Facility Location with Modular Capacity Under Demand Uncertainty : An Industrial Case Study

We investigate a facility location problem with modular capacity under demand uncertainty arising at Hydro-Québec, the largest public utility in Canada. We propose a mathematical model to locate the facilities, determine the capacity levels, and compute the number of service teams needed in each facility to satisfy the service demand of all customers. We implement a two-stage stochastic optimization framework to address the uncertainty in customer demand. We present a traditional scenario-based stochastic optimization method and a linear decision rule (LDR)-based solution method. We highlight the significant reduction in the computational time provided by the latter, particularly for large instances. These gains in computational performance come at the expense of probable overly robust location decisions. To manage this possible outcome, we adapt a feedback concept found in process system controllers, and we develop two LDR robust trade-off heuristic algorithms that combine a linear decision method with the feedback mechanism. The benefits are empirically illustrated via numerical experiments and validated in an industrial case study in which we achieve a 1.37% to 5.20% reduction in average total costs