A robust mathematical model for medical tourism facility location and specialties allocation under hybrid uncertainty

Purpose In the contemporary landscape, medical tourism has emerged as a pivotal industry driving sustainable development. Investors in this sector face significant challenges, such as the optimal location of medical facilities, the range of medical services offered and the capacity of these centers. This study aims to introduce an innovative model to address these complexities. Design/methodology/approach A mixed-integer mathematical model is proposed that integrates a scenario-based robust optimization (SRO) framework with possibilistic chance-constrained programming (PCCP). It accounts for the stochastic nature of construction costs while treating the availability of human resources and their salaries as fuzzy parameters. The SRO method is used to deal with stochastic data, and its goal is to reduce the deviation of the objective function in different scenarios from the expected optimal value. The PCCP method is used to deal with fuzzy data, and the necessity criterion is used. Findings To demonstrate the practical applicability of the proposed model, a case study in Iran was conducted. Using mixed-integer linear programming, the model effectively identified suitable cities, specialties and the capacity for each specialty in each center. The outcomes of this research provide a standardized framework for researchers and organizations aiming to establish medical tourism centers in diverse countries while accommodating uncertainty. Originality/value Given the dual presence of random and epistemic uncertainties, this research is pioneering in its application of hybrid uncertainty to the medical tourism sector, offering valuable insights for future studies.