Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be challenging as they are exposed to many uncertainties regarding supply and demand processes, travel times, and quantity/quality of returned products. In this paper, we study the production planning, inventory management, and vehicle routing decisions of a CLSC of beverage glass bottles. We propose an MILP model and rely on a multi-stage adjustable robust optimization (ARO) formulation to deal with the uncertainties in demand for filled bottles and in requests to pick up empty bottles. We develop a novel branching technique to solve the ARO problem and design a heuristic search approach to decrease the solution time. Numerical experiments not only show the incompetency of the customary method, namely the affine decision rule approach but also illustrate how the developed branching and heuristic techniques can solve the small-size problems and improve the quality of the obtained solution dramatically. Furthermore, our numerical results show that the robust plannings tend to be sparse, meaning the routes are chosen so that empty bottles are transported to production sites in such a way they order a few new bottles. Thus, the robust plannings make the CLSC more environmentally friendly.