Previous research identified various attributes influencing the decision maker’s mode choice in freight transport [5, 27,28,29], the most important being internal cost and haulage time. To assess these variables and the climate impact of multimodal and international freight transport chains, a multi-dimensional simulation model was developed. It is established as a detailed short-term performance calculation tool combined with an aggregate modal split model. The former uses detailed input data to determine performance attributes and their structure. The latter is implemented as a discrete choice model (Logit) based on random utility theory. Here, the shippers act as decision makers and intend to maximize their utility of freight transport on a scenario-specific origin-destination (O-D) pair. The utility is derived from micro-economic theory and is dependent on three performance attributes: internal cost, GHG emissions and transport time. External costs beyond emissions with global impact (e.g. network congestion, noise and local air pollution) are excluded because currently, these are not subject to the trade-offs in mode choice made by shippers. An inclusion thereof would alter the choice of transport mode to be the optimal solution for society as a whole which would most probably promote the rail mode. See Fig. 1 for a simplified illustration of the two-stage model structure.
2.1 Transport chain modelling
In every scenario, the performance of several transport chains comprising one or more transport modes on a defined O-D pair is calculated based on the characteristics of the attributed transport vehicles. There are four major mode types; road, rail, water and air (focus here: road and rail). Every transport chain is designed as a linear concatenation of L links which can hold one transport carrier tc of the corresponding mode each. Usually, the key aspect of research is attributed to the main carriage link(s). Beside the modes, a pseudo mode transhipment is integrated, which is not dependent on vehicles but on loading and unloading processes. Based on this set-up, the calculation of transport chain- and carrier-dependent performance attributes (i.e. C costs, EM emissions and T transport time) is carried out for each transport chain. These attributes consist of several impact factors as follows:
$$ C={\sum}_{\left(l=1\right)}^L{q}_{t{c}_l}\ast \left[ ED\left({v}_l, unit{s}_l\ast \uprho, \mathrm{e}{{\mathrm{d}}_{\max, 0}}_{tc},{\upmu}_{tc},{\lambda}_{tc},{v}_{ma{x}_{tc}}\right)\ast {d}_l\ast FP\left( fue{l}_{tc}, countr{y}_l\right)+{c}_{ma in{t}_{tc}}\ast {d}_l+{c}_{per{s}_{tc}}\ast TD\left({v}_l,{v_{ma x}}_{tc},{d}_l, sts{t}_{tc}\right)+{c}_{ca{p}_{tc}}\ast {d}_l+ INFC\left( countr{y}_l\right)\ast {d}_l\right]+{c}_{trans- fi{x}_l}+{c}_{trans- va{r}_l}\ast \left( loadin{g}_l+ unloadin{g}_l\right) $$
(1)
$$ EM={\sum}_{\left(l=1\right)}^L{q}_{t{c}_l}\ast \left[ ED\left({v}_l, unit{s}_l\ast \uprho, \mathrm{e}{{\mathrm{d}}_{\max, 0}}_{tc},{\upmu}_{tc},{\lambda}_{tc},{v}_{ma{x}_{tc}}\right)\ast {d}_l\ast FEM\left( fue{l}_{tc}, countr{y}_l\right)\right]+e{m}_{tran{s}_l}\ast \left( loadin{g}_l+ unloadin{g}_l\right) $$
(2)
$$ T={\sum}_{\left(l=1\right)}^L TD\left({v}_l,{v_{max}}_{tc},{d}_l, sts{t}_{tc}\right)+{t}_{trans- fi{x}_l}+{t}_{trans- va{r}_l}\ast \left( loadin{g}_l+ unloadin{g}_l\right) $$
(3)
Transport costs (1) comprise energy, maintenance \( {\mathrm{c}}_{\mathrm{main}{\mathrm{t}}_{\mathrm{t}\mathrm{c}}} \), capital \( {\mathrm{c}}_{\mathrm{c}\mathrm{a}{\mathrm{p}}_{\mathrm{tc}}} \), infrastructure (e.g. track charges or road fees), personnel \( {\mathrm{c}}_{\mathrm{per}{\mathrm{s}}_{\mathrm{tc}}} \), and transhipment costs. The first four components are dependent on the driving distance of that link dl, while total transhipment costs depend on the number of units loaded and unloaded (\( {\mathrm{c}}_{\mathrm{trans}-\mathrm{va}{\mathrm{r}}_{\mathrm{l}}}\ast \left(\mathrm{loadin}{\mathrm{g}}_{\mathrm{l}}+\mathrm{unloadin}{\mathrm{g}}_{\mathrm{l}}\right) \)) plus a fixed fee to enter a transhipment point \( {\mathrm{c}}_{\mathrm{trans}-\mathrm{fi}{\mathrm{x}}_{\mathrm{l}}} \). These costs occur in case that link l is of type transhipment. Personnel costs depend on the time demand calculated from the maximum velocity of the transport carrier \( {\mathrm{v}}_{\max_{\mathrm{tc}}} \) on that link, the link’s maximum speed vl, and a transport carrier specific standstill time ststtc to model congestion:
$$ TD\left({v}_l,{v_{max}}_{tc},{d}_l, sts{t}_{tc}\right)=\mathit{\min}\left\{\frac{d_l}{{v_{max}}_{tc}},\frac{d_l}{v_l}\right\}+{stst}_{tc}\ast {d}_l $$
(4)
The energy cost is a product of energy demand ED, dl and the fuel price function FP(fueltc, countryl). The latter, as well as the infrastructure cost function INFC(countryl) and fuel emissions function FEM(fueltc, countryl), maps country and fuel dependent values in the input data. ED of all modes’ possible transport vehicles is calculated with a linearized function (5). It is two-dimensionally dependent on the velocity vl and the load (as a product of transport units unitsl and their density ρ), with edmax, 0tc as intercept at maximum velocity and zero load [kWh/km], μtc as slope of gross vehicle weight [kWh/(kg*km)] and λtc as slope of the difference between vl and \( {v}_{ma{x}_{tc}} \) [kWh/((km/h)*km)]:
$$ \mathrm{ED}\left({\mathrm{v}}_{\mathrm{l}},\mathrm{unit}{\mathrm{s}}_{\mathrm{l}}\ast \uprho, \mathrm{e}{{\mathrm{d}}_{\max, 0}}_{tc},{\upmu}_{tc},{\lambda}_{tc},{v}_{ma{x}_{tc}}\right)=\mathrm{e}{{\mathrm{d}}_{\max, 0}}_{tc}+{\upmu}_{tc}\ast \mathrm{unit}{\mathrm{s}}_{\mathrm{l}}\ast \uprho +{\lambda}_{tc}\ast \left({v}_{ma{x}_{tc}}-{v}_l\right) $$
(5)
Emissions EM (2) depend on the fuel demand of the transport carrier on that link or the transhipment process. The variable vehicle driving emissions are calculated in the same way as the fuel costs, just mapping emission data instead of prices. Variable emissions in case of a transhipment link \( e{m}_{tran{s}_l} \) are dependent on loadingl and unloadingl.
For costs and emissions, each link’s value is multiplied with the quantity of transport carriers on that link \( {q}_{t{c}_l} \) to model situations where several vehicles are needed to satisfy a given transport demand. \( {q}_{t{c}_l} \) is the round-up ratio of the difference between loading and unloading until that link in the transport chain and the maximum load (maxloadtc multiplied by maximum load factor τtc) of that link’s transport carrier (6):
$$ {\mathrm{q}}_{\mathrm{t}{\mathrm{c}}_{\mathrm{l}}}=\left\lceil \frac{\sum_{\left(\mathrm{i}=1\right)}^{\mathrm{l}}\mathrm{loadin}{\mathrm{g}}_{\mathrm{i}}-\mathrm{unloadin}{\mathrm{g}}_{\mathrm{i}}}{\mathrm{maxloa}{\mathrm{d}}_{\mathrm{t}\mathrm{c}}\ast {\uptau}_{\mathrm{t}\mathrm{c}}}\right\rceil $$
(6)
Transport time T (3) is calculated as a sum of the time demand for transport carriers TD (4) and both, a fix and variable transhipment time for every transhipment link (\( {t}_{trans- fi{x}_l} \) and \( {t}_{trans- va{r}_l} \), the latter being dependent on the number of loaded and unloaded transport units).
2.2 Mode choice modelling
The implemented mode choice model is a reproduction of the decision maker’s choice behaviour within a discrete choice set (discrete, behavioural model) which is derived from random utility theory. Logit models have been best practice in discrete choice modelling for decades, especially in transport literature [30,31,32]. They are subject to several assumptions (see [33, 34]):
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every individual is a rational decision maker maximizing the utility of his or her choices;
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decision maker i considers mutually exclusive alternatives, which make up his or her choice set Ii;
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each alternative j has a perceived utility \( {U}_j^i \), based on microeconomic consumer theory;
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\( {U}_j^i \) depends on a number of measurable attributes \( {\boldsymbol{X}}_j^i \) (as a vector) and
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\( {U}_j^i \) is not known with certainty by an external observer, which is why it is split into a systematic utility \( {V}_j^i \) and a random residual \( {\varepsilon}_j^i \) considering unobservable errors: \( {U}_j^i={V}_j^i+{\upvarepsilon}_j^i\kern1em \forall j\in {I}^i \)
In this model, the individual shippers are aggregated to one generic decision maker, which is why the index i is not required in all upcoming mathematical descriptions. Random residuals comprise all influences of decision making that are not addressed in the systematic utility and other errors in the analytical expression of performance attributes, errors in the input data, errors due to omitted performance attributes and errors occurring due to the aggregation of decision makers.
The probability that the utility of alternative j, Uj, is greater than all the other alternatives in the choice set I can be expressed as follows (7):
$$ \mathrm{p}\left[\mathrm{j}/\mathrm{I}\right]\kern0.5em =\kern0.5em {\mathrm{P}}_{\mathrm{j}}\kern0.5em =\kern0.5em \Pr \left[{\mathrm{U}}_{\mathrm{j}}\kern0.5em >\kern0.5em {\mathrm{U}}_{\mathrm{k}}\kern0.5em \forall \mathrm{k}\ne \mathrm{j},\kern0.5em \mathrm{k}\in \mathrm{I}\right] $$
(7)
An appropriate statistical model must be applied to estimate the perceived utility of the decision maker. The simplest and most common utilization of random utility theory is represented by the Multinomial Logit model (MNL). It is assumed that random residuals εj are independently and identically distributed according to a Gumbel random variable of zero mean and parameter θ, which leads to the following expression for the mode choice probability (8):
$$ {\mathrm{P}}_{\mathrm{j}}=\frac{\exp \left(\frac{{\mathrm{V}}_{\mathrm{j}}}{\uptheta}\right)}{\sum_{\mathrm{j}=1}^{\mathrm{m}}\exp \left(\frac{{\mathrm{V}}_{\mathrm{j}}}{\uptheta}\right)} $$
(8)
2.3 Model calibration
The perceived utility must be calculated, to estimate a modal split. Hence, a vector β is defined consisting of a cost sensitivity of 1 (i.e. neutral perception of cost), a value of time (VoT) in EUR/(h*t) and an emissions penalty in EUR/tCO2eq (e.g. CO2-tax to internalise external cost from GHG emissions). The VoT describes the decision maker’s appreciation for the acceleration of goods. It positively relates to the weight-specific value, interest rates and deterioration of goods and is independent of distance and transport mode [5]. Most commonly, data is gathered with Stated Preference surveys and evaluated in a Logit model [35, 36]. β is multiplied with the performance attributes C, EM and T to bring them on a common scale (EUR per transport unit), wherefore the VoT is rescaled to transport units under use of the scenario-specific unit density. C, EM and T are considered as unit-specific values because shipment sizes vary between transport carriers and the decision-maker considers load-specific performance values.
Parameter θ is a control variable for the selectivity of the mode share estimation results, i.e. the variance of the probability distribution [33]. Studies that gather micro data for discrete choice modelling usually estimate the perceived utility \( {U}_j^i \) directly, making θ obsolete (see [37, 38]). The present study uses literature values for β to compute Vj which requires the calibration of θ depending on possible error sources described in the previous subsection. We find a value of 0.5 for this study’s model structure based on the simulation of conventional intermodal rail-road and unimodal road transport relations on distances ranging from 100 to 1000 km in Germany.
While it is intended to model the full internal cost and time of a transport chain, emissions calculation does not happen according to a life-cycle analysis. Vehicle, infrastructure and terminal building emissions are excluded from all components and only well-to-wheel CO2eq emissions from fuel consumption (including well-to-tank and tank-to-wheel) are accounted. Costs of transport exclude logistics operations (other than cargo carriage), margins and business overheads of any service providers above the level of carriers. The expression “fuel” includes electricity in this paper.
