COVID-19 vaccine distribution planning using a congested queuing system—A real case from Australia

Crisis-induced vaccine supply chain management has recently drawn attention to the importance of immediate responses to a crisis (e.g., the COVID-19 pandemic). This study develops a queuing model for a crisis-induced vaccine supply chain to ensure efficient coordination and distribution of different COVID-19 vaccine types to people with various levels of vulnerability. We define a utility function for queues to study the changes in arrival rates related to the inventory level of vaccines, the efficiency of vaccines, and a risk aversion coefficient for vaccinees. A multi-period queuing model considering congestion in the vaccination process is proposed to minimise two contradictory objectives: (i) the expected average wait time of vaccinees and (ii) the total investment in the holding and ordering of vaccines. To develop the bi-objective non-linear programming model, the goal attainment algorithm and the non-dominated sorting genetic algorithm (NSGA-II) are employed for small- to large-scale problems. Several solution repairs are also implemented in the classic NSGA-II algorithm to improve its efficiency. Four standard performance metrics are used to investigate the algorithm. The non-parametric Friedman and Wilcoxon signed-rank tests are applied on several numerical examples to ensure the privilege of the improved algorithm. The NSGA-II algorithm surveys an authentic case study in Australia, and several scenarios are created to provide insights for an efficient vaccination program.