Cordilleran orogenic systems such as the Andes are controlled by shortening rates, climatically-controlled erosion rates, and, in some cases, eclogite production and delamination. All of these processes are coupled, however, making it difficult to uniquely determine the relative importance of each process and the feedbacks among them. In this paper we develop a mass-balanced numerical model that couples an actively-shortening orogen and crustal root with eclogite production, delamination, and climatically controlled erosion. The model provides a first-order quantification of the sources (shortening) and sinks (erosion and eclogite production and delamination) of crustal volume during the Cenozoic in the Andes as a function of latitude and time. Given reasonable estimates for the rates of eclogite production and the threshold size of the eclogitic root required for delamination, the model suggests that, in the central Andes between 5° S and 32° S, the orogen has grown to a sufficient height to produce and maintain eclogite, which in turn has promoted delamination in the lower crust and mantle. In this region, climatically controlled erosion rates influence the size of the orogen through two separate mechanisms: by exporting mass via surface processes and by controlling the lithostatic pressure in the lower crust, which modulates the rates of eclogite production and/or delamination. To the north and south of the central Andes, relatively low shortening rates and high precipitation and erosion rates have slowed eclogite production such that delamination likely has not occurred during the Cenozoic.