Design of a bi-objective reliable healthcare network with finite capacity queue under service covering uncertainty

•We model the design and planning of reliable healthcare network.•A bi-objective reliable location model is proposed for health care management.•Our framework investigates a patient queue system with two patient groups.•Proposing an interval-valued fuzzy-stochastic-game theory solution approach.•Implementation of the model on a real-life case study in healthcare sector in Iran.

This paper designs a reliable healthcare network. Under limited capacity, queue of patients may deteriorate the condition and leads to risk of death. Consequently, it is vital to investigate a queue system that considers the condition and changes over the time. Besides, treatment units just serve patients that are in their coverage threshold, while this threshold is affected by several factors. This paper considers number of patients and covering threshold under uncertainty. To handle uncertainty, an integrated approach is proposed. Two meta-heuristic algorithms are developed for the given problem. Finally, we carried out experiments to assess proposed model and approaches.