Optimizing the Distribution and Allocation of COVID-19 Vaccines Using Mathematical Programming Approach: A Case Study in Indonesia

Effective distribution of COVID-19 vaccines is crucial for pandemic control. This study utilized a multi-product mixed-integer nonlinear programming (MINLP) model to optimize the distribution of five vaccine types across (AstraZeneca, Sinopharm, Moderna, Pfizer, and Sinovac). The population, segmented into five age groups (12-18 years, 19-30 years, 31-45 years, 46-59 years and over 60 years), accesses vaccines through 59 healthcare facilities in one of the large cities in Indonesia. With a budget of IDR 150 billion, the model procured five vaccine a total of 574,748 vaccine doses, distributed as follows: 112,954 of type 1, 115,733 of type 2, 115,649 of type 3, 112,171 of type 4, and 118,241 of type 5 vaccines. The model successfully optimized the distribution, achieving a delivery-to-demand ratio of 0.049, which reflects the proportion of vaccine demand met under various scenarios, particularly in scenario 4, which represents actual conditions. Decision-makers can further enhance vaccine allocation by adjusting the total budget; for instance, an additional IDR 10 billion would enable the distribution of 123,474 more doses, increasing the delivery-to-demand ratio to 0.056. This ratio of 0.056 was obtained by adjusting the total budget allocated for vaccine distribution in scenario 5, based on the results from AMPL and Gurobi software. A significant contribution of this study is the development of a MINLP model that ensures equitable distribution tailored to age-specific pandemic requirements. Validation using real-world data enhances the existing literature on vaccine distribution strategies. This study provides valuable insights for policymakers and managers aiming to optimize resource allocation and distribution strategies for COVID-19 vaccination programs, thereby improving overall pandemic management efficiency.