An algorithm for the planar three-index assignment problem

A branch and bound algorithm for the planar three-index assignment problem is presented. The branching operation is performed on sets of variables belonging to a common constraint rather than on a single variable. The algorithm comprises an upper and lower bound procedure. The upper bound procedure consists of two parts: one for finding an initial solution and one for improving it. The local improvement rule takes advantage of the Latin square structure of the solution. The lower bound procedure combines a new dual heuristic and a Lagrangean relaxation scheme solved by subgradient optimization. The use of reduced costs in the evaluation of bounds is another feature of the algorithm. Computational experience both on the exact algorithm and on the primal heuristics as standalone procedures is reported.