Solving a two-stage facility location problem with second-stage activation costs

We study a stochastic scenario-based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in both the initial location, and then in the activation, of facilities. The first-stage variables in our problem are the traditional binary facility-location variables, while the second-stage variables involve a mix of binary facility-activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second-stage integer activation variables, and so we instead derive cutting planes tailored to the problem under investigation. These cutting planes are tighter than the general cuts established by Laporte and Louveaux for two-stage binary programming problems. We prove the validity of our proposed cutting planes, and demonstrate the computational efficacy of our approach on a set of randomly generated test problems.