Capacitated facility location problem under uncertainty with service level constraints

Classic facility location models often assume customer demands to be deterministic, although real-world demand is usually uncertain, especially in long-term strategic planning. While stochastic programming models are widely used to address uncertainty, the default approach of ensuring that the facility capacities are met at all times, i.e., for every scenario, can sometimes produce overly conservative solutions. This paper presents a novel stochastic programming model that incorporates a range of service level restrictions that allow demand to be unsatisfied with a certain probability and up to a certain amount. Concerning the former, we use two α-service level constraints, a well-known local and a new global constraint, while the latter is controlled through two β-service level constraints that take the expected value and the maximum value of the excess demand into account. The service levels are incorporated in the stochastic programming model using chance constraints. To solve the model’s deterministic equivalent, we implement a Benders’ decomposition and a modified sample average approximation algorithm with concentration sets. We carry out experiments on randomly generated data sets and a real-world inspired case study in Scotland to compare the performance of models with different service level combinations, as well as with the classical penalty model.