Journal of the Operational Research Society

, Volume 55, Issue 3, pp 298–307

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

Theoretical Paper

DOI: 10.1057/palgrave.jors.2601655

Cite this article as:
Appa, G., Magos, D. & Mourtos, I. J Oper Res Soc (2004) 55: 298. doi:10.1057/palgrave.jors.2601655


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.


integer programming linear programming Branch & Cut orthogonal Latin squares 

Copyright information

© Palgrave Macmillan Ltd 2004

Authors and Affiliations

  1. 1.London School of EconomicsLondonUK
  2. 2.Technological Educational Institute of AthensGreece

Personalised recommendations