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

Abstract

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.

Keywords: COVID-19 pandemic; Crisis-induced vaccine supply chain; Goal attainment optimisation; NSGA-II; Queuing system.

Fig. 1

Proposed conceptual vaccine allocation network.

Fig. 2

Structure of the chromosome defined in the NSGA-II algorithm.

Fig. 3

Melbourne regional area and its suburbs and hospitals — colours show the population range for each suburb.

Fig. 4

Number of people who received at least one dose of a COVID-19 vaccine in Victoria during the past 106 days (12 Apr 2021–27 Jul 2021) and its decomposed trend and seasonality (COVID LIVE, 2021).

Fig. 5

Optimal inventory and ordering levels for large (Box Hill) and small (Williamstown) hospitals for the first Pareto front in the best scenario.

Fig. 6

Number of servers and utilisation rate for large (Box Hill) and small (Williamstown) hospitals considering the best scenario for demands.

Fig. 7

Demonstration of the contradiction within the objective functions using $p{z}_1,(1-p)z_2$.

Fig. 8

Expected service rate of hospitals for large (Box Hill) and small (Williamstown) hospitals in the best scenario.

Fig. 9

Probability distribution function (PDF) and cumulative distribution function (CDF) of wait times in a queue of vaccines concerning various risk aversion coefficients.

Fig. A.1

Average $S/N$ for different levels of parameters in the NSGA-II model.

Fig. A.2

Average $S/N$ for different levels of parameters in the modified NSGA-II model.

Fig. B.3

Optimal ordering levels for the Melbourne’s suburbs in the best scenario.