facility location

Facility location problems have often vagueness and uncertain properties. In P-center problems, this uncertainty can be in the parameters of demand nods. Firstly, in this paper, a vertex-center problem with uncertain demand nodes is considered in which the demand nodes are fuzzy and fuzzy random variables. Then, new solving methods are proposed based on possibility and necessity measures, using fuzzy and fuzzy random programming, respectively. Finally, a real case study in the city of Tabriz in Iran is presented to clarify the methods discussed in this paper. The computational results of the study indicate that these methods can be implemented for center problem with uncertain framework.

Objective : This paper develops a single-objective and a bi-objective mixed-integer linear programming model to optimize the post-earthquake relief logistics network involving transfer points, hospitals, and relief centers in Tehran, Iran. The primary aim is to minimize the total time required to transfer injured individuals through the system, while the bi-objective model additionally minimizes penalties for failing to transfer casualties due to capacity shortages.  Methodology: The methodology involves formulating location-allocation models in which demand points, transfer points, hospitals, and relief centers are represented by specific capacity and travel-time parameters. The models are applied to two earthquake scenarios in south-central Tehran: a magnitude-6 event with lower casualties and selective facility activation, and a magnitude-7 event requiring full capacity utilization and a 30% assumed increase in hospital capacity. Results : The model’s effectiveness in optimizing the relief network is demonstrated. For the magnitude-6 scenario, the model selects 10 transfer points, 15 hospitals, and 25 relief centers to minimize total transfer time. For the magnitude-7 scenario, utilizing all available facilities, the model optimally allocates casualties despite severe capacity constraints. Conclusion : The proposed models offer a practical decision-support tool for designing efficient humanitarian supply chains in earthquake-prone urban areas. They underscore the necessity of pre-disaster planning, including establishing transfer points with triage and outpatient capabilities, increasing hospital surge capacity, and ensuring public awareness to direct casualties to designated transfer points.