As the novel coronavirus pandemic wreaked havoc globally, governments have implemented massive vaccination programs to tackle it. However, since the pandemic's emergence moves beyond the second year, some issues have stymied vaccination programs, including vaccine hesitancy, vaccine distribution inequality, new strains of the virus, and a possibility that the virus enters a stage of a requirement for cyclical vaccination. These challenges highlight the need for an appropriate mass COVID-19 vaccination program. Therefore, we attempt to address this problem by developing a bi-objective integrated vaccine allocation and inventory management framework. The goal is to minimize the system costs while maximizing the vaccination service level. Several important factors, such as multiple types of vaccines, the vaccines' perishability concept, demand uncertainty, and motivational strategy, have been addressed using dynamic planning. Besides that, the model development mechanism is carried out to be compatible and applicable to the current general vaccination program policies, forcing few strategic changes. Then, a case study concerning the vaccination program of the city of Mashhad in Iran is applied to the model. The results demonstrated significant advantages in total cost, vaccine shortage, and wastage compared to the current policy. Finally, the Lagrangian relaxation method is implemented on the model to strengthen further its capacity to handle larger-scale problems.