Directional approach to gradual cover: the continuous case
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Directional approach to gradual cover: the continuous case Tammy Drezner1 · Zvi Drezner1 · Pawel Kalczynski1 Received: 5 December 2019 / Accepted: 13 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Location · Genetic algorithm · Cover location models · Partial cover · Gradual cover
1 Introduction Cover location models constitute a main branch of location analysis. A demand point is covered by a facility within a certain distance (Church and ReVelle 1974; ReVelle et al. 1976). A given number of facilities need to be located in an area so as to provide
In order to calculate the joint cover, existing cover location 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.
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Zvi Drezner [email protected] Tammy Drezner [email protected] Pawel Kalczynski [email protected]
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Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA 92834, USA
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T. Drezner et al.
as much cover as possible. Such models are used for modeling cover provided by emergency facilities such as ambulances, police cars, or fire trucks. They are also used to model cover by transmission towers for cell-phone, TV, radio, radar among others. In gradual cover models (also referred to as partial cover) it is assumed that up to a certain distance r the demand point is fully covered and beyond a greater distance R it is not covered at all. Between these two extreme distances the demand point is partially covered. There exist several formulations of the partial cover. Berman and Krass (2002) suggested a declining step function between r and R. Drezner et al. (2004) suggested a linear decline in cover between r and R, and Drezner et al. (2010) suggested a linear decline between random values of r and R. Drezner et al. (2019) proposed that the demand point is represented by a circle of diameter R − r and the cover is the
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