A Lagrangian heuristic for the multicommodity capacitated location problem with balancing requirements

We consider the multicommodity capacitated location problem with balancing requirements. This problem has applications in transportation and was introduced in the context of planning the movements of containers between ports and terminals, identified as depots in the problem formulation. We propose a Lagrangian relaxation based on a reformulation of the problem that allows the subproblem to be decomposed by depot, giving rise to a series of continuous knapsack subproblems. We optimize the Lagrangian dual by a bundle method and we develop a Lagrangian heuristic based on slope scaling. Numerical results are presented on a set of large-scale benchmark instances. We obtain good quality solutions within short computing times using the Lagrangian heuristic approach.