Ensuring a consistent supply of vaccines from manufacture to distribution, storage, and administration relies on efficient management of the Vaccine Supply Chain (VSC). However, in recent years, vaccine shortages have emerged as a major issue for vaccine producers and child immunization programs, especially in low- and middle-income countries, which hampers VSC overall performance. This study aims to address the ongoing problem of vaccine shortages in India’s child immunization program by identifying the main causes and investigating possible solutions to address the shortage issue. To do this, we propose an integrated framework that combines the Analytic Hierarchy Process (AHP) and Complex Proportional Assessment with Grey Theory (COPRAS-G) methodologies. This framework yields 12 potential solutions for the 10 issues causing shortages. We show that demand uncertainty is the primary cause of vaccine shortages and that a better monitoring system is necessary to detect and treat shortages in a timely manner. To validate the stability of the results, we run a Monte Carlo simulation using a uniform probability distribution on the interval [0, 1]. The results of this study will provide valuable insights for policymakers on how to effectively manage the vaccine shortage issue and improve the performance of child immunization programs.