Lower bounds for the axial three-index assignment problem

This paper describes new bounding methods for the axial three-index assignment problem (3AP). For calculating 3AP lower bounds, we use a projection method followed by a Hungarian algorithm, based on a new Lagrangian relaxation. We also use a cost transformation scheme, which iteratively transforms 3AP costs in a series of equivalent 3APs, which provides the possibility of improving the 3AP lower bound. These methods produce efficiently computed relatively tight lower bound.