds any acceptable limit for available optimization software. It must be noted, that the numbers of served users and possible service center locations may take the value of several hundreds or thousands. To avoid this obstacle, the approximate approach based on a radial formulation with homogenous system of radii given by so-called dividing points has been developed. In this paper, we present both exact and approximate approaches to the weighted p-median problem and study, how the number of dividing points used for distance approximation impacts the solution accuracy and computational time. All reported models of the decision problems are described by means of mathematical programming. To obtain the optimal solution, the universal optimization environment XPRESS-IVE was used.