A Branch & Cut algorithm for a four-index assignment problem
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- Appa, G., Magos, D. & Mourtos, I. J Oper Res Soc (2004) 55: 298. doi:10.1057/palgrave.jors.2601655
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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.