Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2014/1: A New Semi-Lagrangean Relaxation for the K-Cardinality Assignment Problem

Ivan Belik () and Kurt Jörnsten ()
Additional contact information
Ivan Belik: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Kurt Jörnsten: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Recently Beltrán-Royo, Vial & Alonso-Ayuso (2012) presented a semi-Lagrangean relaxation for the classical p-median location problem and for the incapacitated facility location problem. The results, obtained using the semi-Lagrangean relaxation approach, were quite impressive. In this paper we use a semi-Lagrangean relaxation to obtain an efficient solution method for the kcardinality assignment problem. The method has only one semi-Lagrangean multiplier that can only take on a limited number of values, making the search for the optimal multiplier easy. Since the semi-Lagrangean relaxation closes the duality gap, this leads to an extremely reliable and easily implementable method for finding k-cardinality assignments in large-scale cases. The method is computationally tested on the examples commonly used in the literature.

Keywords: K-cardinality assignment; Lagrangean Relaxation; Mathematical Programming

JEL-codes: C00; C60; C61

24 pages, January 15, 2014

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