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The environmental sustainability is a globally important issue, particularly in the global warming. There are many institutions and people who are interested in the greenhouse gases emissions issue and policies that attempt to improve the problem. The aviation industry is not an exception. Under this background, there has been much research on airport efficiency analysis, undesirable outputs, and on evaluating productivity with respect to environmental factors. In the efficiency analysis models with the undesirable outputs in the airports, there are two main types of production possibility frontiers. The first type is the frontier based on the Shephard technology, which involves a weak-disposability concept, using a single abatement factor. The second one is the frontier on the Lozano-Gutierrez technology, which tries to take the weak disposability into account by regarding the undesirable outputs as input. However, they have limitations. Additionally, no study has provided how to apply weak disposability correctly. To find out the limitations and give standard to utilize weak disposability, we compare models with two issues that must be scrutinized. In this paper, we show that these two concepts have limitations in making the production possibility area. To overcome this limitation, we propose an undesirable-output model using multiple abatement factors based on weak disposability with the slack-based measure (SBM) approach. We analyze, comparatively, the different social efficiency performances according to two issues among the three approaches in estimating production possibility frontier, using the Shepard model, the Lozano-Gutierrez model, and our proposed model. To provide correct standard of measurement and apply characteristics of undesirable outputs, we study not only theoretically, but also empirically, with data from Korea's 13 domestic airports.