STraM: A strategic network design model for national freight transport decarbonization

Full text

Contents lists available at ScienceDirect
Transportation Research Part E
journal homepage: www.elsevier.com/locate/tre
STraM: A strategic network design model for national freight
transport decarbonization
Steffen J.S. Bakker a,∗, Jonas Martin a,d, E. Ruben van Beesten b,a, Ingvild
Synnøve Brynildsen a, Anette Sandvig a, Marit Siqveland a, Antonia Golab c
aDepartment of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Alfred Getz veg 3, NO
7491 Trondheim, Norway
bEconometric Institute, Erasmus University Rotterdam, Burgemeester Oudlaan 50, Rotterdam 3062 PA, The Netherlands
cEnergy Economics Group (EEG), Technische Universität Wien, Gusshausstraße 25-29, E370-3, Vienna, 1040, Austria
dInstitute of Future Fuels, German Aerospace Center (DLR), 51147 Cologne, Germany
A R T I C L E I N F O
Keywords:
Network design modeling
Transport infrastructure investment planning
Long-term uncertainty
Decarbonization analysis
National freight transport modeling
A B S T R A C T
National freight transport models are valuable tools for assessing the impact of various policies
and investments on achieving decarbonization targets under different future scenarios. However,
these models struggle to address several critical elements necessary for strategic planning,
such as the development and adoption of new fuel technologies over time, inertia in transport
fleets, and uncertainty surrounding future transport costs. In this paper, we develop a strategic
network design model, named STraM, that explicitly incorporates these key factors. STraM,
being a two-stage stochastic program, effectively handles long-term uncertainty by considering
different future scenarios in its decision-making process.It provides a network design plan
that includes infrastructure investments and fuel technology decisions, aiming to achieve cost-
effective decarbonization of the freight transport system. The model output can be used as input
for higher-resolution national freight transport models to yield results with greater operational
detail. We demonstrate the application of STraM through a case study of Norway, offering
valuable insights into the strategic planning of decarbonizing freight transport.
1. Introduction
In the context of the energy transition, decarbonizing freight transport is an important step to achieve emission targets set
by national governments (Meyer, 2020). This process requires a shift from fossil to renewable fuels and possibly from higher to
lower emission transport modes. To facilitate these shifts, governments can implement policies focusing on specific infrastructure
investments. These include the construction of new roads or railways, new charging or fuel stations, terminal capacity expansions,
or enhancements to existing infrastructure. Additionally, fiscal measures, like fuel pricing or road tolls, and regulatory measures,
like limits on truck size and weight, can further promote these changes (Nassar et al., 2023).
However, making decisions about what policies to implement – especially those involving significant infrastructure investments
– is challenging due to the high uncertainty regarding future developments. This raises a critical question for national govern-
ments: which policies and infrastructure investments will most effectively contribute to achieving their desired decarbonization
targets (Kaack et al., 2018)? To answer this question, various decision support tools can be employed.
∗Corresponding author.
E-mail address: steffen.bakker@ntnu.no (S.J.S. Bakker).
https://doi.org/10.1016/j.tre.2025.104076
Received 7 September 2024; Received in revised form 27 January 2025; Accepted 7 March 2025
Transportation Research Part E 197 (2025) 104076
Available online 24 March 2025
1366-5545/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
( http://creativecommons.org/licenses/by/4.0/ ).

S.J.S. Bakker et al.
The decision support tools most commonly used by governments are so-called national freight transport models (de Jong et al.,
2013b). These models describe the national freight transport system with a high level of granularity. They include a detailed
description of transport demand of various product types, transport infrastructure, different types of transport modes and vehicles,
and many other logistics elements. These models are very useful for analyzing the impacts of proposed policy measures or specific
infrastructure investments in a given future scenario.
However, a drawback of national freight transport models is that they are static (one-period) and deterministic. This is problematic
in a setting where strategic decisions need to be made having long-term effects that significantly depend on the uncertain outcomes
of future events. The problem of decarbonizing the freight transport system is precisely such a setting: policy measures and
infrastructure decisions have to be taken today, while their effects take place over the coming decades and depend heavily on
uncertain future factors, such as the development of new fuel technologies.
In this paper, we develop a decision support tool for decarbonizing national freight transport, called STraM (Strategic Transport
Model), that is tailored to answer strategic questions in an uncertain system. STraM complements the existing high-resolution national
freight transport models. While it sacrifices some operational detail, it explicitly incorporates important elements for strategic
decision-making. These include long-term uncertainty and a spatial representation of the freight transport network. The output of
STraM includes a set of infrastructure investments designed to minimize the total (risk-corrected) expected system cost. Additionally,
it provides an assignment of transport demand to routes across the transportation network, specifying the modes and fuels to be
used.
STraM is based on the multimodal transport network design modeling framework STAN (Crainic et al., 1990a). To this starting
point, we add two aspects that have not traditionally been included in national freight transport models, but that are crucial for
strategic planning of transport systems decarbonization. First, STraM encompasses multiple strategic time periods. This allows for an
accurate representation of the development of elements such as: the development and adoption of new technologies (Mohammed
et al., 2020), inertia in transport fleets, a decreasing emission budget, and investments over time. Second, STraM explicitly
models long-term uncertainty in cost and technology development. As a two-stage stochastic program, STraM handles this long-term
uncertainty by considering different future scenarios in its decision-making process. This is especially relevant in the context of
decarbonizing freight transport, where the future development of new, renewable fuel technologies is inherently uncertain.
To illustrate its capabilities, we apply STraM to a case study of the Norwegian freight transport sector. One important input here
is data on the generalized transport costs of different transport modes and fuels. Because mode and fuel choice is a main driver
for the model’s output, we take extra care to use harmonized generalized transport cost data, by using and expanding on the cost
model of Martin et al. (2023).
The case study results show that the explicit modeling of multiple time periods leads to significantly different outcomes in
terms of the resulting fuel mix and the associated investments made, compared to static model runs. Similarly, we demonstrate
that explicitly considering uncertainty leads to a significant improvement in expected total system costs compared to deterministic
planning. In terms of policy insights, we find that a carbon price is an effective instrument to achieve decarbonization of the freight
transport system. Finally, the results show interesting regional differences in optimal infrastructure investments.
The remainder of this paper is organized as follows. In Section 2, we discuss the literature on (national) freight transport models,
with a specific focus on decarbonization, and identify relevant gaps. In Section 3, we introduce our general modeling approach in
STraM, discuss the scope and main assumptions, and provide a mathematical formulation of our model. In Section 4, we apply the
STraM framework on a case study of the Norwegian freight transport system and define all the required data input. In Section 5,
we present results, and provide insights into the performance of our modeling framework. Section 6 presents a discussion. Finally,
Section 7 concludes the paper.
2. Literature review
The literature contains various approaches to decision support models for decarbonizing national freight transport. For example,
policy analyses, often targeting modal and/or fuel shift, have been performed using system dynamics models (Nassar et al., 2023;
Ghisolfi et al., 2024) and energy system models (Rosenberg et al., 2023; Hoehne et al., 2023). However, the representation of
the underlying physical transport infrastructure in these approaches is often insufficient, making it difficult to analyze the efficacy
of various specific infrastructure investments. An alternative modeling paradigm that recognizes the importance of modeling the
transport network explicitly is the use of national freight transport models, which we embrace.
In the remainder of this section, we first sketch the historical development of these models and their application to decarboniza-
tion of freight transport. Next, we explain how STraM builds upon and extends these approaches to provide insights into the effects
of policy measures and infrastructure investments.
During early years, national freight transport models were typically established as network design models. Specific examples
include STAN (Guelat et al., 1990; Crainic et al., 1990a), NODUS (Jourquin and Beuthe, 1996) and TLSS (Arnold et al., 2004).
In this approach, the freight transport system is modeled ‘‘bottom-up’’ as a graph. An optimization problem is then formulated on
this graph to identify infrastructure investments that minimize the sum of investment and operational costs for the entire system
(Crainic et al., 2021). Operational costs are computed by assigning transport demand between node pairs to specific modes and routes
within the graph. Examples of these models have been used in different countries, including Brazil, Sweden and Norway (Guelat
et al., 1990; De Jong and Johnson, 2009).
Over the past decades, national freight transport models have shifted away from the simpler network design models. Instead,
they have evolved into more elaborate, high-resolution models. These models capture various tactical and operational planning
Transportation Research Part E 197 (2025) 104076
2

S.J.S. Bakker et al.
elements (Crainic and Laporte, 1997) and often resemble simulation models (Crainic et al., 2018). In particular, many authors
have focused on developing advanced logistics modules that accurately reflect the logistics decision-making processes in the
freight transport system (de Jong et al., 2013b; Archetti et al., 2022). For example, the Norwegian National Freight Transport
Model (Madslien et al., 2015) uses a so-called aggregate-disaggregate-aggregate approach by Ben-Akiva and de Jong (2013), in
which aggregate production and consumption levels are translated to disaggregated firm-level transportation demands. Many other
national governments, including Canada, Germany, Finland, Italy, the Netherlands, Sweden and the United Kingdom, have developed
similar models (de Jong et al., 2013b).
Most national freight transport models are based on the four-step procedure originally developed for passenger transport mod-
els (de Jong et al., 2004). In this framework, the modeling task is divided into four steps. The first two steps, ‘‘production/attraction’’
and ‘‘distribution’’ consist of generating production and consumption levels at different locations in the network, and translating
these to specific demands for transportation of goods (defined by an origin and destination location). The third step, ‘‘modal split’’,
consists of dividing the demand over different modes of transport, such as road, sea, or rail. The final step, ‘‘assignment’’, assigns
the demand to specific vehicles and routes in the network, given the selected mode. The STraM model, presented in this paper,
focuses on the third and fourth step.
In recent years, national freight transport models have been applied to answer questions about decarbonization of freight
transport. For example, de Bok et al. (2020) evaluate the effect of an emission-based truck charge on vehicle and shipment size
choices, using the Dutch national freight transport model BASGOED. Furthermore, Wangsness et al. (2021) consider the introduction
of a double-track railway between Oslo and Gothenburg in the Norwegian Freight Transport model, and analyze its effect on carbon
emissions. The existing national freight transport models are indeed very useful for providing insights into the effects of specific
policy measures and infrastructure investments, as in these examples.
However, in the context of decarbonizing freight transport, the existing national freight transport models struggle to answer
strategic questions involving, for example, the impact of uncertainty, the interaction between many investment options, or the
development of the transport system over time. One issue is that these models need highly detailed input data, which is hard to
obtain for future states of the system (Meersman and Van de Voorde, 2019). A more fundamental issue is that the existing models
are static (one time period) and do not include long-term uncertainty, whereas strategic infrastructure decisions have effects that
unfold over long periods of time and depend heavily on uncertain developments regarding, e.g., novel renewable fuels.
To deal with the inherent long-term uncertainty, some authors perform what-if analyses on the existing static models (Crainic
et al., 1990b; Pinchasik et al., 2020). However, the limitations of what-if analyses are well known (Higle and Wallace, 2003). For
example, an infrastructure investment might seem suboptimal in every future scenario. However, it could still be worthwhile if
it offers flexibility to handle many different scenarios. What-if analyses do not see the value of flexibility. This is problematic in
strategic decision-making situations, in which infrastructure investments should be decided on today, but their effects take place
over the coming decades and are inherently uncertain.
While research on long-term uncertainty in strategic freight transport models is limited, several works do address short-term
uncertainty. For example, Demir et al. (2016) deal with uncertainty in short-term transport demand and travel times in service
network design modeling, and Yang et al. (2016) consider uncertainty in both transportation cost and travel times for an intermodal
freight transport planning problem.
With STraM, we aim to fill the gaps identified above, by developing a strategic network design model with multiple time periods,
a long planning horizon, and the consideration of long-term uncertainty.
3. Model
In this section, we present STraM. We first provide an overview of its scope and the main assumptions, and then provide the
mathematical formulation.
3.1. Model scope and assumptions
STraM is a modeling framework for strategic national freight transport network design, based on two-stage stochastic program-
ming. The model takes the perspective of a social planner and decides on major infrastructure investments and flows of transport
through a multimodal network. The objective is to minimize overall investment and transportation costs, including carbon fees. The
model outputs a collection of investment decisions for each time period and scenario. It also provides choices for transport mode,
fuel, and route for each transportation demand. See Fig. 1 for an overview of the model.
STraM focuses on line-haul transport in a specific country. Line-haul refers to the transport of goods over long distances between
two major points of interest, such as cities or harbors. It focuses on the main segment of the journey, excluding potential local or
regional transport, and can include various transport modes, like road, rail, or sea. To achieve this, the country is represented
by a graph, with each node corresponding to one of the country’s regions. Demand for transport is aggregated by region and
product group and represented as demand for transport between pairs of nodes. Transport within regions is outside the model’s
scope and is therefore ignored. The available transport connections between regions are represented by the edges in the graph,
with separate edges for different transport modes (e.g., sea, road, rail). On each edge, vehicles using different fuels (e.g., diesel,
ammonia, battery-electric, etc.) can be used. This is modeled using a representative vehicle for each fuel and product group which
is assumed to dominate the market. If additional vehicle types are needed due to variations in factors like payload or costs, they
Transportation Research Part E 197 (2025) 104076
3

S.J.S. Bakker et al.
Fig. 1. Conceptual overview of STraM.
Fig. 2. Example of three edges and eight arc-fuel combinations on the same pair of nodes.
can be incorporated by defining additional product groups. We find this an effective solution, as cost minimization typically favors
the selection of a single vehicle type per product group.
There are limitations on how much each mode and fuel can be used. Freight transport on rail is restricted by limited capacity
in both railways and terminals, while sea transport is only restricted by harbor capacity. We model aggregated terminal capacities
at each node, representing the combined capacity of all terminals located within that node. Moreover, the use of specific fuels in
each time period is restricted by the availability of necessary infrastructure (e.g., charging and fueling infrastructure on road). These
capacities can be expanded by means of infrastructure investments, which are the main strategic decisions in STraM.
We take a strategic perspective by including a long planning horizon as well as uncertainty in the development of new fuel
technologies. The system is modeled at different time periods from today until the planning horizon. Uncertainty is included through
a set of scenarios for the random parameters in the model. We use a two-stage structure, meaning that the time periods are divided
between a deterministic first-stage and a random second-stage. The first-stage decisions (e.g., infrastructure investments) should
anticipate on the future uncertainty.
3.2. Mathematical formulation
We now present the mathematical formulation of STraM. We first provide an overview of the sets, parameters and variables in
the model. Then, we present the objective and constraints.
3.2.1. Sets, parameters and variables
The underlying transportation network is modeled as a directed graph = (,). Nodes  represent the major areas in a
country, while directed arc (𝑖, 𝑗, 𝑚, 𝑟) ∈  represents the link from node 𝑖∈ to node 𝑗∈ for a transport mode 𝑚∈ and
route alternative 𝑟∈. Route alternatives are used to model multiple ways to go from 𝑖 to 𝑗 using mode 𝑚, for example when there
are parallel rail tracks going through different valleys. While flow of goods can be expressed in terms of the directed arcs, we also
define the corresponding undirected edges 𝑒∈ to represent the underlying infrastructure. Along every arc 𝑎= (𝑖, 𝑗, 𝑚, 𝑟) on the
path, different fuels 𝑓∈𝑚 can be used for transporting the goods. Fig. 2 illustrates our use of arcs and edges.
Demand for transportation from origin 𝑜∈ to destination 𝑑∈ is differentiated by product group 𝑝∈. This demand
can be fulfilled along paths 𝑘∈ in the network, which are defined as ordered sequences of directed arcs, i.e., 𝑘= (𝑎1,…, 𝑎𝑛) for
Transportation Research Part E 197 (2025) 104076
4

S.J.S. Bakker et al.
𝑎1,…, 𝑎𝑛∈. To restrict the feasible space of the model, only a limited set  of admissible paths is used. For each transport mode,
we define a set of representative vehicles 𝑚. We assume that transport of a given product group is always performed using the
same representative vehicle type on each mode.
Several elements of the network are capacitated. First, some of the edges (e.g., those representing railroads) have a maximum
capacity. Moreover, certain edges 𝑒 can be upgraded to allow the usage of a specific fuel 𝑓. These upgrade possibilities are collected
in the set ⊆× and most notably contain the electrification of certain rail edges. Additionally, within each node there are
capacitated terminals that are used to load and unload goods at their origin and destination, and to transfer goods between different
modes along a path.
The time dimension is modeled using a set of time periods ={0,1,…, 𝑇 }, where period 0 is the present year, and 𝑇 is the
end of the planning horizon. Each period represents a number of years in the planning horizon. Uncertainty is modeled using a
scenario tree that lives on this timeline, and is represented by the set  of scenarios (i.e., we use a scenario-based formulation of our
stochastic program). We assume a two-stage setting, meaning that there is one realization of uncertainty. The first stage consists of
the set of time periods 1𝑠𝑡 before the realization of uncertainty, and the second stage consists of the set of time periods 2𝑛𝑑 after
the realization of uncertainty. Section 4.6 elaborates on the procedure to generate the scenario tree that describes the uncertainty.
For each time period 𝑡∈ and scenario 𝑠∈ we define a range of decision variables. The annual flow (in tonnes) of a product
type 𝑝∈ on a path 𝑘∈ is given by the continuous non-negative variable ℎ𝑘𝑝𝑡𝑠. These path-flow variables are linked to the
arc-flow variables 𝑥𝑎𝑝𝑓𝑡𝑠 , representing the flow (in tonnes) of a product 𝑝∈ over arc 𝑎∈, where the index 𝑓∈ specifies
which fuel type is being used. Due to geographical imbalances in transport demand, vehicles sometimes have to make empty trips.
We model these using path-flow variables 
ℎ𝑘𝑣𝑡𝑠 and arc-flow variables 𝑏𝑎𝑓 𝑣𝑡𝑠. From these flow variables, we can derive the total
transport amount (in tonne-km) of a mode-fuel combination (𝑚, 𝑓 ) throughout the entire network, which we denote by 𝑞𝑚𝑓𝑡𝑠 .
The strategic decisions in the model are investments in transport infrastructure. The continuous variable 𝜈𝑛𝑚𝑡𝑠 represents the
extent of terminal capacity expansion at node 𝑛 for mode 𝑚, expressed as a proportion rather than an absolute amount. Investments
in edge capacities are represented by the binary variables 𝜀𝑒𝑡𝑠 . The charging/fueling capacity of a fuel 𝑓 on edge 𝑒 can be increased
by means of the continuous variable 𝑦𝑒𝑓 𝑡𝑠 . Finally, infrastructure on an edge can be upgraded to allow for the use of a new fuel 𝑓
using the binary variable 𝜐𝑒𝑓 𝑡𝑠 . For all these investment decisions, we assume that the investment is finished after a predefined lead
time.
See Tables 1–3 for a complete overview of all sets, parameters and variables in the model.
3.2.2. Objective function
The main objective is to minimize the total (generalized) costs of transport and investment in infrastructure. We first discuss
how the total costs are computed for each scenario and then how the scenarios are aggregated in a way that reflects risk-averse
preferences.
The total discounted costs 𝑓(𝜉, 𝐱) are a function of the uncertain parameters summarized as 𝜉 and the first-stage decision variables
summarized as 𝐱. For scenario 𝑠∈, it is defined as:
𝑓(𝜉𝑠,𝐱) ∶= 
𝑡∈
𝑌𝑡+1−1

𝑙=𝑌𝑡
𝛿𝑙
𝑎∈
𝑓∈𝑎
𝑝∈
𝐶𝑎𝑓𝑝𝑡𝑠 𝑥𝑎𝑓 𝑝𝑡𝑠 +
𝑣∈𝑎

𝐶𝑎𝑓𝑣𝑡𝑠 𝑏𝑎𝑓 𝑣𝑡𝑠 +
𝑝∈
𝑘∈
𝐶transf
𝑘𝑝 ℎ𝑘𝑝𝑡𝑠
+𝛿𝑌𝑡
𝑚∈{sea,rail}
𝑛∈𝑚
𝐶node
𝑛𝑚 𝜈𝑛𝑚𝑡𝑠 +
𝑒∈𝑅𝑎𝑖𝑙
𝐶edge
𝑒𝜀𝑒𝑡𝑠 +
(𝑒,𝑓)∈
𝐶upg
𝑒𝑓 𝜐𝑒𝑓𝑡𝑠 +
𝑒∈road 
𝑓∈𝑚
𝐶charge
𝑒𝑓 𝑦𝑒𝑓𝑡𝑠 .(1)
The cost function consists of a discounted sum of transport costs (within the first pair of round brackets) and investment costs (within
the second pair of round brackets). The annual transport costs consist of: (i) the generalized cost of transporting the goods over the
arcs in the network (including balancing trips); and (ii) the cost of transferring goods from one transport mode to another along the
routes. The investment costs consist of (i) the cost of expanding terminal capacities, (ii) the cost of expanding edge capacities, (iii)
the cost of upgrading edges to allow more fuel types, and (iv) the cost of building charging/fueling stations along edges. For each
year in a period 𝑡, the yearly transport costs, including carbon fees, are discounted and added separately. In contrast, investment
costs are only added once.
In strategic planning situations, it is common for a social planner (government) to have a preference for solutions that are
cost-efficient, but also robust across different future scenarios. To model such risk-averse preferences regarding uncertainty, we
use a so-called mean-CVaR objective function. That is, the objective function is a weighted average of the expected value and the
conditional value at risk (CVaR) of the total discounted costs 𝑓(𝜉, 𝐱):
min
𝐱(1 − 𝜆)E𝑓(𝜉, 𝐱)+𝜆CVaR𝛾𝑓(𝜉 , 𝐱),(2)
where 𝜆∈ [0,1] represents the relative weight of CVaR compared to the expectation. This formulation strikes a balance between
good performance on average and avoiding risk, which is captured by CVaR: the expected value of the 𝛾-tail of the distribution of
the total costs (Rockafellar and Uryasev, 2002).
The choice of CVaR as our risk measure has two main advantages. First, it is coherent (Artzner et al., 1999), meaning that it
satisfies a number of properties that are desirable to accurately reflect risk-averse preferences. The second advantage is that CVaR
can be computed using a minimization problem:
CVaR𝛾(𝑍) ∶= min
𝑢∈R𝑢+ (1 − 𝛾)−1E(𝑍−𝑢)+.(3)
Transportation Research Part E 197 (2025) 104076
5

S.J.S. Bakker et al.
Table 1
Sets and indices.
Set of directed arcs 𝑎= (𝑖, 𝑗, 𝑚, 𝑟), defined from node 𝑖 to 𝑗 with mode 𝑚 on route 𝑟.
𝑒⊆Arcs 𝑎 on edge 𝑒.
𝑚⊆Arcs 𝑎 using mode 𝑚.
in
𝑛𝑚 ⊆Arcs 𝑎= (𝑖,𝑛, 𝑚, 𝑟) entering node 𝑛, using mode 𝑚.
out
𝑛𝑚 ⊆Arcs 𝑎= (𝑛,𝑗 , 𝑚, 𝑟) leaving node 𝑛, using mode 𝑚.
Set of undirected edges defined as =undir(), indexed by 𝑒.
𝑚⊆Set of edges 𝑒 for a specific mode 𝑚.
Set of fuels, indexed by 𝑓.
𝑎⊆Set of allowed fuels on arc 𝑎.
𝑚⊆Set of allowed fuels for a mode 𝑚.
new
𝑚⊆Set of new fuels that are allowed on mode 𝑚.
Set of paths, indexed by 𝑘.
𝑎⊆Set of paths that include arc 𝑎.
𝑜𝑑 ⊆Set of paths that lead from origin 𝑜 to destination 𝑑.
cap
𝑖𝑚 ⊆Set of all paths that use terminal capacity in node 𝑖 for mode 𝑚.
uni ⊆Set of all unimodal paths.
uni
𝑚⊆Set of all unimodal paths using mode 𝑚.
Set of modes, indexed by 𝑚. We have ={𝑅𝑎𝑖𝑙, 𝑅𝑜𝑎𝑑, 𝑆 𝑒𝑎}.
Set of nodes, indexed by 𝑛,𝑖, 𝑗 , 𝑜, or 𝑑.
𝑚⊆Set of all nodes with the possibility to invest in terminals for mode 𝑚.
Set of product groups, indexed by 𝑝.
Set of route alternatives, indexed by 𝑟.
Set of scenarios, indexed by 𝑠.
𝑡
𝑠⊆Set of scenario’s that share the same history as scenario 𝑠, up to, and including, time period 𝑡.
Set of time periods, indexed by 𝑡.
1𝑠𝑡 ⊆Set of first-stage periods, indexed by 𝑡.
2𝑛𝑑 ⊆Set of second-stage periods, indexed by 𝑡.
edge
𝑒𝑡 ⊆Set of time periods during which, when investing in rail infrastructure on edge 𝑒,
the investment will be completed and operational by time 𝑡.
upg
𝑒𝑓𝑡 ⊆Set of time periods during which, when upgrading rail infrastructure on edge 𝑒 for fuel 𝑓,
the investment will be completed and operational by time 𝑡.
node
𝑛𝑚𝑡 ⊆Set of time periods during which, when investing in terminal infrastructure in node 𝑛 for mode 𝑚,
the investment will be completed and operational by time 𝑡.
⊆×Set of possible upgrades in terms of edge-fuel combinations.
𝑚Set of vehicle types on mode 𝑚.
𝑎Set of vehicle types on mode 𝑚 used in arc 𝑎= (𝑖, 𝑗, 𝑚, 𝑟).
Set of all years within the planning horizon.
Table 2
Parameters.
𝐴𝑚𝑓𝑡 ∈[0,1]Theoretical maximum technology adoption level of a mode-fuel combination in time period 𝑡 based on the associated Bass diffusion model.
𝐶𝑎𝑓𝑝𝑡𝑠 Generalized cost of transporting one tonne of product 𝑝, using arc 𝑎 and fuel 𝑓 in time period 𝑡 and scenario 𝑠 (EURO/tonne).

𝐶𝑎𝑓𝑣𝑡𝑠 Generalized cost of transporting one tonne of empty capacity of vehicle 𝑣, using arc 𝑎 and fuel 𝑓 in time period 𝑡 and scenario 𝑠 (EURO/tonne).
𝐶transf
𝑘𝑝 Total transfer costs on path 𝑘 for product 𝑝 (EURO/tonne).
𝐶charge
𝑎𝑓 Unit cost of increasing charging/fueling capacity on arc 𝑎 for fuel 𝑓 (EURO/tonne).
𝐶edge
𝑒Investment cost of increasing the capacity of edge 𝑒 (EURO).
𝐶node
𝑛𝑚 Investment cost of increasing the capacity at node 𝑛 for mode 𝑚 (EURO).
𝐶upg
𝑒Investment cost of upgrading edge 𝑒 (EURO).
𝐷𝑜𝑑𝑝𝑡 Demand for transport of product 𝑝 from origin 𝑜 to destination 𝑑 in time period 𝑡 (tonnes).
𝐿𝑎Length of an arc 𝑎 (km).
𝑀Sufficiently large number (big M).
𝑁𝑚Lifespan of the representative vehicle for mode 𝑚 (years).
𝑃𝑠∈[0,1]Probability assigned to scenario 𝑠.
𝑄charge
𝑒𝑓 Initial charging/fueling capacity of edge 𝑒 for fuel 𝑓 (tonnes).
𝑄edge
𝑒Initial capacity of edge 𝑒 (tonnes).
𝑄edge
𝑒Capacity increase from investing in infrastructure on edge 𝑒 (tonnes).
𝑄node
𝑛𝑚 Initial capacity in node 𝑛 for mode 𝑚 (tonnes).
𝑄node
𝑛𝑚 Maximum possible capacity increase from investments at node 𝑛 and mode 𝑚 (tonnes).
𝑈𝑚𝑓 ∈ [0,1] Potential adoption share of mode 𝑚 and fuel 𝑓.
𝑌𝑡Years passed at the beginning of time period 𝑡 (years).
𝛼𝑚𝑓𝜏 𝑠 Coefficient of innovation in the Bass diffusion model for mode-fuel combination (𝑚,𝑓 ) in year 𝜏 in scenario 𝑠.
𝛽𝑚𝑓𝜏 𝑠 Coefficient of imitation in the Bass diffusion model for mode-fuel combination (𝑚,𝑓 ) in year 𝜏 in scenario 𝑠.
𝛿∈[0,1]Yearly discount factor.
𝜌𝑚𝑡 ∈[0,1]Maximum allowed relative decrease in transport work of mode 𝑚 compared to time period 𝑡− 1.
This representation allows us to recast the risk-averse problem as a standard risk-neutral stochastic program (Rockafellar and
Uryasev, 2002) with an additional first-stage decision variable 𝑢. This is indeed how we solve our mean-CVaR model.
Transportation Research Part E 197 (2025) 104076
6

S.J.S. Bakker et al.
Table 3
Variables.
Continuous variables
𝑏𝑎𝑓𝑣𝑡𝑠 Flow of balancing movements over arc 𝑎 using fuel 𝑓 and vehicle type 𝑣 in time period 𝑡 in scenario 𝑠 (tonnes of carrying capacity).
ℎ𝑘𝑝𝑡𝑠 Flow of product 𝑝 on path 𝑘 in time period 𝑡 in scenario 𝑠 (tonnes).

ℎ𝑘𝑣𝑡𝑠 Flow of balancing movements for vehicle type 𝑣 on path 𝑘 in time period 𝑡 in scenario 𝑠 (tonnes of carrying capacity).
𝑞𝑚𝑓𝑡𝑠 Total transport amount using mode-fuel combination (𝑚, 𝑓 ) in period 𝑡 in scenario 𝑠 (tonne-km).
𝑞𝑚𝑓𝜏 𝑠 Total transport amount using mode-fuel combination (𝑚, 𝑓 ) in year 𝜏 in scenario 𝑠 (tonne-km).
𝑞tot
𝑚𝜏𝑠 Total transport amount on mode 𝑚 in year 𝜏 in scenario 𝑠 (tonne-km).
𝑞−
𝑚𝑓𝑡𝑠 Total decrease in transport amount using mode-fuel combination (𝑚, 𝑓 ) from period 𝑡− 1 to period 𝑡 in scenario 𝑠 (tonne-km).
𝑥𝑎𝑓𝑝𝑡𝑠 Flow of product 𝑝 over arc 𝑎 using fuel 𝑓 in time period 𝑡 in scenario 𝑠 (tonnes).
𝑦𝑒𝑓𝑡𝑠 Increase in charging/fueling capacity on edge 𝑒 for fuel 𝑓 in time period 𝑡 in scenario 𝑠 (tonnes).
𝜈𝑛𝑚𝑡𝑠 Terminal capacity expansion (as proportion of maximum possible expansion) for mode 𝑚 in node 𝑛, time period 𝑡, and scenario 𝑠.
Binary variables
𝜐𝑒𝑓𝑡𝑠 1 if edge 𝑒 is upgraded in time period 𝑡 in scenario 𝑠 to allow fuel 𝑓; 0 otherwise.
𝜀𝑒𝑡𝑠 1 if the capacity of edge 𝑒 is expanded in time period 𝑡 in scenario 𝑠; 0 otherwise.
3.2.3. Constraints
The demand, arc-path and fleet balancing constraints are given by:

𝑘∈𝑜𝑑
ℎ𝑘𝑝𝑡𝑠 =𝐷𝑜𝑑𝑝𝑡 , 𝑜, 𝑑 ∈, 𝑝 ∈, 𝑡 ∈, 𝑠 ∈,(4)

𝑓∈𝑎
𝑥𝑎𝑓𝑝𝑡𝑠 =
𝑘∈𝑎
ℎ𝑘𝑝𝑡𝑠, 𝑎 ∈, 𝑝 ∈, 𝑡 ∈, 𝑠 ∈,(5)

𝑓∈𝑎
𝑏𝑎𝑓𝑣𝑡𝑠 =
𝑘∈𝑎∩uni
𝑚

ℎ𝑘𝑣𝑡𝑠, 𝑎 ∈, 𝑣 ∈𝑎, 𝑡 ∈, 𝑠 ∈,(6)

𝑎∈in
𝑛𝑚 𝑏𝑎𝑓𝑣𝑡𝑠 +
𝑝∈𝑣
𝑥𝑎𝑓𝑝𝑡𝑠 =
𝑎∈out
𝑛𝑚 𝑏𝑎𝑓𝑣𝑡𝑠 +
𝑝∈𝑣
𝑥𝑎𝑓𝑝𝑡𝑠 , 𝑛 ∈, 𝑚 ∈, 𝑓 ∈𝑚, 𝑣 ∈𝑚, 𝑡 ∈, 𝑠 ∈.(7)
Here, constraint (4) ensures that the demand for transport between all origins and destinations is satisfied. Constraints (5) and (6)
describe the arc-path relation for the freight flow variables and for the vehicle balancing variables, respectively. The fleet balancing
constraint (7) ensures that every vehicle that leaves a node eventually comes back. This constraint sometimes induces trips with
empty vehicles, a feature that is present in Crainic et al. (1990b), but has been neglected in some more recent models.
Capacity constraints limit the flow of goods on nodes and edges:

𝑓∈𝑎
𝑝∈
𝑥𝑎𝑓𝑝𝑡𝑠 +
𝑣∈𝑎
𝑏𝑎𝑓𝑣𝑡𝑠 ≤1
2
𝑄edge
𝑒+𝑄edge
𝑒
𝑡′∈edge
𝑒𝑡
𝜀𝑒𝑡′𝑠
, 𝑒 ∈rail, 𝑎 ∈𝑒, 𝑡 ∈, 𝑠 ∈,(8a)

𝑡∈
𝜀𝑒𝑡𝑠 ≤1, 𝑒 ∈rail, 𝑠 ∈,(8b)

𝑝∈
𝑘∈cap
𝑖𝑚
ℎ𝑘𝑝𝑡𝑠 ≤𝑄node
𝑛𝑚 +𝑄node
𝑛𝑚 
𝑡′∈node
𝑛𝑚𝑡
𝜈𝑛𝑚𝑡′𝑠, 𝑚 ∈{sea,rail}, 𝑛 ∈𝑚, 𝑡 ∈, 𝑠 ∈,(8c)

𝑡∈
𝜈𝑛𝑚𝑡𝑠 ≤1, 𝑚 ∈{sea,rail}, 𝑛 ∈𝑚, 𝑠 ∈,(8d)

𝑎∈𝑒
𝑝∈
𝑥𝑎𝑓𝑝𝑡𝑠 +
𝑣∈𝑎
𝑏𝑎𝑓𝑣𝑡𝑠 ≤𝑄charge
𝑒𝑓 +𝑦𝑒𝑓𝑡𝑠 , 𝑒 ∈road, 𝑓 ∈𝑒, 𝑡 ∈, 𝑠 ∈,(8e)

𝑝∈
𝑎∈𝑒
𝑥𝑎𝑓𝑝𝑡𝑠 ≤𝑀
𝑡′∈upg
𝑒𝑓𝑡
𝜐𝑒𝑓𝑡′𝑠,(𝑒, 𝑓) ∈ , 𝑡 ∈, 𝑠 ∈.(8f)
Constraints (8a) and (8b) limit the flow of goods on arcs by the corresponding edge capacity, which is split equally between the
arcs going in opposite directions. Similarly, constraints (8c) and (8d) restrict the amount of goods transferred between modes at a
given node to the sum of the initial terminal capacity and a fraction of the maximum possible capacity increase from investments.
Constraint (8e) models the fact that for certain fuels, transport can only take place on edges that have the necessary charging/fueling
infrastructure installed. Finally, (8f) models that some fuels can only be used on edges that have been upgraded.
Fleet renewal constraints prevent the fleet mix from changing too suddenly, to model the fact that significant inertia exists in
transport fleets:
𝑞𝑚𝑓𝑡𝑠 =
𝑝∈
𝑎∈𝑚
𝐿𝑎𝑥𝑎𝑓𝑝𝑡𝑠 , 𝑚 ∈, 𝑓 ∈𝑚, 𝑡 ∈, 𝑠 ∈,(9a)
Transportation Research Part E 197 (2025) 104076
7

S.J.S. Bakker et al.
𝑞−
𝑚𝑓𝑡𝑠 ≥𝑞𝑚𝑓 (𝑡−1)𝑠−𝑞𝑚𝑓 𝑡𝑠 , 𝑚 ∈, 𝑓 ∈𝑚, 𝑡 ∈⧵{0}, 𝑠 ∈,(9b)

𝑓∈𝑚
𝑞−
𝑚𝑓𝑡𝑠 ≤𝑌𝑡−𝑌𝑡−1
𝑁𝑚
𝑞tot
𝑚(𝑡−1)𝑠, 𝑚 ∈, 𝑡 ∈⧵{0}, 𝑠 ∈,(9c)

𝑓∈𝑚
𝑞𝑚𝑓𝑡𝑠 ≥(1 − 𝜌𝑚𝑡 )
𝑓∈𝑚
𝑞𝑚𝑓,𝑡−1,𝑠 , 𝑚 ∈, 𝑡 ∈⧵{0}, 𝑠 ∈.(9d)
Constraint (9a) defines the total transport amount (in tonne-km) of a mode-fuel combination, which is a proxy of the number of
vehicles used. Constraint (9b), in combination with the non-negativity constraints on 𝑞−
𝑚𝑓𝑡𝑠 , define the latter variable as the decrease
in the total transport amount of mode-fuel (𝑚, 𝑓 ) from period 𝑡−1 to period 𝑡. These variables are used in constraint (9c) to limit the
total decrease in the fleet of vehicles on each mode 𝑚. Constraint (9d) limits decreases in modal transport work over time, capturing
that existing supply chains do not change too rapidly.
Technology adoption constraints (10) restrict the (rate of) adoption of new fuel technologies:
𝑞𝑚𝑓 ,𝑌𝑡,𝑠 =𝑞𝑚𝑓 𝑡𝑠, 𝑚 ∈, 𝑓 ∈𝑚, 𝑡 ∈, 𝑠 ∈,(10a)
𝑞tot
𝑚𝜏𝑠 =
𝑓∈𝑚
𝑞𝑚𝑓 𝜏𝑠 , 𝑚 ∈, 𝜏 ∈, 𝑠 ∈,(10b)
𝑞𝑚𝑓 𝜏𝑠 ≤𝐴𝑚𝑓 𝜏 𝑞tot
𝑚𝜏𝑠 , 𝑚 ∈, 𝑓 ∈new
𝑚, 𝜏 ∈, 𝑠 ∈,(10c)
𝑞𝑚𝑓 𝜏𝑠 −𝑞𝑚𝑓 ,𝜏−1,𝑠 ≤𝛼𝑚𝑓 ,𝜏 −1,𝑠 𝑈𝑚𝑓 𝑞tot
𝑚,𝜏−1,𝑠 +𝛽𝑚𝑓 ,𝜏 −1,𝑠 𝑞𝑚𝑓 ,𝜏−1,𝑠 , 𝑚 ∈, 𝑓 ∈new
𝑚, 𝜏 ∈⧵{0}, 𝑠 ∈.(10d)
Adoption of new fuel technologies (i.e., mode-fuel pairs (𝑚, 𝑓 )) is expressed in terms of the variables 𝑞𝑚𝑓 𝜏 𝑠. These are yearly
counterparts to the variables 𝑞𝑚𝑓 𝑡𝑠 and defined in constraint (10a). Constraint (10b) defines the total transport amount on mode 𝑚
for year 𝜏. The remaining constraints are based on the diffusion model for technology adoption by Bass (1969). The original Bass
model is governed by the Bass equation
𝑑
𝑑𝑡 𝐹(𝑡)
1−𝐹(𝑡)=𝛼(𝑡) + 𝛽(𝑡)𝐹(𝑡). Here, 𝐹(𝑡) is the extent to which a technology has been adopted, as a
fraction of its potential 𝑈. The coefficient of innovation, 𝛼(𝑡), describes the base rate of adoption. The coefficient of imitation, 𝛽(𝑡),
describes how the adoption rate increases at higher levels of adoption. We use the adoption level 𝐴𝑚𝑓𝜏 of a new technology (𝑚,𝑓 )
derived from the Bass model as an upper bound in constraint (10c). Moreover, we extract constraint (10d) on the rate of adoption
as follows. We linearize the Bass equation by (1) ignoring the fraction 1
1−𝐹(𝑡) on the left-hand side (which is close to one at low
adoption levels), (2) writing it in terms of the absolute adoption level rather than the fraction, and (3) discretizing the equation.
The equation is included as an inequality, providing an upper bound on the adoption rate of a new technology.
Non-anticipativity constraint (11) is required to model the fact that the scenario is learned after the first-stage, i.e., the first-stage
decisions should be the same in every scenario:
𝐱𝑡𝑠 −𝐱𝑡𝑠′= 0, 𝑡 ∈1𝑠𝑡, 𝑠, 𝑠′∈,(11)
where 𝐱𝑡𝑠 is defined as the vector consisting of all decision variables that are indexed by period 𝑡 and scenario 𝑠. Note that the
vector equation above includes non-anticipativity constraints for all decision variables that have an index 𝑡 and 𝑠. For example, for
variables 𝑦𝑒𝑓𝑡𝑠, (11) includes the equations 𝑦𝑒𝑓 𝑡𝑠 −𝑦𝑒𝑓𝑡𝑠′= 0 for all 𝑒∈, 𝑓 ∈, 𝑡 ∈1𝑠𝑡 , 𝑠, 𝑠′∈. We use this short-hand notation
using 𝐱𝑡𝑠 to avoid writing non-anticipativity constraints for each decision variable separately.
Finally, the domains of the variables are given by:
𝑏𝑎𝑓𝑣𝑡𝑠 ≥0, 𝑎 ∈, 𝑓 ∈𝑎, 𝑣 ∈𝑎, 𝑡 ∈, 𝑠 ∈,(12a)
ℎ𝑘𝑝𝑡𝑠 ≥0, 𝑘 ∈, 𝑝 ∈, 𝑡 ∈, 𝑠 ∈,(12b)

ℎ𝑘𝑣𝑡𝑠 ≥0, 𝑘 ∈uni, 𝑣 ∈, 𝑡 ∈, 𝑠 ∈,(12c)
𝑞𝑚𝑓𝑡𝑠 ≥0, 𝑚 ∈, 𝑓 ∈𝑚, 𝑡 ∈, 𝑠 ∈,(12d)
𝑞−
𝑚𝑓𝑡𝑠 ≥0, 𝑚 ∈, 𝑓 ∈𝑚, 𝑡 ∈⧵{0}, 𝑠 ∈,(12e)
𝑞𝑚𝑓 𝜏𝑠 ≥0, 𝑚 ∈, 𝑓 ∈𝑚, 𝜏 ∈, 𝑠 ∈,(12f)
𝑞tot
𝑚𝜏𝑠 ≥0, 𝑚 ∈, 𝜏 ∈, 𝑠 ∈,(12g)
𝑥𝑎𝑓𝑝𝑡𝑠 ≥0, 𝑎 ∈, 𝑓 ∈𝑎, 𝑝 ∈, 𝑡 ∈, 𝑠 ∈,(12h)
𝑦𝑒𝑓𝑡𝑠 ≥0, 𝑒 ∈road, 𝑓 ∈𝑒, 𝑡 ∈, 𝑠 ∈,(12i)
𝑧𝑡𝑠 ≥0, 𝑡 ∈, 𝑠 ∈,(12j)
𝜐𝑒𝑓𝑡𝑠 ∈{0,1},(𝑒, 𝑓 ) ∈ , 𝑡 ∈, 𝑠 ∈,(12k)
𝜀𝑒𝑡𝑠 ∈{0,1}, 𝑒 ∈rail, 𝑡 ∈, 𝑠 ∈,(12l)
𝜈𝑛𝑚𝑡𝑠 ∈[0,1], 𝑚 ∈{sea,rail}, 𝑛 ∈𝑚, 𝑡 ∈, 𝑠 ∈.(12m)
Transportation Research Part E 197 (2025) 104076
8

S.J.S. Bakker et al.
Fig. 3. Final configuration of the STraM-Norway topology in (c) compared with (a) the demand and (b) the infrastructure network.
4. Case study: Norway
We apply STraM in a case study of the Norwegian freight transport system, and refer to this implementation as STraM-Norway.
This case study has a dual purpose: to illustrate the capabilities and advantages of STraM and to gain insight in the decarbonization
of the Norwegian freight transport system. As a time resolution, we use the years 2023, 2028, 2034, 2040, and 20501, and assume the
system between any subsequent pair of years operates as in the first of the two. We use a social discount rate of 3.8%, in line with
estimated values for Norway (Groom et al., 2022).
4.1. Network topology
To represent the transportation network in Norway, we divide the country into zones with a centroid (city) and map each centroid
to a node in the graph. To get a good graph representation, two criteria should be met: (i) the nodes should accurately map to the
origins and destinations of transport demand and (ii) the edges should accurately map to the physical transportation infrastructure.
We take the Norwegian counties as a starting point for the zones, with their capital cities as centroids. We also add a zone for the
Norwegian continental shelf, northern and southern Sweden, as well as for Europe and the rest of the world, each with a suitable
centroid. To achieve criteria (i) and (ii) above, a few adjustments are made based on Figs. 3(a) and 3(b), showing the transport
demand and physical infrastructure, respectively. In particular, we made the following adjustments: splitting Troms/Finnmark into
Troms and Finnmark for better demand center representation; dividing Nordland into Nordland and Ofoten/Lofoten/Vesterålen to
match rail infrastructure; separating Vestland into Hordaland and Sogn og Fjordane, as the latter lacks rail connections; and merging
Viken and Oslo due to a shared demand center. The final result is shown in Fig. 3(c).
4.2. Demand
For the demand of transport, we use detailed data on product movements from Madslien and Hovi (2021), used in the Norwegian
National Freight Transport Model (NGM). We aggregate the original 39 product types from NGM into five product groups with
similar characteristics: dry bulk, liquid bulk, break bulk, neo bulk, and container. A mapping of these original product types into
product groups can be found in the online supplementary material. The product groups break bulk and container are further
subdivided into two subgroups each: one group of products with a high time urgency (e.g., fresh food) and one with a low time
urgency. For the other groups, the time urgency varies little within the groups, so these are not subdivided further. This leaves us
with a total of 7 product groups.
Demand is further aggregated by origin and destination zone, using the geographical zones defined in Section 4.1. Demand for
transport within zones is neglected, in line with our focus on line-haul transport. The end result is a commodity flow matrix which
shows annual demand for transport of products of each group to each pair of origin and destination zone.
1We have picked this time resolution to balance realism and computational complexity. Short intervals at the start ensure that initial investment decisions
are modeled realistically, while longer intervals towards the end reduce computational demands. The periods are chosen to align with investment lead times.
Transportation Research Part E 197 (2025) 104076
9

S.J.S. Bakker et al.
Fig. 4. Generalized cost of transport breakdown.
4.3. Modes, fuels and emissions
Transport can be performed by three modes: road, rail, and sea. On each mode, a number of fuel technologies are available,
some of which are established and mature and some of which are novel and developing. The term ‘‘fuel’’ is used in a broad sense
and also includes technologies such as batteries (e.g., battery-electric trucks).
On road, we consider the established fuel diesel and the novel fuels hydrogen and batteries. On rail, we consider the established
fuels diesel and electric (catenary trains) and the novel fuels hydrogen and batteries. Finally, on sea we consider the established
fuels heavy fuel oil (HFO) and marine gas oil (MGO), and the novel fuels hydrogen, ammonia, and methanol. Current shares of fuels
on each mode are based on data from DNV (2022, 2014), Jernbanedirektoratet (2021b). We estimate 20% of the market share of
long-haul road transport to be hard-to-electrify, thus requiring diesel or hydrogen trucks.
We omit biofuels due to potential limits in production volumes and required land resources (Gray et al., 2021). Low-carbon
technologies like liquid natural gas are excluded since carbon neutrality cannot be reached (Gray et al., 2021). The availability of
renewable fuel technologies increases over time (Gray et al., 2021; Zenith et al., 2019).
For each fuel, we consider its scope 1 and 2 carbon emissions, considering tailpipe emissions for fossil fuels and emissions during
electricity generation for renewable fuels (Martin et al., 2023). For fossil fuels, emission factors are based on data from SSB (2021).
For renewable fuels, we assume the fuels are produced from Norwegian grid electricity, and emission factors are based on individual
value chain efficiencies from production to consumption, utilizing the model by Martin et al. (2023).
4.4. Transport costs
Crucial for our model are accurate data regarding transport cost parameters. These costs consist of two parts: transport costs on
arcs and transfer costs in nodes.
We compute the generalized cost of transport for each mode, fuel, and product group combination using an extended version of
the methodology proposed by Martin et al. (2023). This extension incorporates several enhancements, including the addition of
rail freight, differentiation across product groups, consideration of non-monetary costs, and improved interpolation between years.
Incorporating the value of (transport) time, the approach decomposes the total cost of ownership into its constituent components,
as illustrated in Fig. 4. These components include capital expenditures (CAPEX) and operational expenditures (OPEX), which
together determine the levelized cost per tonne-kilometer. By estimating these elements in a harmonized and consistent manner,
the methodology ensures a fair and robust comparison across different modes and fuels, supporting informed mode and fuel choice
decisions in our model.
Besides costs for the physical transportation of the goods, transfer costs occur on multimodal paths. Estimated transfer costs at
harbors or rail terminals cover non-monetary factors, like the waiting time of cargo in the terminal, as well as the monetary costs
of loading and unloading processes and any associated fees, such as port charges.
4.5. Infrastructure capacities and investments
Some transport infrastructure in STraM is capacitated. For road freight, we only consider fueling stations as capacity elements,
neglecting road capacity limitations. Fueling stations are assumed to be needed every 100 kilometers for battery-electric trucks and
every 150 kilometers for hydrogen trucks (Thema, 2022), with associated investment cost based on Transport and Environment
(2021).
Rail freight faces capacity constraints on railways and in terminals. The following investment possibilities are included: single
to double track, electrification of non-electrified tracks, and the construction of a new railway along the route Bodø-Narvik-
Tromsø(i.e., Nord-Norgebanen), with associated capacities and investment costs based on Kystverket et al. (2020), Jernbaneverket
(2015), Jernbanedirektoratet (2021c,a). Capacities of rail terminals and the cost of capacity investments are based on (Kystverket
et al., 2020; Grønland and Hovi, 2014; Jernbanedirektoratet, 2019)
Sea freight is only capacitated in terminals (i.e., harbors), given the assumed unlimited traffic volumes at sea. Terminal capacities
are based on (SSB, 2022), while investment costs are extrapolated from Karmsund harbor in Rogaland.
Transportation Research Part E 197 (2025) 104076
10

S.J.S. Bakker et al.
Fig. 5. Schematic illustration of the scenario tree used in STraM. The scenario names consist of two letters, corresponding to the electricity price and oil price,
respectively, indicating whether the price is high (H), medium (M), or low (L) in the scenario.
4.6. Scenario generation
The stochastic programming structure of STraM requires the setup of a scenario tree to describe long-term uncertain parameters.
Careful selection and definition of these uncertain parameters are crucial, as including too many can lead to an explosion in the
number of scenarios, resulting in significant computational challenges. A two-stage setup is chosen to capture the uncertainty
relevant to the first-stage decisions, with the understanding that decisions in later stages can be updated through a rolling horizon
approach. Although adding more stages could provide additional insight, the marginal value of adding more stages often drastically
drops after including a second stage (see, e.g., Pantuso and Boomsma (2020), so we chose not to do this to avoid computational
problems.
While operational models, dealing with short-term uncertainty often incorporate stochastic elements like demand or travel times,
we argue that these are not the primary factors influencing strategic investments2,3. Instead, we account for long-term uncertainty in
the cost competitiveness of different fuels. This is the main parameter affecting mode-choice, fuel choice, and investment decisions.
We construct the scenarios for cost uncertainty as follows. First, we observe that in terms of transport costs, the most significant
uncertainty is fuel costs (Martin et al., 2023). For renewable fuel technologies, we therefore generate scenarios based on the future
electricity price as the main cost lever. We take the high/medium/low scenarios for Norwegian market zones generated by Statnett
(2023). These prices are used as input in the transport cost model from Martin et al. (2023), which captures the fact that the cost
of different fuels respond differently to electricity price fluctuations. For fossil fuels, the international oil price is the fuels’ largest
cost lever. Here, we take the high/medium/low scenarios for the oil price presented by IEA (2023), which are used as an index to
generate scenarios of all fossil fuel types considered. For the first-stage time periods, we constrain each scenario realization to align
with the medium price levels. The resulting scenario tree is illustrated in Fig. 5. It includes 32= 9 scenarios, for all combinations
of electricity and oil prices. We assume this uncertainty to realize in 2034, which means that the periods 2023 and 2028 are the
first (deterministic) stage, while those from 2034 to 2050 are the second (stochastic) stage. Moreover, we utilize a discrete uniform
distribution, assigning equal probability to each scenario
Fig. 6 shows the impact of these uncertain electricity- and oil prices on fuel costs, which are the driving factor in the calculation
of the generalized cost of transport described in Section 4.4. We observe that the impact of electricity price uncertainty correlates
with the energy efficiencies of individual fuel value chains. Large fuel cost variations occur in low-efficiency chains, such as those
for methanol production.
Finally, Fig. 7 illustrates the impact of fuel uncertainty on the levelized cost of transport. This cost is the main constituent of the
generalized cost of transport and is demonstrated using the example of road container transport. We observe a cost reduction over
time for battery and hydrogen fuels, while diesel costs show a slight increase due to rising carbon prices. Battery-electric trucks
become more cost-effective than diesel trucks before 2034, while hydrogen trucks become cost-competitive by 2050.
4.7. Path generation
Our path-flow model formulation requires the a priori generation of a set of admissible paths for each origin–destination
pair (𝑜, 𝑑). The purpose of this procedure is to efficiently identify promising paths, thereby enhancing the model’s computational
performance. On the one hand, this set should be flexible enough, in the sense that it allows for many different choices of mode. On
the other hand, to keep the size manageable, we should only include ‘‘reasonable’’ paths (e.g., no unnecessary detours). We strike
a balance between these two criteria as follows. We define a set of admissible sequences of modes (e.g., road–sea): all sequences of
2We have conducted a scenario analysis to evaluate the impact of uncertainty in transport demand. Although varying demand levels altered the overall
costs, it had minimal effect on the investment decisions and modal fuel shares.
3Uncertainty in freight demand model outputs is often not explicitly characterized. However, recent research indicates that results tend to remain relatively
stable and robust at higher levels of aggregation. Aguas and Bachmann (2022).
Transportation Research Part E 197 (2025) 104076
11

S.J.S. Bakker et al.
Fig. 6. Fuel cost variation due to electricity and oil price uncertainty. The shaded area is generated by using the high and low price scenarios.
Fig. 7. Levelized costs of container transport in line-haul road freight for several fuel technologies and years. Note that negative costs show the vehicle’s levelized
residual values. Error bars show the electricity and oil price uncertainty for renewable and fossil fuels, respectively.
length at most two. As our model does not include first- and last-mile transport, this is not a very restrictive assumption. Then, for
each origin–destination pair (𝑜, 𝑑 ) and for each admissible sequence, we include the cheapest path from 𝑜 to 𝑑 using that sequence.
This can be done using the ‘‘BuildChain’’ module in the Norwegian National Freight Model System (de Jong et al., 2013a).
One complication is that the question which path of a given mode sequence is cheapest depends on several factors: the product
type transported, the fuel used, and the cost scenario. To account for this, we follow the idea in Zhang et al. (2008) and run
the procedure above repeatedly for each product type, fuel, and scenario. We then merge all the results. It turns out that in the
overwhelming majority of cases, the same cheapest path is found, so the resulting total number of paths remains limited.
5. Results
We now present the results of the case study described in the previous section. Section 5.1 discusses the key outputs, focusing
primarily on the resulting investment decisions and modal and fuel mixes. In Section 5.2 we analyze the implications of various
Transportation Research Part E 197 (2025) 104076
12

S.J.S. Bakker et al.
Fig. 8. Expected modal fuel mixes for the different transport modes. Standard deviations of second-stage results are visualized using error bars.
carbon pricing schemes. Finally, Section 5.3 evaluates the significance of considering the multi-period aspect, while Section 5.4
explores the value of modeling long-term uncertainty.
STraM-Norway is implemented in Python 3.10.4, formulated using Pyomo, with the extensive form of the two-stage stochastic
programming model solved by the commercial MILP solver Gurobi 10.0. The model, and corresponding data, is openly available on
https://github.com/ntnuiotenergy/STraM. The analyses are carried out on a Dell Lattitude 7420 computer with an Intel i5-1145G7,
2.60 GHz processor, 16 GB RAM, running Windows 10 and using 1 thread. The path generation procedure initially identifies 3,486
optimal paths, which are reduced to 387 unique paths after eliminating duplicates. The extensive form of the base model with 9
scenarios consists of 4,554,245 constraints, 1,833,986 continuous variables and 306 binary variables.4 after pre-solve. It solves to
optimality (gap of 0.0000%) in approximately 6 minutes5
5.1. Modal fuel mixes and investment decisions
We first discuss results from the base case corresponding to the case study described in Section 4 and risk parameters 𝜆= 0.3
and 𝛾= 0.8.
Fig. 8 shows the cost-optimal modal fuel mix. All modes witness an increase in demand with a considerable shift towards
road transport, which almost doubles toward 2050. Battery-electric trucks dominate road transport in 2050, with a minor role
for hydrogen trucks. On rail, most diesel trains are replaced by catenary trains. Battery and hydrogen trains play a small role,
operating on tracks that are too expensive to electrify. Sea transport shows only a limited shift towards carbon-free fuels, with MGO
remaining the dominant fuel in 2050 in most scenarios. Ammonia and Hydrogen take up some market share, depending very much
on the fuel cost scenario.
In terms of costs, we can distinguish between transport costs and investment costs, illustrated in Figs. 9(a) and 9(b), respectively.
Total transport costs increase steadily over the years as a result of increasing demand and price levels. The overall cost structure
remains stable, with rising emission prices being offset by a decrease in fossil fuel use. Regarding investment costs, we see
major investments in the current year. The main driver is investment in rail capacity from Hamar to Oslo, Ålesund and Southern
Sweden, as well as from North Sweden to Trondheim and Tromsø, as can be seen from Fig. 10(a). These railway connections are
operating at maximum capacity in both directions in the first time periods, necessitating capacity expansions. Later years see no
additional rail investments, as these projects have long lead times. Besides, additional investments in terminals are made, mainly
in Oslo, Tromsøand Ålesund, see Fig. 10(b). In the second-stage, substantial investments are directed towards charging stations for
battery-electric trucks and fuel stations for hydrogen trucks. As an example, Fig. 11 illustrates the geographical distribution of the
investments in charging infrastructure over time. We observe a gradual increase in charging capacity all over Norway, with higher
capacities concentrated along major routes linking the capital Oslo with neighboring areas.
4The limited number of binary variables arises because we only model binary investments in rail infrastructure, while capacity investments in charging
infrastructure and aggregated terminals are represented as continuous variables.
5When solving the extensive form of the stochastic program, computational challenges can arise as the number of scenarios increases. For instance, a model
with 42= 16 scenarios did solve to optimality within 10 minutes. However, expanding the model to 52= 25 scenarios resulted in excessive memory usage, making
it infeasible to solve.
Transportation Research Part E 197 (2025) 104076
13

S.J.S. Bakker et al.
Fig. 9. Expected cost structures for (a) transport and (b) infrastructure. Implied emissions (relative to the base emissions in 2023) are presented in (a). The
error bars denote standard deviations.
Fig. 10. Investments in rail infrastructure in 2023.
5.2. Carbon price analysis
To explore the impact of varying carbon policies on emission reduction in the transport system, we conduct a sensitivity analysis.
The Norwegian Ministry of Finance (2023) prescribes different carbon price scenarios to be used in techno-economic studies in
Norway. We analyze three of these (base, intermediate, and high), as visualized in Fig. 12. In addition, we consider a case where
we force the system to meet Norwegian emission reduction targets.
Fig. 13(a) plots the total carbon emissions associated with the transport for the base case. By 2050, we see a decrease to
approximately 20% of the emissions in 2023. This falls short of the target of 10% by 2050. Moreover, the variability in the 2050
emissions is very high, driven by the fuel cost uncertainty. Thus, meeting the 2050 emission target seems both unrealistic and highly
dependent on fuel cost developments under the current carbon price system.
Figs. 13(b)–13(d) show that all intensified policies are effective in reaching the 2050 emission target, but only the last two
achieve the 2030 target. The associated system costs are presented in Table 4. The table shows that intermediate carbon pricing has
a similar cost as the forced emission reduction case, while not managing to reach 2030 targets.
Transportation Research Part E 197 (2025) 104076
14

S.J.S. Bakker et al.
Fig. 11. Development of established charging infrastructure over time. The line’s thickness illustrates the magnitude of the investment volumes.
Fig. 12. The baseline carbon price scenario, along with an intermediate and high scenario.
Fig. 13. Effect of carbon policies on expected emission reductions: (a) baseline carbon price; (b) intermediate carbon price (c); high carbon price; and (d) system
forced to meet Norwegian emission targets. Error bars show the standard deviation caused by second-stage electricity and oil price uncertainty.
5.3. Dynamic vs. static models
A common approach to strategic analyses using existing static transport models is to solve the static model for a specific future
time period, relying on fixed parameter forecasts (see e.g., Crainic et al. (1990b), Pinchasik et al. (2020). This is often referred to
Transportation Research Part E 197 (2025) 104076
15

S.J.S. Bakker et al.
Table 4
Total expected discounted costs for the system transition under various carbon price scenarios.
Emission scenario Total system costs [Be] Percentage increase
Baseline Norwegian Regulation 244.5 –
Forced Emission Reduction 249.4 2.01%
Intermediate Carbon Price 249.1 1.92%
High Carbon Price 251.8 2.99%
Fig. 14. Modal fuel mix comparison of the base case with two static cases: a transition and target period. The error bars denote standard deviations.
as a what-if approach. In contrast, STraM explicitly models the dynamic evolution of the transport system over time, representing a
key contribution of this work.
To assess the importance of this multi-period approach, we compare our results with a static and deterministic version of STraM
which optimizes the fuel mix for a specific year but neglects critical factors like fleet renewal and technology adoption, both of
which affect the practical feasibility of the optimized fuel mix.
The key difference between static and dynamic models lies in how they address the evolution of the transport system over time.
A static model optimizes the transport system for a specific target year, such as 2050, but overlooks inter-temporal constraints
related to, e.g., fleet renewal and technology adoption, which affect feasibility and optimality of the static solution. In contrast, our
explicit multi-period approach accounts for the ‘‘path to 2050’’, rather than merely ‘‘optimizing for 2050’’. The static approach finds
the system that would be best in 2050 and investments are made to achieve that configuration, typically deferring expenditures to
the latest possible period to minimize costs due to discounting. To align with this logic, we do not impose restrictions on capacity
expansion for edges and terminals, as the model naturally schedules these investments at the latest feasible time to ensure the
required infrastructure is operational by 2050.
Specifically, the static model is constructed by (i) neglecting the fleet renewal constraint (9) and technology adaption con-
straint (10), (ii) only activating the demand, arc-path and fleet balancing constraints (4)–(7) in the given static time period, and (iii)
considering a single deterministic scenario.
Fig. 14 compares the modal fuel mix resulting from the full, dynamic version of STraM (indicated as ‘‘base’’) with two different
static runs. The static run for 2034 represents a transition period, while the static run for 2050 can be seen as the target period.
While the fuel mixes on rail are fairly similar, both in the transition and target period, we observe significant differences in the
fuel mixes on road and sea. More transport work on road is performed in the static case, compared to the dynamic case, which can
be explained by the exclusion of, e.g., fleet renewal constraints. The same observation can be made for maritime transport, where
the fuel mixes changes significantly for the static case between 2034 and 2050. Thus, STraM is able to give better insights into the
dynamic nature of this transition and can sketch a roadmap for how to arrive at a low-carbon transport system in 2050. Moreover,
STraM also provides insight into the timing of the corresponding infrastructure investments.
5.4. The value of uncertainty
Another important aspect of STraM is that it explicitly models long-term uncertainty in technology development. We assess
the importance of this aspect by comparing the results from our stochastic programming solution (SP) in the base case with the
so-called expectation of the expected value solution (EEV). The EEV is the expected objective value associated with the expected
value solution (EV), which is the solution obtained from fixing all uncertain parameters at their expected values. Thus, the EEV
represents the expected performance of a solution based on a model that does not explicitly model uncertainty.
Transportation Research Part E 197 (2025) 104076
16

S.J.S. Bakker et al.
We solved both the SP and EV model and find an objective value of e244.5 Billion (B) (total system cost) for the SP model, and
an EEV of e283.6B. This means that the value of the stochastic solution (VSS), defined as the difference between the EEV and SP
objective is equal to e39.1B, i.e., the SP solution improves upon the EV solution by 13.81%. In addition, the average total emissions
(across all scenarios) are 2.2 Mega Tonnes CO2 lower for SP than EEV (8.53%). Thus, our stochastic programming approach can
help reduce both total costs and emissions, compared to a deterministic approach. Appendix provides a more in-depth analysis of
uncertainty and risk preferences.
6. Discussion
In this section, we discuss the key findings of our analysis, the limitations of our model, and its potential real-world applications.
Our results show that road freight will be dominated by battery-electric trucks in 2050 across all scenarios, reaching cost-
competitiveness compared to diesel before 2034. The 20% market share of line-haul road transport that we assume hard-to-electrify
is served by either hydrogen or diesel. The choice between the two depends heavily on if and when hydrogen becomes more cost-
effective than diesel. Investments in hydrogen fueling stations are postponed accordingly. Policymakers might want to hedge the
activities of hydrogen truck and infrastructure providers to bridge the gap until full market adoption of hydrogen. This transition
could be supported by synergies with other sectors.
For rail freight, capacity expansion of existing connections with catenary lines is the primary investment strategy. Full
electrification of tracks currently operated by diesel trains is too expensive. Instead, these trains are replaced by battery-electric
or potentially hydrogen trains, depending on the relative cost developments.
Sea freight appears the most expensive to decarbonize, showing only a partial shift towards ammonia and hydrogen in the base
case. The market share of each fuel is highly variable and depends on the realized cost scenario, because fuel costs dominate in
maritime transport. Our model excludes fueling infrastructure costs for maritime transport. As a result, the relative attractiveness
of both alternatives may be somewhat distorted in our results. Thus, we recommend further detailed research to find the most
attractive renewable fuel system for maritime transport.
Our findings indicate that the minimum carbon prices regulated by the Norwegian government fall short of meeting 2030 and
2050 decarbonization targets. While rail freight achieves carbon neutrality by fully transitioning away from diesel, road and sea
freight continue to rely on fossil fuels to varying degrees, with the maritime sector representing the greatest challenge to Norway’s
emission goals. Thus, we recommend that policymakers prioritize decarbonization efforts in the maritime sector. Backcasting from
the 2050 targets, our analysis highlights the importance of adopting more ambitious, technology-neutral carbon pricing policies,
which is explored in detail in this paper. To ensure a harmonized transition across transport modes, technology- and mode-specific
measures may be needed as well. To analyze this in more detail, higher-resolution models of, e.g., individual modes and technologies
can be used to find the policy measures needed (subsidies, technology-push policies, demand-pull policies, etc.) to achieve the
optimal transport system from our model.
We acknowledge some limitations and simplifications of our model. First, we sacrifice some of the detailed logistics elements
implemented in state-of-the-art national freight transport models. This was necessary to incorporate desired strategic elements, such
as long-term uncertainty and the adoption of new technologies. We believe that this is an acceptable limitation as our focus lies
on evaluating long-term investments. Moreover, by explicitly modeling the flow of goods in the system in each time period, we
still obtain a good approximation of the performance of the operations. Second, we solve a cost-optimization model from a social
planning perspective. Although the output can provide valuable information to policymakers about a socially desirable freight
transport system, it does not recognize the variety of actors with divergent preferences, resulting in complex decision dynamics.
Furthermore, we consider a closed, national system, whereas international freight transport relies on global standardization and
infrastructure availability, which could significantly impact national decisions. Lastly, our model considers scope 1 and 2 emissions,
but neglects life-cycle emissions across fuel technologies.
Finally, we would like to address the real-world application of the model. STraM serves as a decision-support tool for various
strategic planning applications, including transport policy and infrastructure investment prioritization. The results presented in
this paper demonstrate STraM’s applicability through a medium-scale case study of Norway, showcasing its capabilities. Given
the model’s flexibility, it can also be applied to other countries with similar graph network sizes. The open-source Python
code is designed in a modular and general manner, with minimal hard-coding, making it easy to adapt to different contexts.
However, applying STraM to larger countries or case studies could introduce significant computational challenges, requiring the
development of specialized solution methods. This represents an important avenue for future research and would merit a dedicated,
methodologically-focused publication.
7. Conclusion
In this article, we presented STraM, a strategic network design model for national freight transport decarbonization. By explicitly
accounting for the dynamic nature of long-term planning, as well as the development and adoption of new fuel technologies with
corresponding uncertainties, STraM is tailored to identify decarbonization pathways and evaluate the impact of government or
industry policies.
Our case study results, targeting the freight transport sector in Norway, show that STraM is able to provide valuable insights into
investment strategies and fuel adoption for different transport modes across space and time. In addition, the explicit consideration
of uncertainty in transport costs and technology development leads to a significant improvement in results. In particular, we identify
Transportation Research Part E 197 (2025) 104076
17

S.J.S. Bakker et al.
a value of the stochastic solution of approximately 13.6%. An interesting result from a policy-maker’s perspective is that carbon
pricing proves to be an efficient measure to reach emission targets, although relatively high prices are needed. Moreover, we find that
the commonly used what-if approach does not manage to consider technology adaption and fleet renewal, leading to a forecasted
transport system that is considerably different from the solution that results from STraM. This clearly illustrates the need for a
dynamic, multi-period transport model.
Overall, we conclude that all the contributions, i.e., the harmonizing of transport cost data; the consideration of multiple
time periods with endogenous infrastructure investments; the description of (new) fuel technology adoption; and the inclusion of
long-term cost-uncertainty, contribute to better strategic freight transport modeling.
In future work, we want to connect STraM to a high-resolution national freight transport model (specifically for the ADA
framework) to validate its solutions and obtain more detailed insights. Similarly, we aim to investigate the relationship with energy
infrastructure currently beyond the scope of the model and assess the impact of sector-specific policy instruments. Other directions
for future work include improving model accuracy—for example, by adopting a multi-stage approach with more than two stages or
incorporating new elements, such as vessel retrofitting. Additionally, enhancing computational performance by developing tailored
solution methods, such as decomposition (e.g., by product groups (Guelat et al., 1990), mode-fuel combinations, or uncertainty
scenarios) or heuristic techniques, is a promising avenue.
CRediT authorship contribution statement
Steffen J.S. Bakker: Writing – original draft, Visualization, Software, Project administration, Methodology, Formal analysis,
Conceptualization. Jonas Martin: Writing – original draft, Visualization, Methodology, Formal analysis, Data curation, Concep-
tualization. E. Ruben van Beesten: Writing – original draft, Software, Methodology, Formal analysis, Conceptualization. Ingvild
Synnøve Brynildsen: Software, Methodology, Data curation, Conceptualization. Anette Sandvig: Software, Methodology, Data
curation, Conceptualization. Marit Siqveland: Software, Methodology, Data curation, Conceptualization. Antonia Golab: Writing
– review & editing, Visualization.
Declaration of Generative AI and AI-assisted technologies in the writing process
During the preparation of this work the authors used ChatGPT in order to suggest alternative formulations for individual
sentences. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for
the content of the publication.
Declaration of competing interest
This paper was prepared as a part of the Norwegian Research Center on Mobility Zero Emission Energy Systems (FME MoZEES.
p-nr: 257653) and the Norwegian Research Centre for Energy Transition Studies (FME NTRANS, p-nr: 296205), funded by the
Research Council of Norway. These funding sources have had no involvement in the research process. No other interests to declare.
Appendix. Risk analysis
An interesting question is how the risk-aversion modeled in STraM affects the solution. Fig. A1 shows the investment costs
when solving the model using the EEV solution, a risk neutral objective function (only using the expected value), the base case
(with 𝜆= 0.3 and 𝛾= 0.8) and a maximally risk-averse objective function (only counting the worst scenario). We observe that the
deterministic EEV plan shown in Fig. A1(a) results in lower investment levels compared to the stochastic approaches. Additionally,
Figs. A1(b)–A1(d) reveal that higher levels of risk aversion (i.e., increased weight on the expensive scenarios) lead to greater and
earlier investments, although the differences are not very pronounced. Notably, the investment decisions show little change when
𝜆 exceeds its base level of 0.3. Thus, we conclude that incorporating uncertainty significantly impacts investment decisions, while
the influence of higher risk aversion diminishes as 𝜆 increases.
Finally, we have to comment that the significant uncertainty in the second-stage time periods for the fully risk-averse case
(Fig. A1(d)) arises because only the performance of the worst-case scenario is considered. As a result, the model has considerable
flexibility in determining the decision variables for the other scenarios, which influences the visual representation in the graph.
Data availability
The model and data is openly available on Github.
Transportation Research Part E 197 (2025) 104076
18

S.J.S. Bakker et al.
Fig. A1. Expected investment costs for different risk preferences. The error bars denote standard deviations.
References
Aguas, O., Bachmann, C., 2022. Assessing the effects of input uncertainties on the outputs of a freight demand model. Res. Transp. Econ. 95, 101234.
http://dx.doi.org/10.1016/j.retrec.2022.101234.
Archetti, C., Peirano, L., Speranza, M.G., 2022. Optimization in multimodal freight transportation problems: A Survey. European J. Oper. Res. 299 (1), 1–20.
http://dx.doi.org/10.1016/j.ejor.2021.07.031.
Arnold, P., Peeters, D., Thomas, I., 2004. Modelling a rail/road intermodal transportation system. Transp. Res. Part E: Logist. Transp. Rev. 40 (3), 255–270.
http://dx.doi.org/10.1016/j.tre.2003.08.005.
Artzner, P., Delbaen, F., Eber, J.-M., Heath, D., 1999. Coherent measures of risk. Math. Finance 9 (3), 203–228.
Bass, F.M., 1969. A new product growth for model consumer durables. Manag. Sci. 15 (5), 215–227.
Ben-Akiva, M., de Jong, G., 2013. The Aggregate-Disaggregate-Aggregate (ADA) Freight Model System. In: Freight Transport Modelling. Emerald Group Publishing
Limited, pp. 69–90. http://dx.doi.org/10.1108/9781781902868-004.
Crainic, T.G., Florian, M., Guelat, J., Spiess, H., 1990a. Strategic Planning of Freight Transportation: ST AN, An Interactive-Graphic System. Transp. Res. Rec.
1283 (97).
Crainic, T.G., Florian, M., Léal, J.-E., 1990b. A Model for the Strategic Planning of National Freight Transportation by Rail. Transp. Sci. 24 (1), 1–24, URL
https://www.jstor.org/stable/25768403.
Crainic, T.G., Genderau, M., Gendron, B., 2021. Network Design with Applications to Transportation and Logistics. In: Network Design with Applications To
Transportation and Logistics. Springer International Publishing, Cham, http://dx.doi.org/10.1007/978-3-030-64018-7.
Crainic, T.G., Laporte, G., 1997. Planning models for freight transportation. European J. Oper. Res. 97 (3), 409–438. http://dx.doi.org/10.1016/S0377-
2217(96)00298-6.
Crainic, T.G., Perboli, G., Rosano, M., 2018. Simulation of intermodal freight transportation systems: a taxonomy. European J. Oper. Res. 270 (2), 401–418.
http://dx.doi.org/10.1016/j.ejor.2017.11.061.
de Bok, M., Bal, I., Tavasszy, L., Tillema, T., 2020. Exploring the impacts of an emission based truck charge in the Netherlands. Case Stud. Transp. Policy 8 (3),
887–894. http://dx.doi.org/10.1016/j.cstp.2020.05.013.
de Jong, G., Ben-Akiva, M., Baak, J., Erik Grønland, S., 2013a. Method Report-Logistics Model in the Norwegian National Freight Model System (Version 3).
Technical Report, Significance.
Transportation Research Part E 197 (2025) 104076
19

S.J.S. Bakker et al.
de Jong, G., Gunn, H., Walker, W., 2004. National and international freight transport models: An overview and ideas for future development. Transp. Rev. 24
(1), 103–124. http://dx.doi.org/10.1080/0144164032000080494.
De Jong, G., Johnson, D., 2009. Discrete mode and discrete or continuous shipment size choice in freight transport in Sweden. In: European Transport Conference.
de Jong, G., Vierth, I., Tavasszy, L., Ben-Akiva, M., 2013b. Recent developments in national and international freight transport models within Europe.
Transportation 40 (2), 347–371. http://dx.doi.org/10.1007/s11116-012-9422-9.
Demir, E., Burgholzer, W., Hrušovský, M., Arıkan, E., Jammernegg, W., Woensel, T.V., 2016. A green intermodal service network design problem with travel
time uncertainty. Transp. Res. Part B: Methodol. 93, 789–807. http://dx.doi.org/10.1016/j.trb.2015.09.007.
DNV, 2014. Teknisk vurdering av skip og av infrastruktur for forsyning av drivstoff til skip. DNV GL AS Maritime, Oslo.
DNV, 2022. Energy transition Norway 2022: A national forecast to 2050. DNV AS, Oslo.
Ghisolfi, V., Antal Tavasszy, L., Homem de Almeida Rodriguez Correia, G., de Lorena Diniz Chaves, G., Mattos Ribeiro, G., 2024. Dynamics of freight transport
decarbonization: A simulation study for Brazil. Transp. Res. Part D: Transp. Environ. 127, http://dx.doi.org/10.1016/j.trd.2023.104020.
Gray, N., McDonagh, S., O’Shea, R., Smyth, B., Murphy, J.D., 2021. Decarbonising ships, planes and trucks: An analysis of suitable low-carbon fuels for the
maritime, aviation and haulage sectors. Adv. Appl. Energy 1, 100008.
Grønland, S.E., Hovi, I.B., 2014. Referansealternativet – utgangspunkt for analyse av terminalstrukturer. Transportøkonomisk Institutt, Oslo.
Groom, B., Drupp, M.A., Freeman, M.C., Nesje, F., 2022. The Future, Now: A Review of Social Discounting. Annu. Rev. Resour. Econ. 14 (1), http:
//dx.doi.org/10.1146/annurev-resource-111920-020721.
Guelat, J., Florian, M., Crainic, T.G., 1990. Multimode multiproduct network assignment model for strategic planning of freight flows. Transp. Sci. 24 (1), 25–39.
http://dx.doi.org/10.1287/trsc.24.1.25.
Higle, J.L., Wallace, S.W., 2003. Sensitivity Analysis and Uncertainty in Linear Programming. Interfaces 33 (4), 53–60.
Hoehne, C., Muratori, M., Jadun, P., Bush, B., Yip, A., Ledna, C., Vimmerstedt, L., Podkaminer, K., Ma, O., 2023. Exploring decarbonization pathways for USA
passenger and freight mobility. Nat. Commun. 14 (1), http://dx.doi.org/10.1038/s41467-023-42483-0.
IEA, 2023. World Energy Outlook 2023. International Energy Agency, Paris.
Jernbanedirektoratet, 2019. Videre utvikling av Alnabruterminalen. Jernbanedirektoratet, Oslo.
Jernbanedirektoratet, 2021a. In: Jernbanedirektoratet (Ed.), Investigation of Nord-Norgebanen submitted to the ministry. Oslo, URL https://www.
jernbanedirektoratet.no/nordnorgebanen (Accessed on: 14 Nov 2023).
Jernbanedirektoratet, 2021b. In: Jernbanedirektoratet (Ed.), Jernbanen må også redusere utslippene sine. Oslo, URL https://jernbanemagasinet.no/artikler/
jernbanen-ma-ogsa-redusere-utslippene-sine/(Accessed on: 24 Oct 2023).
Jernbanedirektoratet, 2021c. Nullfib2: Nullutslipp - batteridrift på jernbanen.
Jernbaneverket, 2015. Strategi for driftsform på ikke - elektrifiserte baner. Jernbaneverket, Oslo.
Jourquin, B., Beuthe, M., 1996. Transportation policy analysis with a geographic information system: The virtual network of freight transportation in Europe.
Transp. Res. Part C: Emerg. Technol. 4 (6), 359–371. http://dx.doi.org/10.1016/S0968-090X(96)00019-8.
Kaack, L.H., Vaishnav, P., Morgan, M.G., Azevedo, I.L., Rai, S., 2018. Decarbonizing intraregional freight systems with a focus on modal shift. Environ. Res. Lett.
13 (8), http://dx.doi.org/10.1088/1748-9326/aad56c.
Kystverket, vegvesen, S., Jernbanedirektoratet, 2020. Godsterminalstruktur i Oslofjordområdet: Konseptvalgutredning. Kystverket and Statens vegvesen and
Jernbanedirektoratet, Oslo.
Madslien, A., Hovi, I.B., 2021. Projections for freight transport 2018–2050.. Transportøkonomisk Institutt, Oslo.
Madslien, A., Steinsland, C., Grønland, S.E., 2015. Nasjonal godstransportmodell. En innføring i bruk av modelen. Technical Report, The Norwegian Institute of
Transport Economics, URL https://www.toi.no/publikasjoner/nasjonal-godstransportmodell-en-innforing-i-bruk-av-modellen-article31775-8.html.
Martin, J., Dimanchev, E., Neumann, A., 2023. Carbon abatement costs for renewable fuels in hard-to-abate transport sectors. Adv. Appl. Energy 12, 100156.
http://dx.doi.org/10.1016/j.adapen.2023.100156.
Meersman, H., Van de Voorde, E., 2019. Freight transport models: Ready to support transport policy of the future? Transp. Policy 83, 97–101. http:
//dx.doi.org/10.1016/j.tranpol.2019.01.014.
Meyer, T., 2020. Decarbonizing road freight transportation – A bibliometric and network analysis. Transp. Res. Part D: Transp. Environ. 89, http://dx.doi.org/
10.1016/j.trd.2020.102619.
Mohammed, L., Niesten, E., Gagliardi, D., 2020. Adoption of alternative fuel vehicle fleets – a theoretical framework of barriers and enablers. Transp. Res. Part
D: Transp. Environ. 88, 102558. http://dx.doi.org/10.1016/j.trd.2020.102558, URL https://www.sciencedirect.com/science/article/pii/S1361920920307458.
Nassar, R.F., Ghisolfi, V., Annema, J.A., van Binsbergen, A., Tavasszy, L.A., 2023. A system dynamics model for analyzing modal shift policies towards
decarbonization in freight transportation. Res. Transp. Bus. Manag. 48, http://dx.doi.org/10.1016/j.rtbm.2023.100966.
Norwegian Ministry of Finance, 2023. Carbon price pathways for use in socioeconomic analyses in 2023. URL https://www.regjeringen.no/no/tema/okonomi-
og-budsjett/statlig-okonomistyring/karbonprisbaner-for-bruk-i-samfunnsokonomiske-analyser-i-2023/id2878113/.
Pantuso, G., Boomsma, T.K., 2020. On the number of stages in multistage stochastic programs. Ann. Oper. Res. 292 (2), 581–603. http://dx.doi.org/10.1007/
s10479-019-03181-7.
Pinchasik, D.R., Hovi, I.B., Mjøsund, C.S., Grønland, S.E., Fridell, E., Jerksjö, M., 2020. Crossing borders and expanding modal shift measures: Effects on mode
choice and emissions from freight transport in the nordics. Sustainability 12 (3), http://dx.doi.org/10.3390/su12030894.
Rockafellar, R.T., Uryasev, S., 2002. Conditional value-at-risk for general loss distributions. J. Bank. Financ. 26 (7), 1443–1471.
Rosenberg, E., Espegren, K., Danebergs, J., Fridstrøm, L., Beate Hovi, I., Madslien, A., 2023. Modelling the interaction between the energy system and road
freight in Norway. Transp. Res. Part D: Transp. Environ. 114, http://dx.doi.org/10.1016/j.trd.2022.103569.
SSB, 2021. In: Statistics Norway (Ed.), Emission factors used in the estimations of emissions from combustion. Oslo, URL https://www.ssb.no/_attachment/404602/
(Accessed on: 29 Jul 2022).
SSB, 2022. In: Statistics Norway (Ed.), 10916: Godsmengde, etter havn, retning, opprinnelse/destinasjon og lastetype (tonn) 2013 - 2022. Oslo, URL https:
//www.ssb.no/statbank/table/10916/(Accessed on: 14 Nov 2023).
Statnett, 2023. Langsiktig markedsanalyse: Norge, Norden og Europa 2022–2050. Statnett, Oslo.
Thema, 2022. Infrastructure costs for establishing a network of energy stations for heavy transport. THEMA Consulting Group, Oslo.
Transport and Environment, 2021. How to decarbonise long-haul trucking in Germany. An analysis of available vehicle technologies and their associated costs.
Brussels.
Wangsness, P.B., Madslien, A., Hovi, I.B., Hulleberg, N., 2021. Double-track railway between Oslo and Gothenburg: An analysis using the Norwegian Freight
Transport model. Technical Report, Transportøkonomisk Institut, URL www.toi.no.
Yang, K., Yang, L., Gao, Z., 2016. Planning and optimization of intermodal hub-and-spoke network under mixed uncertainty. Transp. Res. Part E: Logist. Transp.
Rev. 95, 248–266. http://dx.doi.org/10.1016/j.tre.2016.10.001.
Zenith, F., Isaac, R., Hoffrichter, A., Thomassen, M.S., Møller-Holst, S., 2019. Techno-economic analysis of freight railway electrification by overhead line,
hydrogen and batteries: Case studies in Norway and USA. J. Rail Rapid Transit 1–12.
Zhang, K., Nair, R., Mahmassani, H.S., Miller-Hooks, E.D., Arcot, V.C., Kuo, A., Dong, J., Lu, C.C., 2008. Application and validation of dynamic freight
simulation-assignment model to large-scale intermodal rail network. Transp. Res. Rec. (2066), 9–20. http://dx.doi.org/10.3141/2066-02.
Transportation Research Part E 197 (2025) 104076
20