Continuumization and Approximation of Discrete Spatial Data for Optimal Facility Location Design

The paper proposes methodologies to convert discrete spatial data into continuous functions in a metric space so that the continuous approximation (CA) optimization framework can be applied to a general class of discrete facility location problems. We integrated a range of computational geometry methods to estimate the optimal system costs and the optimal number of facilities, and then developed an enhanced disk model to compute near optimal facility location design, both based on discrete input data. The results from the proposed CA method can be further improved by neighborhood search algorithms. Numerical experiments show that the proposed CA framework effectively finds near-optimum solutions to very large problem instances within a short time.