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Location science. (English) Zbl 1329.90003
Cham: Springer (ISBN 978-3-319-13110-8/hbk; 978-3-319-13111-5/ebook). xvi, 644 p. (2015).
After a quite explosive growth during the last fifty years, location science, or optimal facility location, has become a mature field of enquiry at the interface of economics, geography and mathematics, mixing questions from business, regional science, logistics, production engineering with computational techniques of geometry, optimization, operations research and computer science. This collective book of over $$600$$p. is a quasi encyclopedic attempt at covering ‘basic aspects, fundamental problems and properties defining the field ($$\dots$$), advanced models and concepts that are crucial to the solution of many real-life complex problems ($$\dots$$), applications ($$\dots$$) to several fields.’
After an introductory chapter with the older history and the aims and ways to use the book, we find a first part around the following five basic models: $$p$$-median, fixed-charge facility location, $$p$$-center and covering problems, all mainly in a discrete setting, and anti-covering problems in the plane. Then we find a long series of extended and more advanced model-types. In a continuous environment one may have to locate dimensional facilities such as lines, hyperplanes, circles and spheres. When (discrete) model data are uncertain one seeks robust solutions or objectives become stochastic. There can be several objective functions shifting attention towards finding all or some efficient solutions. Some objectives may require prior ordering of distances, leading to the wide and complicated family of ordered median problems. Data may be time-dependent, adding the new dimension of ‘when’ to the basic ‘where’ questions. Hub facilties, or transshipment points, should be located to accomodate given flows between origin/destination pairs. Quadratic assignment problems ask how to place $$n$$ facilities on $$n$$ given sites with least total weighted distance between all facility pairs. The location decision often involves competition with other prior, simultaneous or future facilities, leading to questions of equilibrium or involving several stages. The facility to be located may require design of routes to service demand of customers or the arcs of a network. More generally (re)design of a whole logistics network may be sought. To complicate matters demands may be stochastic streams generating congestion problems, such as waiting queues and/or lost demand. Finally, demand is usually so widespread that its modelling requires aggregation, which leads to evaluation errors to be taken into account.
Although all of location science may be considered to be application oriented, as exemplified by the topics mentioned above, many special application fields generate their own specific types of questions and techniques, leading to a real interplay. The last 6 chapters amply exemplify this. Geographic information systems (GIS) not only offer the ideal digital support to handle the geographically oriented data basic to most location questions, but their widespread use leads to novel insights and questions. Design of telecommunication networks spawns a wealth of innovative location questions due to its constantly evolving technology with many particular constraints. Emergencies also generate lots of special requirements, not only for timely reaching of patients asking for adequate hospital siting and quick ambulance availability, but also for their efficient healthcare as influenced by the inner hospital layout. The efficiency of public transport calls for careful design of rapid transport networks. Politics, geography and distribution are all in need of districts that should be compact, contiguous and balanced in size, design of which yield extremely difficult optimization questions. Finally, in times of disaster, which can happen anywhere, existing networks are disrupted, modifying necessary accessibility; novel models attempt to limit such adverse effects by adequate prior design of the network.
Each of these 24 chapters is a stand-alone overview by well-known researchers on either one particular model-type or an application field in which they are active. It usually consists of basics, survey, state of the art, technical aspects and/or novel contribution parts of varying lengths and technicality, and always with an amply selected up-to-date bibliography. Although some overlap between the chapters is unavoidable it remains rather minimal, restricted to the basic models presented. This format makes the book an excellent tool for both applied and theoretical researchers discovering or working in the field, the wealth of topics allowing to focus directly on a particular model or application area, as well as for teachers and students of specialised courses, for which several proposals of contents are suggested. For theoretical details and proofs the reader will most of the time have to refer to the referenced literature, though.

##### MSC:
 90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming 90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming 90B80 Discrete location and assignment 90B06 Transportation, logistics and supply chain management 90B10 Deterministic network models in operations research 90B18 Communication networks in operations research 90B50 Management decision making, including multiple objectives
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