A Branch & Cut algorithm for a four-index assignment problem

G Appa (), D Magos and I Mourtos
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G Appa: London School of Economics
D Magos: Technological Educational Institute of Athens
I Mourtos: London School of Economics

Journal of the Operational Research Society, 2004, vol. 55, issue 3, 298-307

Abstract: Abstract In this paper, we examine the orthogonal Latin squares (OLS) problem from an integer programming perspective. The OLS problem has a long history and its significance arises from both theoretical aspects and practical applications. The problem is formulated as a four-index assignment problem whose solutions correspond to OLS. This relationship is exploited by various routines (preliminary variable fixing, branching, etc) of the Branch & Cut algorithm we present. Clique, odd-hole and antiweb inequalities implement the ‘Cut’ component of the algorithm. For each cut type a polynomial-time separation algorithm is implemented. Extensive computational analysis examines multiple aspects concerning the design of our algorithm. The results illustrate clearly the improvement achieved over simple Branch & Bound.

Keywords: integer programming; linear programming; Branch & Cut; orthogonal Latin squares (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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DOI: 10.1057/palgrave.jors.2601655

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