# Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function
## 2 The Proposed Cost Function
### Monetary Cost
#### 2.1.2 The Proposed Monetary Cost Function  
In this paper, monetary costs of railway transport have been calculated basing partially on the research performed by [PERSON] [6], while some reference costs, regarding staff, locomotives and wagons, have been determined basing on [8]. It must be underlined that: the authors determined all resistances to motion in detail, on the analyzed network, which consists of a large part of Europe. The authors considered the different railway track usage prices and the different electricity prices charged by each European country. The proposed cost function is the following:  
\[C\left[\mathbf{\xi}\right]=t\left[\mathbf{h}\right]\cdot(n_{d}\cdot P)+l\left[ \mathbf{km}\right]\cdot\left[n_{L}\cdot(A_{L}+M_{L}+I_{L})+n_{W}\cdot(A_{W}+M_ {W}+I_{W})+R+T(V_{A},i,R_{C})\right]+2\cdot H\cdot n_{\Pi TU} \tag{1}\]  
where:  
* \(C=\) in \(\mathbf{\xi}\) per train service, is the monetary cost on each rail link, having length \(l\) and travel time \(t_{2}\)
* \(P=\) staff cost [\(\mathbf{\xi}/(\mathbf{h}\cdot\text{driver})\)]: cost of the train drivers. The staff cost is not the same in the whole Europe: in Italy an average cost per hour, for each train driver, of 35 \(\mathbf{\xi}\) was detected (this cost comprises not only the net salary but also pension contributions and healthcare) (Source: Trenitalia, relazione annuale [9]), while in Germany, it resulted in a cost of 42 \(\mathbf{\xi}\) per hour per driver [8]. Therefore, for the whole Europe an average staff cost of 38.5 \(\mathbf{\xi}/\mathbf{h}\) per European driver has been considered. * \(n_{d}\) is the number of drivers of each freight train (independently of the number of locomotives). Two train drivers per freight train are necessary in Italy, while only one driver is sufficient in the rest of Europe (sources: interviews to Rete Ferroviaria Italiana and [10]);
* \(A_{L}=\) amortization cost of one locomotive. In [8] it is reported that a reference amortization cost for a locomotive used for freight transport is 330,670 \(\mathbf{\xi}\) per year. Mercitalia Rail (the main Italian rail freight company) has provided a reference value for the number of km travelled each year by a locomotive: 200,000 km. Therefore, the average amortization cost of a locomotive, expressed in \(\mathbf{\xi}/(\text{locomotive}\cdot\mathbf{km})\), has been estimated: 1.653 \(\mathbf{\xi}/(\text{locomotive}\cdot\mathbf{km})\);
* \(M_{L}=\) maintenance cost of one locomotive: in [8] it is suggested to take it as 5.5% of the amortization cost, that is: 0.091 \(\mathbf{\xi}/(\text{locomotive}\cdot\mathbf{km})\);
* \(I_{L}=\) insurance cost of one locomotive. In [8], it is suggested to take it as 1.5% of the amortization cost: that is, 0.025 \(\mathbf{\xi}/(\text{locomotive}\cdot\mathbf{km})\);
* \(n_{L}=\) number of locomotives. The number of locomotives depends on the gradient of the railway link, and it ranges from 1 to 3. The calculation of the number of locomotives is described in detail in the following;
* \(A_{W}=\) amortization cost of one wagon; Sgns flat wagons for containers have been considered. In [8] it is reported that the amortization cost for a Sgns is 4898 \(\mathbf{\xi}/\text{year}\). Mercitalia Rail has provided a reference value for the number of km travelled each year by a wagon of 50,000 km. Therefore, the average amortization cost of a wagon, is 0.098 \(\upxi\)/(wagon-km);
* \(M_{W}\) = maintenance cost of one wagon: in [8] it is suggested to take it as 10% of the amortization cost: that is, 0.0098 \(\upxi\)/(wagon-km);
* \(I_{W}\) = insurance cost of one wagon: in [8] it is suggested to take it as 1.3% of the amortization cost: that is, 0.0013 \(\upxi\)/(wagon-km);
* \(R\) = railway track cost [\(\upxi\)/km], i.e., cost for the usage of the railway infrastructure, paid by the railway transport company to the infrastructure manager. This cost has been determined, for all countries involved in this research, according to the values provided in [11] for Italy and in [12] for the other European countries.