Design of a reliable hierarchical location-allocation model under disruptions for health service networks: A two-stage robust approach

•A hierarchical location model is proposed for health service network design.•Uncertainty associated with demand and service is considered by a queuing system.•The model is formulated based on a two-stage robust optimization approach.•A Benders decomposition algorithm is implemented to solve the model.

This study proposes a novel reliable hierarchical location-allocation model for health service network designs where facilities are subject to the risk of disruptions. To characterize the relationship between various levels of the concerned health network, a two-level multi-flow nested hierarchy with service referral is taken into account. The queuing system is considered in the model which handles uncertainty associated with demand as well as service. To ensure the service quality, a minimum limit reflected in the probability of patients' waiting time is defined. The proposed model is formulated based on a two-stage robust optimization approach in which decisions are defined in two stages such that a first-stage solution should be robust against the possible realizations of the disruption that can only be revealed in a second stage. A solution procedure based on Benders decomposition type algorithm is implemented to solve the model. To illustrate the applicability of the proposed model, a practical case study is presented. The results show that the proposed model can be applied as a flexible decision support tool for decision makers to adopt appropriate strategies and policies in designing a reliable and robust health service network.