Table 1 Comparison of rail-haul costs using different equations on s = 400 km

Janic [16], Braekers et al. [17], Kim N.S. et al. [27]

c_T(w, s) = 0.58(ws)^0.74 [€/train trip ]

Arnold et al. [40], Kim N.S. et al. [27]

c_T2TEU(s) = 0.65 ∙ 5.46 s^−0.278s [€/2TEU ]

Janic [42]

c_T(w, s, q) = (4.60n_l + 0.144n_w + 0.3)s+

+12.98(n_l + n_w) + 5.6q + 0.0019ws+

\( +\sum \limits_{l=1}^L\left[\ 0.227\bullet \frac{10^{-6}{v}_l^2}{\ln {d}_l}+0.000774\right] ws+ \)

\( +33{n}_d\left({t}_{dp}+\frac{s}{v}+D\right)\ \left[\text{\EUR} /\mathrm{train}\ \mathrm{trip}\ \right] \)

Janic [42], Santos [43]

\( {c}_T(s)=0.59325+0.019s+0.001804\left(\frac{s}{\ln s}\right) \)

[€/train trip ]