Ordered median problem with demand distribution weights
Włodzimierz Ogryczak , Paweł Olender
AbstractThe 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.
|Journal series||Optimization Letters, ISSN 1862-4472|
|Publication size in sheets||0.75|
|Keywords in English||Location Ordered median Weighted ordered median OWA WOWA Mixed integer linear programming|
|project||Development 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
|License||Journal (articles only); author's original; ; after publication|
|Score|| = 25.0, 27-03-2017, ArticleFromJournal|
= 35.0, 27-03-2017, ArticleFromJournal
|Publication indicators||: 2016 = 1.31 (2) - 2016=1.282 (5)|
|Citation count*||3 (2018-06-10)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.