The distribution of vaccines is constrained by a number of practical issues such as uncertainty about vaccine demand, small stock holdings, inadequate cold-chain capacity, logistical delays, and access to vaccines across regions. In this study, an implementable optimization model is developed to optimize the allocation of vaccines in the regional warehouses and health centers. A Multi-Objective Mixed-Integer Linear Programming (MO-MILP) model is used to reduce the transportation cost, delivery delay and enhance the demand fulfilment. Available vaccine stock, vaccine vehicle capacity, stock and storage capacity, regional demand, priority groups, travel distance and delivery schedules are incorporated into the methodology. Simulated distributions for various regions reveal a decrease of 11.8% in transportation cost, 14.6% in mean delivery time and an improvement in demand fulfilment from 89.7% to 95.2% as proven through experimental analysis. The innovation is that the logistics, equity and cold chain considerations are all integrated in one allocation model. The proposed framework offers a scalable decision support tool for realistic healthcare planning and decision making on vaccines, and suggests that optimized allocation would enable a more efficient distribution and better access to vaccines.