In this paper, a new responsive-green-cold vaccine supply chain network during the COVID-19 pandemic is developed for the first time. According to the proposed network, a new multi-objective, multi-period, multi-echelon mathematical model for the distribution-allocation-location problem is designed. Another important novelty in this paper is that it considers an Internet-of-Things application in the COVID-19 condition in the suggested model to enhance the accuracy, speed, and justice of vaccine injection with existing priorities. Waste management, environmental effects, coverage demand, and delivery time of COVID-19 vaccine simultaneously are therefore considered for the first time. The LP-metric method and meta-heuristic algorithms called Gray Wolf Optimization (GWO), and Variable Neighborhood Search (VNS) algorithms are then used to solve the developed model. The other significant contribution, based on two presented meta-heuristic algorithms, is a new heuristic method called modified GWO (MGWO), and is developed for the first time to solve the model. Therefore, a set of test problems in different sizes is provided. Hence, to evaluate the proposed algorithms, assessment metrics including (1) percentage of domination, (2) the number of Pareto solutions, (3) data envelopment analysis, and (4) diversification metrics and the performance of the convergence are considered. Moreover, the Taguchi method is used to tune the algorithm's parameters. Accordingly, to illustrate the efficiency of the model developed, a real case study in Iran is suggested. Finally, the results of this research show MGO offers higher quality and better performance than other proposed algorithms based on assessment metrics, computational time, and convergence. [ABSTRACT FROM AUTHOR]