Appendix
Nomenclature
A1
Operating regime that allow 14 h operations
B
Operating regime that allows continuous operations
C
fee
Annual VT contribution fee cost (€/year)
C
LV
Annual LV cost created by providing the leading service (€/year)
C
VT
Annual VT technology cost (€/year)
D
Annual number of operating days (€/year)
d
in
Distance of the FV spent in the VT (km)
i
Original sailing regime of the reference vessel
n
FV
Required number of FVs per LV
n
LV
Number of LV in the transport system
r
Number of crew member roles
T
Annual operating hours (h/year)
V
Cargo capacity of the vessel (t)
v
c
Speed of river current (km/h)
v
VT
Operating speed of VT (km/h)
Δfuel
Change in annual fuel cost (€)
A2
Operating regime that allow 18 h operations
C
FV
Annual follower vessel cost (€/year)
C
R
Annual reference vessel cost ((€/year)
C
int
Bonus wage for every day spent sailing internationally (€/day)
c
w
Annual crew wage (€/year)
d
FV
FV distance (km) i.e. dout + din
d
out
Distance the FV spends sailing on its own (km)
d
int
Distance sailed internationally (km)
f
Fleet size of single company
I
Departure interval of the LVs (h)
P
Annual productivity of a vessel (t/year)
p
ex
Percentage indirect and employment-related crew cost
r
r
Number of crew member roles at reduced crew
t
l
Time spent in lock passage (h)
t
w
VT waiting time due to VT departure (h)
v
R
Operating speed of the reference vessel (km/h)
Δcrew
Change in annual crew cost (€
This annex provides the detailed equations for both the Rhine and the Danube cases calculations. The assessment methodology for the single company and the subscription fee BM is for the most part identical. It differs mainly in the assumptions set for the determination of the number of participants. The information presented in this annex is based on the NOVIMAR deliverable by Hekkenberg and Colling [
15,
29], with the addition of environmental factors of days of navigational suspension.
The calculation approach focuses on the calculation of the FV cost based on their relative productivity changes. All calculations are based on the cost calculation of a currently operating reference vessel and its refit counterpart operating as a follower vessel in a VT.
To start with, the VT operating speed is calculated using Eq.
1. The departure interval of the train is set within the assessment scenario in Sect.
5 of the main paper. The number of LVs in the transport system are determined such that the operating speeds of the VT are as close as possible to the operating speeds of the reference vessels.
$$v_{VT} = \frac{d}{{I n_{LV} - 2t_{p\& l} }} + \sqrt {\frac{{d^{2} }}{{\left( {I n_{LV} - 2t_{p\& l} } \right)^{2} }} + v_{c}^{2} }$$
(1)
Next, the return trip time is calculated. As can be seen from Eq.
2, the main difference between the reference vessel and the FV trip time the addition of the VT waiting time (t
w), but also the fact that the section of the FV trip is calculated at the VT operating speed. As we are dealing with inland navigation, the vessel speeds are influenced by currents experienced on the river. The vessels are set to operate along the same route length all year. Hence, the length of this route, as well as the amount of time spent sailing, and resting per day are also taken into account for the trip time. Port times (including time spend on actions such as (un)loading, berthing, bunkering) also influence a return trip time but are not specific to VT operations. These port times are adjusted depending on the size of the vessel.
$$t_{t} = \left\{ \begin{array}{ll} {\frac{2dv}{{v^{2} - v_{c}^{2} }} + \frac{{\frac{2dv}{{v^{2} - v_{c}^{2} }}}}{{t_{{s_{i} }} }}t_{ri} + 2t_{p\& l} ;} \hfill &\quad { for\,reference\,vessel } \hfill \\ {\frac{{2d_{in} v_{VT} }}{{v_{VT}^{2} - v_{c}^{2} }} + \frac{{2d_{out} v_{R} }}{{v_{R}^{2} - v_{c}^{2} }} + \frac{{\frac{{2d_{out} v_{R} }}{{v_{R}^{2} - v_{c}^{2} }}}}{{t_{sA1} }}t_{rA1} + 2\left( {t_{p\& l} + t_{w} } \right);} \hfill & \quad{ for\,FV} \hfill \\ \end{array} \right.$$
(2)
Knowing the trip time allows the determination of the reference vessels productivity, at its original sailing regime and the productivity of FV at its VT conditions. The productivity is calculated using Eq.
3, for both the reference and FV conditions. Aside from the trip time the difference in computations between the two conditions lies in the annual number of operating hours (T). For the reference vessel, this is the operating hours given the original operating regime (i) minus days of no operations due to holidays (
rh) or navigation restrictions due to water levels (
rw). The number of operating hours for the VT is computed by considering both the time spent in and out of the VT, which allows operations either at a B or an A1 regime, as expressed in Eq.
4.
$$P = \frac{24T}{{t_{t} }}2V$$
(3)
$$\begin{aligned} & for\,P_{R} :T = 24 D_{i} - r_{w} - r_{h} \\ & for\,P_{FV} : T = T_{B + A1} = 24\left( {\frac{{d_{in} }}{{d_{FV} }}*D_{B} + \frac{{d_{out} }}{{d_{FV} }}*D_{A1} } \right) - r_{w} - r_{h} \\ \end{aligned}$$
(4)
Next, the CAPEX and OPEX of the vessel are determined as described in the main body of this paper. The OPEX costs of the reference vessel and the FV includes crew, fuel, maintenance, and administration cost, while the CAPEX costs are composed of depreciation, interest and insurance. The administration, as well as all CAPEX cost, are determined as a function of the newbuilding price of the vessel, which is a common approach that was adopted by for example Kretschmann et al. [
32], Grønsedt [
25], Lyridis et al. [
33] or Verberght [
47]. The new built price and maintenance estimation method for an inland vessel is taken from Hekkenberg [
28].
The fuel costs are determined using Holtrop and Mennen [
30] resistance prediction method, which has been adjusted to take shallow water effects into account according to the method proposed by Zeng et al. [
50]. The specific fuel consumption is modelled as a function of engine loading and based on Caterpillar 3406E [
6].
The VT control system cost and the LV cost calculations are based on the capital cost needed to get the installation of the VT track pilot soft- and hardware (i.e. antenna or distance sensors) on board of the vessels. This is estimated to be € 80,000 by the developer Argonics Gmbh [
2]. The insurance, interest, maintenance, administration and depreciation are calculated as a function of this investment cost. The depreciation time of this technology is five years.
If the VT is operated by a third party additional cost need to be considered apart from the VT control system cost. These cost are platform cost, that allow the coordination of the VT participants, which does not arise when the VT is operated by a single company. This cost includes software cost, but also shore-based staff and offices. The platform cost assumptions are presented as part of the input data in the application cases.
The VT can create positive and negative effects on a vessels’ productivity. The waiting times created before departure as well as the possible slowing down of the operating speed in the VT cause a negative effect on productivity. If compared to reference vessels that operate in a B regime, these negative products are a consequence of using the VT aside from the cost saving achieved by the crew cost saving. Compared to a reference vessel at an A1 regime, however, these negative effects on the FVs’ productivity are largely outweighed by positive effects of sailing through the 10 h of resting period per day.
To ensure that the FV transport condition are at least equivalent to the reference operation, the FV cost is calculated based on the change in productivity and the reference vessels cost using Eqs.
5.
$$C_{FV} = \frac{{P_{FV} }}{{P_{R} }}C_{R}$$
(5)
Equation
6 allows to the net savings per vessel for the single company BM or the maximum contribution fee, a FV can pay to the LV to compensate for their service.
$$C_{fee} = S_{FV} = C_{FV} - C_{R} + \Delta_{crew} + \Delta_{fuel} - C_{VT}$$
(6)
The crew cost savings are determined based on the crew number and the crew wages summarized in the table below. As described in the main text, the crew numbers are taken from CCRN guidelines, and the UNECE Resolution No. 61 [
7,
46]. The crew wages for the Rhine case are from QUOVADIS [
41] and those for the Danube are obtained from interviews with one of the largest shipping company along the Danube (they wish to stay anonymous so as not to disclose this comparative information to their competitors). On the Danube, a significant part of the wage is based on the number of days spent sailing internationally (
cint), outside of their home country. This is not the case for the Rhine; hence there, it is set to 1. The savings are calculated using the data in Table
Table 10
Number of crew and wages summary for the Rhine and Danube case
Boat master | 1 | 2 | 1 | 2 | € 2227 | € 3185 | € 680 |
Helmsman | 1 | 1 | | | € 1829 | € 2603 | € 340 |
Boatman | | 1 | 1 | 1 | € 1802 | € 2577 | € 280 |
Apprentice* | 1 | 1 | 1 | 1 | € 1594 | € 2279 | € 280 |
10. These include the percentage indirect and employment-related cost (
pex) of 30% of the total wage [
24]. These values are plugged into Eq.
7 to obtain the crew cost savings. The first sum in Eq.
7 determines the crew cost of the reference vessel for every crew role (r) at their original operating regime (i). The second sum calculates the cost of the FV operations with the reduced crew roles (
rr) at an A1 operating regime.
$$\begin{aligned} \Delta_{crew} & = \mathop \sum \limits_{j = 1}^{r} \left( {n_{c ,j} \left( {c_{w,j} + \frac{{c_{w,j} p_{ex} }}{{\left( {1 - p_{ex} } \right)}}} \right) + n_{c ,j} \frac{{d_{int} }}{{d_{FV} }}T_{i} c_{int} } \right)_{i} \\ & \quad\, - \mathop \sum \limits_{j = 1}^{{r_{r} }} \left( {n_{c ,j} \left( {c_{w,j} + \frac{{c_{w,j} p_{ex} }}{{\left( {1 - p_{ex} } \right)}}} \right) + n_{c ,j} \frac{{d_{int} }}{{d_{FV} }}T_{B + A1} c_{int} } \right)_{A1} \\ \end{aligned}$$
(7)
The change in fuel consumption (Δ
fuel) is the difference in the estimated fuel consumption between the two conditions, while the last cost component of Eq.
6, the VT cost, is composed of the VT control system cost. This VT cost is expected to be equivalent to the LV cost. The LV cost calculations are based on the capital cost needed to get the installation of the VT track pilot soft- and hardware (i.e. antenna or distance sensors) on board of the vessels. This is estimated to be € 80,000 by the developer Argonics Gmbh [
2]. The insurance, interest, maintenance, administration and depreciation are calculated as a function of this investment cost. The depreciation time of this technology is five years.
With respect to the third party service provider to manage the VT the following cost are determined. For the Rental of office spaces and software licences, updates and other overheads are estimate to be € 50.000, where € 10.000 is the expected annual fee for offices and screens in the remote control centre of the Port of Antwerp. The platform is operated and maintained by four shore-based workers with transport planning and IT skills. It is expected that each employee cost € 60.000 annually, thereby summing up to a cost of € 240.000 per year to cover the shore-based workforce. Finally, it also assumes that the VT operator makes a profit margin of 20% of the total cost. In the case, where the VT operator is an independent agent from the LV operators, additional margins need to be added. Given these additional cost assumptions and the 10 LVs operating on the Rhine VT transport system, the VT operator needs to gain a total of € 422.500 (€ 42.250 per LV) for its services to be economically viable. The calculations for this business model in this assessment are set such that the FV savings are the maximum contribution fee the VT operator can expect the FVs to pay for the service. This does not mean that the FV operators end up paying a subscription fee equivalent to their savings, as they also make financial benefits from joining the VT.
The main difference in the single company vs. third party business model lies in the calculations of the compensation cost for the service performed. The third-party business model needs the platform cost for coordination of the train to be included (i.e. licence, updates and shore-based personal) as well as a margin of profit. All these cost sum up to the VT operator cost and are evenly divided over the number of LV in the transport system, as indicated by Eq.
8. The LV cost the single company needs to compensate for, is equal to the VT control system cost, as it is assumed that no waiting times are created for the LVs.
$$C_{LV} = \left\{ {\begin{array}{*{20}l} {\frac{{(c_{VT} n_{LV} + {\text{c}}_{{{\text{platform}}}} )\left( {1 + p} \right)}}{{n_{LV} }}; } \hfill & {for\,platform \,based\,model} \hfill \\ {c_{VT} ;} \hfill & {\quad for\,single\,company\,model} \hfill \\ \end{array} } \right.$$
(8)
Finding the number of required FV per VT is the point at which the cases differentiate dependenton the BMs. As shown in Eq.
9, the number of FV per VT for a subscription-based BM assumes the best-case scenario for the VT operator and the worse-case for the VT user, i.e. that the entire savings of the vessel operators are paid to the VT operator. For the single company use case, the cost savings generated need to outweigh the cost. Hence, the required FV participants indicate the minimum FVs required. Additionally, the benefits of one vessel type can help make the combined operations with another vessel type viable.
$${\text{n}}_{FV} = \left\{ {\begin{array}{*{20}l} {\min \sum\nolimits_{j = x}^{{n_{FV} }} {S_{FV,j} } \ge C_{LV} \,where\,x = 1 \ldots f;} \hfill & {\quad for{\mkern 1mu} single{\mkern 1mu} company{\mkern 1mu} model} \hfill \\ {\frac{{C_{LV} }}{{C_{fee} }};} \hfill & {\quad for{\mkern 1mu} plaform{\mkern 1mu} based{\mkern 1mu} model} \hfill \\ \end{array} } \right.$$
(9)
In the case that
nFV >
Lc additional lock cycle time needs to be added to the original equations and a second iteration of the calculation method is calculated. As the case study results show, this is not needed, so the total number of participants is determined using Eq.
10.
$$VT_{p} = n_{LV} + n_{LV} n_{FV}$$
(10)
The final feasibility indicator of the fleet share is based on the fleet size of the self-propelled vessels identified in the main body of the paper and is calculated using Eq.
11.
$$M = \frac{{VT_{p} }}{{F_{s} }}100$$
(11)