###### Abstract
A pivotal work is from [5] that modifying the standard constraints of Data Envelopment Analysis approach (i.e., DEA), proposed a hyperbolic efficiency measure able to consider also undesirable outputs. Starting from this application, many researchers tested different models of DEA with the aim to consider also bad outputs of production. For instance, refs [6; 7; 8] applied stochastic frontiers with bad outputs, but the most efficacy model for considering environmental emissions recognized by literature is the Directional Distance Function (i.e., DDF). Indeed, one of the main strengths of this methodology (DDF) is the possibility to modify the direction of the searching vector, without modifying its technological definition [9; 10]. In addition, another benefit of the DDF is the possibility to set the linear program without assuming a specific form of technology function (i.e., additivity property [11]). Starting from the late 1990s, an increasing number of researchers started to apply the DDF methodology in different polluting industries [11; 12; 13]. However, considering the advantages of this technique, in more recent years, many studies considered applying the DDF in many other fields [14; 15; 16; 17; 18]. In summary, for estimating the impact of retrofitting interventions, the more appropriate methodologies are the Life-Cycle Costing and the Life-Cycle Assessment [19; 20; 21], but the difficultness in data availability, especially for the LCA, stimulated researchers to find more effective solutions in proposing hybrid methodologies. Until now, at our knowledge, literature did not present application of non-parametric methodologies, as the Directional Distance Function, to the estimation of retrofitting interventions. Recent studies, for instance [22; 23], analyze the possibility to use directional distance or data envelopment analysis combined with other methodologies for evaluating power plant with nonstandard models. As suggested by [23], the present is a methodological paper aiming at proposing a simple combined methodology for ranking the retrofitting solution considering a multidimensional vision. The methodology proposed aims at covering this lack proposing a synthetic score combined with a key-variables to drive decision-making process in retrofitting field. Indeed, the scores obtained through Directional Distance Function, and more generally, Data Envelopment Analysis, are recognized as composite indicators, and they are applied in many fields [24; 25; 26]. In the present work, we propose a hybrid methodology with the aim to consider the LCA as an input for the DDF model and the CO\({}_{2}\) emissions as an undesirable output. This assumption, together with the bootstrap resampling method, allows to obtain robust efficiency scores useful for comparing different retrofitting solutions [27]. The aim of the paper is to apply a hybrid methodology (i.e., the LCC and the DDF) on the data relating to POSs collected within the HAPPEN project. In this way, we propose to define two efficiency measures (i.e., holistic efficiency scores and environmental efficiency score) to identify which retrofitting intervention is the most efficient inside each POS considering, at the same time, its economic, financial, and social impact. Finally, studying together the holistic efficiency and the primary energy consumption of the buildings after the retrofitting interventions, it is possible to find the optimal solution in each Package of Solutions (POS), considering both climate zone and building typology. The paper is organized as follows: Section 2 presents material and method, and Section 3 discusses the empirical results; final remarks are shown in Section 4.