In the case of disruptions in the blood supply chain, rapid reorganization of distribution processes is required to ensure an effective response to emergency situations. This paper considers the problem of redistributing available blood stocks from the institute and hospitals to hospitals affected by a disruption. A mathematical formulation of the problem is developed, with a multi-objective function aiming to: (i) minimize the blood delivery time to the locations of disruption, (ii) minimize violations of predefined safety stock levels at the institute and hospitals, and (iii) minimize the amount of blood taken from hospitals not affected by the disruption. The formulation also introduces constraints that ensure balanced violations of safety stock levels across unaffected facilities. Computational experiments are conducted on test scenarios generated from real case studies from the healthcare system of the Republic of Serbia. Small-sized instances can be solved exactly, providing benchmarks for evaluating a General Variable Neighborhood Search metaheuristic designed for larger problem instances. The results indicate that the proposed metaheuristic produces high-quality solutions within negligible CPU time.