A branch-and-bound algorithm for the linear ordering problem with cumulative costs

The linear ordering problem with cumulative costs is an NPNP-hard combinatorial optimization problem arising from an application in UMTS mobile-phone communication systems. This paper presents a polynomially computable lower bound that is particularly effective when embedded in a branch-and-bound algorithm. The same idea can be further exploited to sort the children nodes at each node of the search tree, in order to find the optimal solution earlier. A suitable truncation of the resulting branch-and-bound algorithm results in a fast constructive heuristic.