Robust facility location under demand uncertainty and facility disruptions

Facility location decision is strategic: the construction of a new facility is typically costly and the impact of the decision is long-lasting. Environmental changes, such as population shift and natural disasters, may cause today’s optimal location decision to perform poorly in the future. Thus, it is important to consider potential uncertainties in the design phase, while explicitly taking into account the possible customer reassignments as recourse decisions in the execution phase. This paper studies a robust fixed-charge location problem under uncertain demand and facility disruptions. To model this problem, we adopt a two-stage robust optimization framework, where the first-stage location decision is made here-and-now and the second-stage allocation decision can be deferred until the uncertainty information is revealed. We develop a column-and-constraint generation (C&CG) algorithm to solve the models exactly and benchmark it with the other C&CG algorithm in the literature. We further extend our modeling and solution schemes to facility fortification problems under uncertainties, where investment decisions are made for already existing supply chain systems to protect facilities from disruptions and against uncertain demand. We conduct extensive numerical tests to study the differences in solutions produced by the three robust models and the impacts of uncertainties on solution configuration. Results show that our C&CG algorithm can solve more instances to optimality and consume less computing time on average, compared to the benchmark algorithm. Several managerial insights are also drawn from our numerical experiments.