Ebook: Location Theory: A Unified Approach
- Tags: Operations Research/Decision Theory, Regional Science, Operations Research Mathematical Programming
- Year: 2005
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages I-XXI
Mathematical Properties of the Ordered Median Function....Pages 3-20
The Continuous Ordered Median Problem....Pages 23-42
Bisectors....Pages 43-103
The Single Facility Ordered Median Problem....Pages 105-135
Multicriteria Ordered Median Problems....Pages 137-163
Extensions of the Continuous Ordered Median Problem....Pages 165-194
The Ordered Median Problem on Networks....Pages 197-208
On Finite Dominating Sets for the Ordered Median Problem....Pages 209-248
The Single Facility Ordered Median Problem on Networks....Pages 249-274
The Multifacility Ordered Median Problem on Networks....Pages 275-287
Multicriteria Ordered Median Problems on Networks....Pages 289-310
Extensions of the Ordered Median Problem on Networks....Pages 311-327
Introduction and Problem Statement....Pages 331-340
Linearizations and Reformulations....Pages 341-379
Solution Methods....Pages 381-417
Related Problems and Outlook....Pages 419-422
Back Matter....Pages 423-437
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.
Content:
Front Matter....Pages I-XXI
Mathematical Properties of the Ordered Median Function....Pages 3-20
The Continuous Ordered Median Problem....Pages 23-42
Bisectors....Pages 43-103
The Single Facility Ordered Median Problem....Pages 105-135
Multicriteria Ordered Median Problems....Pages 137-163
Extensions of the Continuous Ordered Median Problem....Pages 165-194
The Ordered Median Problem on Networks....Pages 197-208
On Finite Dominating Sets for the Ordered Median Problem....Pages 209-248
The Single Facility Ordered Median Problem on Networks....Pages 249-274
The Multifacility Ordered Median Problem on Networks....Pages 275-287
Multicriteria Ordered Median Problems on Networks....Pages 289-310
Extensions of the Ordered Median Problem on Networks....Pages 311-327
Introduction and Problem Statement....Pages 331-340
Linearizations and Reformulations....Pages 341-379
Solution Methods....Pages 381-417
Related Problems and Outlook....Pages 419-422
Back Matter....Pages 423-437
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