Duality results for extended multifacility location problems. (3rd July 2018)

• Record Type: Journal Article
• Authors: Wanka, Gert; Wilfer, Oleg
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 1095
• Page End: 1119
• Publication Date: 2018-07-03
• Subjects: Gauges -- continuous minimax multifacility location problems -- set-up costs -- conjugate duality -- optimality conditions; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1387549
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Duality statements are presented for multifacility location problems as suggested by Drezner Hiu 1991, where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. We develop corresponding dual problems for the cases with and without set-up costs and present associated optimality conditions. In the concluding part of this note we use these optimality conditions for a geometrical characterization of the set of optimal solutions and consider for an illustration corresponding examples.