Directional approach to gradual cover: the continuous case
This work addresses facility location planning for urban or regional areas, but it is incremental as it builds on existing gradual cover models with a directional modification.
The paper tackled the problem of facility location by introducing a directional approach to gradual cover, where joint coverage depends on facility directions, and developed a genetic algorithm for solving it. The method was tested on a case study in Orange County, California, showing practical applicability.
The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "directional gradual cover". Contrary to all gradual cover models, the joint cover depends on the facilities' directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California.