The Fleet Sizing Problem (FSP) stands as a critical challenge within the realm of logistics and supply chain management, particularly in the context of Closed-Loop Supply Chains (CLSC). The significance of addressing the FSP lies in its direct impact on operational costs, resource utilization, and environmental sustainability. By effectively optimizing fleet size, organizations can streamline transportation operations, minimize fuel consumption, reduce carbon emissions, and ultimately enhance overall supply chain performance. Moreover, in CLSC management, where the coordination of forward and reverse logistics activities is paramount, tackling the FSP becomes even more crucial. Efficient fleet sizing enables businesses to effectively manage product returns, remanufacturing, and recycling processes, thereby fostering circular economy principles and maximizing resource utilization.In this study, we address the FSP and vehicle routing decisions within a CLSC context. We propose an MILP model and employ a multi-stage adjustable robust optimization (ARO) formulation to handle the nondeterministic nature of demand for new products and requests for pickups of used products. We reconfigure an exact oracle-based algorithm and a heuristic search algorithm to derive upper and lower bounds on the optimal solution of the ARO problem. Additionally, we introduce a metaheuristic algorithm to function as the oracle. Our numerical experiments demonstrate that our metaheuristic approach, which is integrated with the aforementioned methods, significantly enhances both the computational efficiency and solution quality.