**DMUs-Countries**

Belgium (BE), Bulgaria (BG), Czech Republic (CZ), Denmark (DK), Germany (DE), Estonia (EE), Ireland (IE), Greece (EL), Spain (ES), France (FR), Italy (IT), Cyprus (CY), Latvia (LV), Lithuania (LT), Luxembourg (LU), Hungary (HU), Malta (MT), Netherlands (NL), Austria (AT), Poland (PL), Portugal (PT), Romania (RO), Slovenia (SI), Slovakia (SK), Finland (FI), Sweden (SE), United Kingdom (UK), Croatia (HR)


**Table 3.** Variables for road, rail and air transport sectors.

1 Non-energy input; 2 Energy input; 3 Desirable output; 4 Million ton of CO2equivalent; 5 Undesirable output.

In our paper, different weights have been delegated to each criterion for each transport sector. We have assigned the same weights to criteria for each year for the **road transport sector**, i.e., the *number of employees* (wi = 0.14), *passenger cars* (wi = 0.15), *freight vehicles* (wi = 0.15), *energy consumed* (wi = 0.18), *volume of passengers* (wi = 0.1), *freight transport* (wi = 0.1), and *GHG emissions* (wi = 0.18).

The weights for criteria in the **rail transport sector** were the *number of employees* (wi = 0.16), *total number of locomotives and railcars* (wi = 0.18), y (wi = 0.2), y (wi = 0.13), *realized ton kilometers* (wi = 0.13), and *GHG emissions* (wi = 0.2). Finally, in the **air transport sector** we assigned the next weights to criteria: *number of employees* (wi = 0.18), the *total number of aircraft by age* (wi = 0.16), *energy consumed* (wi = 0.2), *amount of transported goods* (wi = 0.13), *number of transported passengers* (wi = 0.13), and *GHG emissions* (wi = 0.2).

4. Determination of positive ideal and negative ideal solutions is denoted as *A*<sup>+</sup> and *A*<sup>−</sup>, respectively. In our case, *A*<sup>+</sup> and *A*− represent the most efficient DMU and the most inefficient DMU, respectively, demonstrated as: *A*<sup>+</sup> = *maxi Vijj* ∈ *J*+, *mini Vijj* ∈ *J*−*i* = 1, 2, ... *n* = *V*+1 , ... , *<sup>V</sup>*+*m* and *A*− = *mini Vijj* ∈ *J*+, *maxi Vijj* ∈ *J*−*i* = 1, 2, ... *n* = *V*−1 , ... , *<sup>V</sup>*<sup>−</sup>*m*, where *J*+ =

(*j* = 1, 2, ... *m*) and *J*− = (*j* = 1, 2, ... *m*) are associated with benefit and cost criteria, respectively. In our research benefit criteria represent desirable outputs, while cost criteria include energy input, non-energy inputs and undesirable output (Table 3).


### *3.3. Selection of Data Set and DMUs*

*Energy-environment e*ffi*ciency* (*EEE*) of European road, rail and air transport sectors was examined. *EEE* of these transport sectors was analyzed for countries presented in Table 2.

Each country was defined as a DMU for conducting the non-radial DEA model. There were different rules of thumb for DMUs' number. According to Golany and Roll (1989) in order to make sure that the model was more discriminatory, the number of DMUs should be at least twice the number of inputs and outputs considered. Each of the DMUs was analyzed according to the road, rail and air transport sectors. DMUs were examined based on inputs and outputs represented in Table 3.

An empirical study was performed based on the available data set collected and compiled from "EU energy and transport in figures-statistical pocketbook" for 2006–2008, 2010, 2012–2018 [58–67]. However, only data for *a number of assets*, the *volume of passengers and freight transport* for air sector were combined with data from "Eurostat". This combination was made because the data for *the number of assets*, *volume of passengers and freight transport* for the air sector did not exist in the same form as the data for the road and rail sectors. For the air sector in the EU statistical pocketbooks, there is only the *volume of tra*ffi*c* such as *revenue ton kilometers* and *revenue passenger kilometers* between member states, and similar data only for major airlines-but they are not represented for each country separately. The period of analyzing allowed us to track the changing trends in terms of *EEE* after the White Papers had been published. In case of absence of some data for energy input or undesirable output for particular DMU, the DMU was immediately eliminated from analysis. Consequently, in order to ge<sup>t</sup> reliable results, all numbers in the DEA had to be strictly positive (no zero values). This was mostly the case with the rail and air sectors.

During the application of DEA method, variables for outputs were chosen based on the research objective, while inputs were primarily resources used to generate outputs. However, it was essential to avoid exogenous variables which were not under the complete and direct control of DMUs [68].

Since the selection of inputs and outputs was a difficult task, we mainly chose them according to the literature review shown in Table 1. However, we added several new inputs, which were important in transport *EEE* analysis. Please note that presented inputs and outputs were used as a set of criteria in the application of the TOPSIS method. The inputs and outputs were selected for the road, rail, and air transport sectors in conducting non-radial DEA model and the TOPSIS method (Table 3). Their changes through selected time periods for each transport sector are described in Section 4 and can be seen in Figure 1a,b, Figure 2a,b and Figure 3. Based on the figures, comparison of transport sectors for each variable could be derived and it could be also determined, which one consumes minimum inputs and causes undesirable output for the realization of maximum desirable outputs.

**Figure 1.** Trends of non-energy inputs for labor (**a**) and (**b**) number of assets.

**Figure 2.** Trends of energy input (**a**), desirable outputs (**b**).

**Figure 3.** Undesirable output.

**Non-energy inputs** (*NEI*) for all sectors were the *number of assets* (see Table 4), and the *number of employees (labor)*. The *number of assets* represented the basic input to form the transport, the main energy consumers, and had a direct correlation with energy consumption. Therefore, we introduced them as non-energy inputs. Figure 1 represents the changes of labor (Figure 1a) and the number of assets (Figure 1b) represented as a sum for selected countries per each sector.


**Energy input** (*EI*) represents the *amount of energy consumed* by each country per road, rail and air transport sectors expressed in million ton oil equivalent. Figure 2a shows the trend of energy consumption by each sector in terms of the selected period.

**Desirable outputs** (*DO*) involved a *volume of passengers and freight transport* (Figure 2b). For road transport sector volume of passenger transport represented a sum of realized kilometers by passenger cars, buses, and coaches, while the volume of freight transport consisted of realized national and international haulage. Regarding the rail transport sector, realized passenger and ton kilometers represented a volume of passenger and freight transport. In terms of air transport sector, the volume of passenger and freight transport represented the amount of transported goods and number of passengers, respectively.

**Undesirable output** (*UDO*) was the *total amount of greenhouse gas emissions* by chosen sector. Figure 3 shows the trends of undesirable output as a sum for all selected countries for all sectors.
