Location covering models. History, applications and advancements
type: Item
instance of: scholarly article
title: Location covering models. History, applications and advancements
zbMATH Open document ID: 1432.90004
DOI: 10.1007/978-3-319-99846-6
author: Richard L. Church
author: Alan T. Murray
published in: Advances in Spatial Science
publication date: 2019-01-07T00:00:00Z
review text: Location covering problems are concerned with optimal choice of facilities to provide a certain level of service to given demand. Applications abound in widely differing areas such as surveillance, sensors and antennas, warning systems, emergency response, relief, security and communication provision, fair access to public services, nature reserve design, franchising, marketing, archeaology, hazardous facilities, etc., each calling for its own meaning of optimality, facility, service level, demand, etc. In particular, the notion of coverage itself, usually thought of as lying within a given distance bound, may in fact come in many more disguises. This book gives an overview of the many shapes such problems may take in practice and how these have been or can be formalised as mixed integer programming models (MIP), to be solved to optimality using off the shelf solvers. The following topics are covered throughout the chapters. After a semi-historical introductory chapter on general location questions and their application areas, the two major covering model paradigms are introduced: either complete coverage of demand at least cost (location set covering) or covering the most demand possible under limited budget (maximal covering). Their simple MIP formulations introduce the basic notation for data and variables, which the authors try to maintain throughout the book. Some attention goes to an alternative formulation as \(p\)-median problems. These models are then extended to incorporate additional complications such as multiple coverage provision, multiple service levels, multiple objectives, backup coverage, coordination between facilities and/or hierarchical facility systems. Coverage also often involves uncertainty and risk obliging planners to think probabilistically and consider the reliability of the system design to be optimised, which may be done in several ways. Situations where coverage is not desirable but rather detrimental call for new so-called anti-cover…
reviewed by: Frank Plastria
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 90B80
Mathematics Subject Classification ID: 90C27
Mathematics Subject Classification ID: 00A71
Mathematics Subject Classification ID: 90C11
zbMATH DE Number: 6997779
zbMATH Keywords: location set covering
zbMATH Keywords: maximal covering
zbMATH Keywords: mixed integer programming
zbMATH Keywords: reliability
zbMATH Keywords: anti-cover
zbMATH Keywords: capture
zbMATH Keywords: disruption
zbMATH Keywords: interdiction
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-99846-6
OpenAlex ID: W2946619050
description: scientific article; zbMATH DE number 6997779