A Lagrangian Heuristic for the Capacitated Transshipment Location Problem under Uncertainty

We want to find a location of capacitated transshipment facilities which minimizes the expected total cost when the generalized transportation costs are random variables. Each generalized transportation cost is given by the sum of a deterministic transportation cost and a random transshipment facility throughput cost, whose probability distribution is unknown. A two-stage stochastic program with recourse for this problem and its deterministic nonlinear approximation are already available in literature. Unfortunately, both of them are unable to solve real-life instances in a reasonable computing time. In this paper a heuristic for solving the deterministic nonlinear approximation, which combines a Lagrangian-based method for the flows calculation with a Open&Close procedure for the facility location, is given. Computational results show a high performance of this heuristic.