The growing need for adequate and safe blood and the high costs of health systems have prompted governments to improve the functioning of health systems. One of the most critical parts of a health system is the blood supply chain, which accounts for a significant share of the health system's costs. In the present study, with an operational approach, the total network costs are minimized along with the minimization of transportation time and lead time of delivery of blood products. Also, determining the optimal routing decisions is improved the level of responsiveness and reliability of the network. In this research, a multi-objective stochastic nonlinear mixed-integer model has been developed for Tehran's blood supply chain network. Robust scenario-based programming is capable of effectively controlling parametric uncertainty and the level of risk aversion of network decisions. Also, the proposed reliability approach controls the adverse effects of disturbances and creates an adequate confidence level in the capacity of the network blood bank. Lastly, the model is solved through the Lagrangian relaxation algorithm. Comparison of the results shows the high convergence rate of the solutions in the Lagrangian relaxation algorithm.