Although modern location theory is now more than 90 years old, the focus of researchers in this area has been mainly problem oriented. However, a common theory, which keeps the essential characteristics of classical location models, is still missing.
This monograph addresses this issue. A flexible location problem called the Ordered Median Problem (OMP) is introduced. For all three main subareas of location theory (continuous, network and discrete location) structural properties of the OMP are presented and solution approaches provided. Numerous illustrations and examples help the reader to become familiar with this new location model.
By using OMP classical results of location theory can be reproved in a more general and sometimes even simpler way. Algorithms enable the reader to solve very flexible location models with a single implementation. In addition, the code of some algorithms is available for download.
Tabella dei contenuti
Location Theory and the Ordered Median Function.- Mathematical Properties of the Ordered Median Function.- The Continuous Ordered Median Location Problem.- The Continuous Ordered Median Problem.- Bisectors.- The Single Facility Ordered Median Problem.- Multicriteria Ordered Median Problems.- Extensions of the Continuous Ordered Median Problem.- Ordered Median Location Problems on Networks.- The Ordered Median Problem on Networks.- On Finite Dominating Sets for the Ordered Median Problem.- The Single Facility Ordered Median Problem on Networks.- The Multifacility Ordered Median Problem on Networks.- Multicriteria Ordered Median Problems on Networks.- Extensions of the Ordered Median Problem on Networks.- The Discrete Ordered Median Location Problem.- and Problem Statement.- Linearizations and Reformulations.- Solution Methods.- Related Problems and Outlook.
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