Investigating the Maximal Coverage by Point-based Surrogate Model for Spatial Facility Location Problem

Abstract

Spatial facility location problems (SFLPs) involve the placement of facilities in continuous demand regions. One approach to solving SFLPs is to aggregate demand into discrete points, and then solve the point-based model as a conventional facility location problem (FLP) according to a surrogate model. Solution performance is measured in terms of the percentage of continuous space actually covered in the original SFLP. In this dissertation I explore this approach and examine factors contributing to solution quality. Three error sources are discussed: point representation spacing, multiple possible solutions to the surrogate point-based model, and round-off errors induced by the computer representation of numbers. Some factors—including boundary region surrogate points and surrogate point location—were also found to make significant contributions to coverage errors. A surrogate error measure using a point-based surrogate model was derived to characterize relationships among spacing, facility coverage area, and spatial coverage error. Locating continuous space facilities with full coverage is important but challenging. Demand surrogate points were initially used as a continuous space for constructing the MIP model, and a point-based surrogate FLP was enhanced for extracting multiple solutions with additional constraints that were found to reduce coverage error. Next, a best initial solution was applied to a proposed heuristic algorithm to serve as an improvement procedure. Algorithm performance was evaluated and applied to a problem involving the location of emergency warning sirens in the city of Dublin, Ohio. The effectiveness of the proposed method for solving this and other facility location/network design problems was demonstrated by comparing the results with those reported in recently published papers.