The problem of maximizing the sum of elements below the principal diagonal of an input-output table by permuting the industry order, i.e. the triangularization problem, must necessarily be solved with approximate methods when tables are of large dimension. We suggest a method that bounds the number of permutations by using a convergence condition together with necessary and sufficient conditions for the maximization problem. A branch and bound algorithm taking advantage of these conditions is presented. The triangularization problem is considered to be an alternative approach of maximizing the sum of negative differences between the elements below and the symmetrical elements above the principal diagonal. The convergence property of the algorithm is illustrated by computing the series of suboptimal solutions for input-output tables of the Nordic countries. We find intertemporal similarities between production hierarchies for Denmark, Finland, Norway and Sweden.