A relax-and-fix Pareto-based algorithm for a bi-objective vaccine distribution network considering a mix-and-match strategy in pandemics

Mass vaccination in pandemics is one of the most effective strategies to halt disease transmission. A well-organized vaccination plan is essential for guaranteeing its success in cases with limited vaccines. On the other hand, most vaccines need more than one dose for appropriate immunity, intensifying the vaccine shortage probability and complicating decision-making. This study presents a bi-objective mixed-integer linear model for a vaccine distribution chain problem, simultaneously considering economic and social objectives, with multi-dose vaccination adaptable even for booster doses. Moreover, the compatible vaccines in each vaccination process are considered a mix-and-match strategy to diversify vaccination alternatives and alleviate the vaccine shortage risk. It is shown that the problem is NP-hard, and we develop two heuristic and meta-heuristic algorithms to solve real-size instances in a reasonable time. Both algorithms use problem size reduction and problem decomposition techniques to produce an approximate Pareto front for the problem. The heuristic algorithm employs relax-and-fix and fix-and-optimize techniques, and an epsilon-constraint method to solve the multi-objective problem. The proposed meta-heuristic algorithm is based on the hybrid of two well-known evolutionary algorithms, particle swarm optimization, and genetic algorithm. It also uses a multi-objective framework called PESA-II to generate the Pareto front. Both proposed heuristic and meta-heuristic algorithms can employ parallel computing, which significantly reduces computational time. Finally, we investigate the proposed algorithms’ performance using 30 random problem instances and a case study from Iran. The results demonstrate that heuristic and meta-heuristic algorithms have obtained a reasonable solution with a maximum of 6.9% and 16.3% cost objective function gap respectively. The heuristic algorithm is superior to the meta-heuristic in terms of Pareto front quality metrics.