Summary: Adequate modeling of undesirable outputs in production processes plays an important role in management practice. Nonparametric models that assume jointly weak disposability of desirable and undesirable outputs have become prevalent in the literature although a consensus on how to implement this axiom has not been reached yet. Particularly, there is still an unresolved debate on whether to use single or multiple scaling factors when applying weak disposability to real datasets in practice. In this paper, we shed some new light on the debate from various theoretical and practical viewpoints including disposability, convexity, returns to scale, and computational issues. Furthermore, we introduce a new model and unveil some interesting properties of the current ones, which then help to construct a comprehensive taxonomy of reference technology sets for activity analysis models under variable returns to scale.