# Customized Approach to Greenhouse Gas Emissions Calculations in Railway Freight Transport
## 3 Mathematical Formulation
### Case Study Assumptions and Calculations
The total CO2 emissions produced by return transportation are calculated as Equation (43) (according to Equation (9)):  
\[\text{T = 5167.724435009 [kg\({}_{\text{CO2e}}\)],} \tag{43}\]  
where T represents the total CO2 emissions produced by transportation. The total CO2 emissions R produced by the return transportation are calculated using the WtW approach as Equation (44) (according to Equation (10)):  
\[\text{R = 2908.886118209+2258.838316800 [kg\({}_{\text{CO2e}}\)].} \tag{44}\]  
\(\text{R}_{\text{WtT}}\) is the CO2 emissions calculated using the WtT approach consisting of two parts (Equation (45) according to Equation (11)):  
\[\text{R}_{\text{WtT}}\text{ = 407.635548192 + 2501.250570017 [kg\({}_{\text{CO2e}}\)].} \tag{45}\]  
\(\text{R}_{\text{Ttw}}\) is the CO2 emissions calculated using the Ttw approach consisting of two parts (Equation (46) according to Equation (12)):  
\[\text{R}_{\text{Ttw}}\text{ = 160.390886400 + 2098.447430400 [kg\({}_{\text{CO2e}}\)].} \tag{46}\]  
The CO2 emissions of BO calculated using the WtT approach \(\text{R}_{\text{WtTb}}\) are calculated as Equation (47) (according to Equation (13)):  
\[ \begin{array}{c}\text{R}_{\text{WtTb}}\text{ [kg\({}_{\text{CO2e}}\)] = \{0.62\ [$--$] \times 0.001802327 [kg\({}_{\text{CO2e}}\)/tkm}]}\\ +\ 0.38\ [$--$]\times 0.000109177 [kg\({}_{\text{CO2e}}\)/tkm]) \times 745.2\ [$t$]\times 472\ [km],}\\ \text{R}_{\text{WtTb}}\text{ [kg\({}_{\text{CO2e}}\)] = 407.635548192.}\end{array}  \tag{47}\]  
The CO2 emissions of FO calculated using the WtT approach \(\text{R}_{\text{WtT}}\) are calculated as Equation (48) (according to Equation (14)):  
\[ \begin{array}{c}\text{R}_{\text{WtT}}\text{ [kg\({}_{\text{CO2e}}\)] = \{0.62\ [$--$] \times 0.009762854 [kg\({}_{\text{CO2e}}\)/tkm}]}\\ +\ 0.38\ [$--$]\times 0.002784794 [kg\({}_{\text{CO2e}}\)/tkm]) \times 745.2\ [$t$]\times 472\ [km],}\\ \text{R}_{\text{WtT}}\text{ [kg\({}_{\text{CO2e}}\)] = 2501.250570017.}\end{array}  \tag{48}\]The CO\({}_{2}\) emissions of BO calculated using the TtW approach R\({}_{\rm TtWb}\) are calculated as Equation (49) (according to Equation (15)):  
\[\rm R_{TtWb}\ [kg_{CO2e}]=\{0.62\ [-]\times 0.000000000\ [kg_{CO2e}/tkm]\] \[+0.38\ [-]\times 0.001200000\ [kg_{CO2e}/tkm]\}\times 745.2\ [t]\times 472\ [km], \tag{49}\] \[\rm R_{TtWb}\ [kg_{CO2e}]=160.390886400.\]  
The CO\({}_{2}\) emissions of FO calculated using the TtW approach R\({}_{\rm TtWt}\) are calculated as Equation (50) (according to Equation (16)):  
\[\rm R_{TtWt}\ [kg_{CO2e}]=\{0.62\ [-]\times 0.000000000\ [kg_{CO2e}/tkm]\] \[+0.38\ [-]\times 0.015700000\ [kg_{CO2e}/tkm]\}\times 745.2\ [t]\times 472\ [km], \tag{50}\] \[\rm R_{TtWt}\ [kg_{CO2e}]=2098.447430400.\]  
Finally, the resulting GHG emissions are presented according to the requirements of the company as total GHG emissions, average GHG emissions per 1 km, average GHG emissions per 1 t, and average GHG emissions per 1 km (Table 2, Section 4). The same procedure as in Equations (43)-(50) can be used to calculate SO\({}_{2}\) GHG emissions. The proposed customized approach was also tested except with FC transport instead of PC and CB transport, but due to the range of the manuscript, the individual calculations are not listed here. The proposed customized approach to GHG emission calculations in RFT for the AI (Section 3.3) has been applied and verified.