Solving multi-stage stochastic facility location problems with modular capacity adjustments

We consider a multi-stage stochastic facility location problem with modular capacity adjustments, minimizing the expected costs of allocating uncertain customer demand. We present a general multi-stage mixed-integer programming formulation that allows for multiple facility expansions, reductions, and closing of existing facilities. Given the complexity of this planning problem, we present a solution method based on Lagrangian relaxation, followed by the solution of a restricted model to further improve the solution quality. The computational results show that our solution method provides high-quality solutions within reasonable computing times. We further compare the value of a multi-stage stochastic solution to the solution of a deterministic rolling horizon problem and discuss situations when solving a multi-stage problem is particularly beneficial.