The present study investigates the cause-and-effect relationships between production capacity decisions and the choice of distribution policy aspects of managing an extensive vaccination programme. The Indian COVID-19 vaccine supply chain is taken as a case study, and Indian demographic data is utilised. A Monte Carlo Markov Chain (MCMC) model is developed to estimate time period-wise demand corresponding to each distribution policy. Furthermore, eight different capacity management models involving different capacity addition and transfer strategies for four different distribution policies are formulated. The trade-off between effectiveness and efficiency objectives, namely Vaccine Supply Chain total cost and service level, is investigated by comparing the Pareto frontiers of the proposed models. Furthermore, the models are compared based on capacity transfer cost, capacity addition cost, and variation in region-wise service level. The results reveal that organisations can simultaneously save significant costs and achieve higher service levels if they cautiously align their capacity management approach and the distribution policy on the demand front. Capacity management interventions at the national level result in more service levels and lower variation and costs than at the regional level.