Solving a multi-horizon stochastic facility location problem with capacity expansion

Motivated by the real-world problem of locating hydrogen production facilities and assessing different production technologies which differ in the flexibility of operations and costs, we study a multi-stage multi-horizon stochastic facility location problem with capacity expansion. The objective is to minimize the expected sum of investment, production and distribution costs while satisfying customer demand. The multi-horizon formulation allows to capture the effects of both strategic as well as operational uncertainty on the location decisions. Strategic uncertainty is related to uncertain future demand level, while operational uncertainty is related to uncertain future electricity prices resulting in uncertain production costs. We consider multiple production technologies that have different operational characteristics, but can be combined at a location and operated in parallel. To solve the problem, we implement and compare two solution methods: linear relaxation with a restricted MIP approach and Lagrangian relaxation with a two-step restricted MIP approach. We apply the solution approaches to instances based on the real-world problem of locating hydrogen production in Norway. The results show that both approaches can find near-optimal solutions for small instances, but the Lagrangian-based solution method can also find high-quality solutions for larger instances.