Ordered median problem with demand distribution weights

Włodzimierz Ogryczak , Paweł Olender

Abstract

The ordered median function unifies and generalizes most common objective functions used in location theory. It is based on the ordered weighted averaging (OWA) operator with the preference weights allocated to the ordered distances. Demand weights are used in location problems to express the client demand for a service thus defining the location decision output as distances distributed according to measures defined by the demand weights. Typical ordered median model allows weighting of several clients only by straightforward rescaling of the distance values. However, the OWA aggregation of distances enables us to introduce demand weights by rescaling accordingly clients measure within the distribution of distances. It is equivalent to the so-called weighted OWA (WOWA) aggregation of distances covering as special cases both the weighted median solution concept defined with the demand weights (in the case of equal all the preference weights), as well as the ordered median solution concept defined with the preference weights (in the case of equal all the demand weights). This paper studies basic models and properties of the weighted ordered median problem (WOMP) taking into account the demand weights following the WOWA aggregation rules. Linear programming formulations were introduced for optimization of the WOWA objective with monotonic preference weights thus representing the equitable preferences in the WOMP. We show MILP models for general WOWA optimization.
Author Włodzimierz Ogryczak IAiIS
Włodzimierz Ogryczak,,
- The Institute of Control and Computation Engineering
, Paweł Olender - [Instytut Łączności PIB (IŁ PIB)]
Paweł Olender,,
-
- Instytut Łączności PIB
Journal seriesOptimization Letters, ISSN 1862-4472
Issue year2016
Vol10
No5
Pages1071-1086
Publication size in sheets0.75
Keywords in EnglishLocation Ordered median Weighted ordered median OWA WOWA Mixed integer linear programming
DOIDOI:10.1007/s11590-015-0990-4
URL http://link.springer.com/article/10.1007/s11590-015-0990-4
projectDevelopment of methodology of control, decision support and production management. Project leader: Zieliński Cezary, , Phone: 5102, start date 19-05-2015, end date 31-12-2016, 504/02233/1031, Completed
WEiTI Działalność statutowa
Languageen angielski
LicenseJournal (articles only); author's original; Other open licence; after publication
File
Ogryczak Olennder Opt Lett.pdf 505.03 KB
Score (nominal)35
ScoreMinisterial score = 25.0, 27-03-2017, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 27-03-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.31 (2) - 2016=1.282 (5)
Citation count*3 (2018-06-10)
Cite
Share Share

Get link to the record
msginfo.png


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back