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Transportation Research Part D 112 (2022) 103470
1361-9209/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Contents lists available at ScienceDirect
Transportation Research Part D
journal homepage: www.elsevier.com/locate/trd
Collaborative planning for intermodal transport with eco-label
preferences
Yimeng Zhang a,∗, Arne Heinold b, Frank Meisel b, Rudy R. Negenborn a, Bilge Atasoy a
aDepartment of Maritime and Transport Technology, Delft University of Technology, 2628 CD Delft, The Netherlands
bSchool of Economics and Business, Kiel University, Kiel, Germany
ARTICLE INFO
Keywords:
Collaborative planning
Intermodal transport
Sustainable transport
Eco-label
Vague preferences
ABSTRACT
Sustainability is a common concern in intermodal transport. Collaboration among carriers may
help in reducing emissions. In this context, this work establishes a collaborative planning
model for intermodal transport and uses eco-labels (a series of different levels of emission
ranges) to reflect shippers’ sustainability preferences. A mathematical model and an Adaptive
Large Neighborhood Search heuristic are proposed for intermodal transport planning of carriers
and fuzzy set theory is used to model the preferences towards eco-labels. For multiple car-
riers, centralized, auction-based collaborative, and non-collaborative planning approaches are
proposed and compared. Real data from barge, train and truck carriers in the European Rhine-
Alpine corridor is used for extensive experiments where both unimodal carrier collaboration
and intermodal carrier collaboration are analyzed. Compared with non-collaborative planning
without eco-labels, the number of served requests increases and emissions decrease significantly
in the collaborative planning with eco-labels as transport capacity is better utilized.
1. Introduction
In intermodal transport, containers are routed from their origins to their destinations by using multiple transport modes like
trucks, trains, or barges (SteadieSeifi et al.,2014). While intermodal routings are often triggered by potential cost reductions,
they are also considered as a means for more sustainable transport solutions. For example, Heinold and Meisel (2018) show in
a comprehensive simulation study for Europe that 90% of the shipments have a lower environmental impact if they are routed in
an intermodal rail–road connection instead of using a road-only connection. For shippers, such considerations play an increasing
role as transportation contributes to ‘‘almost a quarter of Europe’s greenhouse gas emissions and is the main cause of air pollution
in cities’’ (European Commission,2020). To achieve sustainable freight transportation, the European Commission proposes to cut
carbon emissions in transport by 60% by 2050 and shift 50% of freight from road to rail and to waterborne transport (European
Commission,2011). China has announced its ‘‘Carbon Peak and Carbon Neutrality’’ policy, which aims at achieving a peak in carbon
emissions by 2030 and carbon neutrality by 2060, for which the volume of rail–ship container transportation should increase by
15% each year between 2021 and 2025 (State Council of China,2021a,b). According to surveys and expert interviews conducted
in Zhang et al. (2022c), reducing emissions is important for carriers and shippers when the government releases policies or sets
emission reduction goals. Shippers and transport companies will need to comply with regulations and they will become motivated
to keep track of their footprint. Moreover, with the raising awareness of global warming, more and more carriers and shippers
will want to contribute to sustainable transportation. Therefore, several approaches and policies have been proposed to reduce
∗Corresponding author.
E-mail addresses: Yimeng.Zhang@tudelft.nl (Y. Zhang), arne.heinold@bwl.uni-kiel.de (A. Heinold), meisel@bwl.uni-kiel.de (F. Meisel),
R.R.Negenborn@tudelft.nl (R.R. Negenborn), B.Atasoy@tudelft.nl (B. Atasoy).
https://doi.org/10.1016/j.trd.2022.103470
Received 6 March 2022; Received in revised form 21 September 2022; Accepted 22 September 2022
Transportation Research Part D 112 (2022) 103470
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Y. Zhang et al.
Fig. 1. Example of non-collaborative and collaborative planning.
the environmental impact of logistics, such as low-emission zones for heavy vehicles (Fensterer et al.,2014), emission reduction
targets (Chen and Wang,2016), or emission trading systems (Demailly and Quirion,2008). Recently, the concept of eco-labels has
been proposed to achieve a more sustainable freight transportation (Heinold and Meisel,2020;Kirschstein et al.,2022). Thereby,
eco-labels use a traffic light-colored preset scheme to indicate a shipment’s relative environmental impact. For example, an eco-label
‘‘A’’ indicates that emissions caused in a transport process are very low whereas somewhat higher emissions lead to eco-label ‘‘B’’,
and so on. Eco-labels can then be used as an indicator for a shipper’s environmental preference, e.g., by requesting for a shipment
that it is transported in accordance to a certain label.
The services of each transport carrier (operators of transport modes) are limited and may not be sufficient to achieve sustainable
transport, especially when emission reduction requirements are high. Collaborative planning may then help in reducing emissions.
Collaborative planning is becoming more and more prevalent due to the intensive competition in the transport market (Li et al.,
2015b). There are different types of collaborative planning and collaboration partners can be shippers, receivers, or carriers (Pan
et al.,2019). This study focuses on collaborative planning among carriers by exchanging shipment requests from shippers. Fig. 1
shows an example of non-collaborative and collaborative planning. In this example, there are three intermodal transport carriers
and each carrier has two requests with high requirements on sustainability. When carriers do not collaborate, requests are served
by their own services and the environmental requirements of some requests are not reached. For example, request 𝑎is served by
carrier 1’s truck service, and request 𝑓is served by carrier 3’s train and truck services with transshipment. In collaborative planning,
carriers decide which requests they are willing to share or serve. After collaboration, carrier 1’s request 𝑎is shared with carrier 2
and carrier 2/3’s requests 𝑑/𝑓are shared with carrier 1. Thus, the capacity of low-cost and low-emission vehicles is better utilized
and all carriers improve service levels and avoid unnecessary trips.
In its essence, collaboration enables the aggregated consideration of each carrier’s demand, which is placed by shippers who own
or supply shipments that can then be transported in a more efficient and sustainable way through a larger and more diverse logistics
network. Large vehicles in intermodal transport, such as trains or barges, benefit from economies of scale by increasing capacity
which reduces costs and emissions per container. Therefore, they are more profitable and sustainable if there is sufficient demand,
which can be achieved through collaboration among carriers (e.g., Groothedde et al.,2005). Collaborating carriers can make better
use of their vehicles’ capacity and avoid empty trips, which then leads to cost and emission reductions, service improvements, and
market share increases (e.g., Krajewska and Kopfer,2006;Cruijssen et al.,2007;Schmoltzi and Wallenburg,2011).
To achieve a more sustainable intermodal transport, we present a collaborative planning model with eco-labels. The considered
carriers each operate networks on their own that differ in structure. For example, the predominant mode might be trains in one
network and barges in another network. We consider shippers with different expectations regarding a shipment request’s eco-
label. However, integrating environmental preferences through eco-labels for each request imposes additional challenges to the
underlying transport planning problem as well as to the collaborative planning model. The transport planning needs to handle
vague preferences on eco-labels, such as ‘‘around eco-label B is fine’’. Appropriate collaborative planning approaches also need
to be proposed to reach the required eco-label at the lowest cost by using different modes of service of carriers. To address these
challenges, we provide a mathematical model and an Adaptive Large Neighborhood Search (ALNS) heuristic for intermodal transport
planning considering vague preferences on eco-labels. We do not view eco-labels exclusively as either ‘‘fulfilled’’ or ‘‘not fulfilled’’
but calculate the degree of how much a request’s routing complies with its requested eco-label using fuzzy set theory. Regarding the
collaboration, we consider centralized, collaborative, and non-collaborative approaches. An auction-based mechanism is adopted
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Y. Zhang et al.
for exchanging requests among carriers in the collaborative planning. We apply our model to a realistic case study in which we
consider collaboration among unimodal or intermodal carriers along the European Rhine-Alpine corridor. Based on obtained results,
we provide insights on situations in which collaboration is beneficial out of reasons of sustainability.
To the best of our knowledge, our paper is the first to propose and analyze the collaborative planning for carriers in intermodal
transport considering shippers’ (vague) sustainability preferences. Our main contributions to the existing literature are as follows.
First, an optimization model with eco-label preferences is developed considering characteristics of intermodal transport and
vagueness of preferences. Second, we provide a conceptual framework for horizontal collaborative planning in the context of
sustainability. Finally, we perform an experimental study that investigates settings in which collaboration leads to more sustainable
solutions.
The rest of this paper is structured as follows. Section 2presents a review of the relevant literature. Section 3describes the studied
problem. Section 4provides the approach for handling vague preferences, the mathematical model and heuristic algorithm for
transport planning of each carrier, and the collaborative planning approach for multiple carriers. Section 5describes the experimental
settings and the results from the case study. Section 6concludes the paper.
2. Literature review
This paper considers horizontal collaboration between intermodal transport carriers that principally offer the same service,
namely, transporting a freight shipment from its origin to its destination. Accordingly, this literature review comprises two fields: (i)
collaborative planning in unimodal freight transportation and (ii) collaborative planning in intermodal transportation. A brief review
of relevant literature in these fields is provided in Sections 2.1 and 2.2, respectively. Note that the first field is very general but, in
the context of our paper, comprises those papers on collaboration that do not belong to intermodal transport but are considered as
relevant for our study. A summary of the reviewed literature is provided in Section 2.3.
2.1. Collaborative planning in freight transport
This section provides a review on collaborative planning in freight transportation. It starts with a general overview of how
collaborations can be classified and continues with a review on collaboration in networks in which only a single mode of
transportation is used. The latter review is included as it introduces general concepts of collaborative planning in freight transport.
These concepts are used in Section 2.3 to highlight the distinct characteristics of our paper.
Gansterer and Hartl (2018) identify three major streams of research for collaborative vehicle routing: centralized collaborative
planning, decentralized planning without auctions, and auction-based decentralized planning. If a central coordinator has full power
on carriers, it is called centralized planning, otherwise called decentralized planning. Further divided by the means of exchanging
requests, decentralized planning can be non-auction or auction-based.
Assuming a powerful central coordinator is not necessarily practical because carriers may not be willing to give full information
to such a party. Moreover, the optimization problems in centralized collaborative planning are usually hard to solve because the
overall transport network is of a large scale. Decentralized approaches without auctions typically involve various steps such as
partner selection, request selection, and request exchange (Gansterer and Hartl,2018). Compared to non-auction-based systems,
the auction-based approaches are more complex due to the bidding procedure. However, it is in the nature of auctions to address
the reassignment of transport requests and the allocation of the profit gained by carrier collaboration simultaneously (Berger and
Bierwirth,2010).
The research on collaborative freight transportation for unimodal transport often focuses on road freight transport be it for Full
Truckload (FTL, size of shipment equal to vehicle capacity) or Less Than Truckload (LTL, size of shipment less than vehicle capacity)
services. Collaborative planning of FTL mainly benefits from avoiding empty trips (Liu et al.,2010) and collaborative planning of LTL
mainly benefits from making better use of vehicle capacity (Dai and Chen,2012;Wang and Kopfer,2014). Berger and Bierwirth
(2010) propose two solution approaches for the LTL request reassignment problem involving decentralized control and auction-
based selection and exchange of requests. Dai and Chen (2011) propose a multi-agent and auction-based framework for carrier
collaboration in LTL transport. Lai et al. (2017) propose an iterative auction approach in FTL transport, which enables carriers to
collaborate by exchanging their shipping requests iteratively. Wang et al. (2014) extend the pickup and delivery problem with time
windows to collaborative transport planning, where both subcontracting and collaborative request exchange are taken into account.
There is also some research on collaborative planning in maritime transport and inter-terminal transport. For example, Agarwal and
Ergun (2010) study collaboration among carriers in liner shipping. Both tactical problems such as the design of large-scale networks
and operational problems such as the allocation of limited capacity on a transport network among the carriers are discussed. Vojdani
et al. (2013) focus on collaborative approaches in the empty container management. They demonstrate the potential for cost savings
through the use of container pooling in comparison to non-cooperative solutions. For inter-terminal transports, Kopfer et al. (2016)
evaluate by experiment scenarios for isolated planning, central planning, and collaborative planning. Their results show there are
discrepancies in the collaboration profits of individual carriers.
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Table 1
Summary of the literature review.
Literature Domain CA T FT OTN S
Liu et al. (2010) FTL DP
Li et al. (2015b) FTL ADP
Lai et al. (2017) FTL ADP
Dai and Chen (2011) LTL ADP
Dai and Chen (2012) LTL CP
Wang and Kopfer (2014) LTL ADP
Berger and Bierwirth (2010) RFT ADP
Wang et al. (2014) RFT ADP
Özener (2014) RFT – Carrier
Agarwal and Ergun (2010) MFT DP
Vojdani et al. (2013) MFT DP
Kopfer et al. (2016) ITT ADP
Zhang et al. (2020) IWT –
Puettmann and Stadtler (2010) IFT ADP
Xu et al. (2015) IFT ADP
Di Febbraro et al. (2016) IFT DP
Li et al. (2017) IFT DP
Sun et al. (2019) IFT ADP
Liotta et al. (2014) IFT CP Carrier
Zhang et al. (2022a) IFT – Carrier
This research IFT ADP Shipper
2.2. Collaborative planning in intermodal transport
Compared to the literature on collaboration in single-mode networks, there is a lack of research on collaborative planning for
intermodal transport (Pan,2017;Gumuskaya et al.,2020). In the last decade, some scholars researched the cooperation in intermodal
transport at a strategical level from a business model perspective (Lin et al.,2017;Saeed,2013). Nevertheless, very few research
effort has been spent on the collaborative planning of independent players in an intermodal transport chain at the tactical and
operational level, see the survey of Gansterer and Hartl (2018). The recent study of Gumuskaya et al. (2020) presents a framework
for such collaboration but no decision support model. An example of a more decision-oriented study is Puettmann and Stadtler
(2010), who investigate the coordination of a long-haul carrier and a drayage carrier in an intermodal transport chain. The carriers
are allowed to keep their private planning information and critical data. The focus of the paper is on analyzing the impact of
stochastic demand. Di Febbraro et al. (2016) propose a multi-actor system for cooperation in intermodal freight transport. They
decompose the optimization problem into a set of sub-problems, each of them representing the operations of one actor. Through
a Lagrangian-based Network Communication Coordinator, each actor receives information from its preceding and successive actor,
and then optimizes its local operations. The dynamics of intermodal transport are studied by developing a discrete event model
based on the concept of a rolling horizon. Li et al. (2017) investigate cooperative planning among multiple carriers that connect
deep-sea ports and inland terminals where the transport networks of these carriers are interconnected with each other. Li et al.
(2017) investigate service networks that are non-overlapping and the cooperative planning is done at the tactical flow level by all
operators.
Only few papers have studied the auctioning of requests in intermodal transport collaboration. Xu et al. (2015) study intermodal
transport auctions for B2B (Business to Business) e-commerce logistics with transaction costs. Sun et al. (2019) focus on intermodal
transport service procurement problem in the context of the ‘‘Belt and Road Initiative’’, where a shipper contains a bundle of requests
in different lanes (origin–destination pairs) and each carrier may cover either one or multiple lanes. The results indicate that the
auctioneer should decrease transaction costs, increase the numbers of shippers/carriers, control the types of shipper demand, and
induce true biding prices of bidders.
2.3. Summary
Table 1 provides a summary of the reviewed papers. We also added our previous work (Zhang et al.,2020,2022a), which
studied routing optimization in inland waterways and intermodal transport but without considering collaborative planning or eco-
label requirements of shippers. All papers are divided by their research domains, i.e., FTL road transport, LTL road transport, Road
Freight Transport (RFT) without specifying FTL/LTL, Maritime Freight Transport (MFT), Inter Terminal Transport (ITT), Inland
Waterway Transport (IWT), and Intermodal Freight Transport (IFT). The collaboration approaches (CA) are divided by the categories
proposed by Gansterer and Hartl (2018), i.e., Centralized Planning (CP), Non-auction-based Decentralized Planning (DP), Auction-
based Decentralized Planning (ADP). The table furthermore reports if papers consider features such as transshipments (T), fixed
timetables (FT), overlapping transport networks (OTN), or sustainability preferences (S).
As shown in Table 1, there are many studies on collaborative vehicle routing in unimodal road freight transportation (including
RFT, LTL and FTL). However, there are significant differences between unimodal and intermodal settings. For example, in many
studies on road freight transport, the carrier has only one type of vehicles (homogeneous fleet). In intermodal transport, the carrier
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Y. Zhang et al.
Fig. 2. Eco-labeling scheme.
potentially owns vehicles of multiple modes and different characteristics. In particular, vehicles can be very large, which has various
implications such as that the emissions of barges and trains are highly influenced by their actual load. Furthermore, the requests
in intermodal transport can be segmented and transported by multiple vehicles, while requests in the road mode usually just
comprise one vehicle. When a request is segmented, it will be transferred between vehicles at transshipment terminals. Therefore,
synchronization at transshipment terminals needs to be considered in intermodal transport. Furthermore, intermodal carriers often
have specific terminals and operating areas where trains and ships typically follow fixed timetables and predefined routes, which
is hardly the case in traditional road freight transportation.
The research in RFT/LTL/FTL, MFT, and ITT only considers one transport mode, either trucks or ships. Some research has been
done in IFT, however, the carriers in these papers are hardly modeled realistically. For instance, the carriers assumed by Puettmann
and Stadtler (2010) and Li et al. (2017) can control different transport networks whereas in reality a transport network may
be occupied by multiple carriers. When considering carriers that serve the same or at least overlapping parts of a transport
network, horizontal collaboration approaches become relevant (Cleophas et al.,2019). Moreover, most papers ignore the individual
sustainability preferences of carriers or shippers. Some papers regard reducing emissions as an objective from the perspective of
carriers (Özener,2014;Liotta et al.,2014;Zhang et al.,2022a). However, they do not study how carriers take shippers’ sustainability
preferences into account and Zhang et al. (2022a) do not even consider collaborative planning.
3. Problem description
We consider a problem in which multiple intermodal transport carriers are willing to achieve increased sustainability through
collaboration. Eco-labels are used to evaluate the relative environmental impact of transporting a shipper’s order from its origin to
its destination. We measure this impact by subsuming relevant greenhouse gases, such as carbon dioxide (CO2), methane (CH4) or
nitrous oxide (N2O), resulting from transportation under the term ‘emissions’ and evaluate their impact on global warming relative
to CO2, the most important greenhouse gas (United States Environmental Protection Agency,2022). With this, we use the single
measure CO2e to state the amount of CO2-equivalents resulting from transportation, and use those emissions (kgCO2e) per container
and per kilometer (km) as a sustainability measure and refer to it as emission rate (kgCO2e/(TEU km)). Thereby, we assume that each
container corresponds to one twenty-foot equivalent unit (TEU) of 13 tons. The eco-labeling scheme is derived from a large-scale
simulation study in Europe’s intermodal rail/road network (Heinold and Meisel,2018) and consists of three classes A, B, and C with
emission rate limits as shown in Fig. 2.
Fig. 3 shows a conceptional sketch of the considered problem. In this figure, there are two requests in the request pool and three
carriers. Each carrier needs to solve an Intermodal Transport Planning Problem with Sustainability Preferences (ITPP-SP) to match
its offered services with the placed requests. In these services, combinations of modes and routes can be used to serve requests while
distinct combinations result in distinct emissions. If the carrier cannot match the services with the preferred eco-label of request 𝑟,
𝑟will be shared with other carriers. In this case, the Collaborative Planning Problem in Intermodal Transport with Sustainability
Preferences needs to be solved to find a suitable carrier.
The notations used for modeling the ITPP-SP are provided in Table 2. Each carrier 𝑐∈𝐶owns a set of heterogeneous vehicles
𝐾𝑐of capacity 𝑢𝑘and speed 𝑣𝑘, and receives a set of requests 𝑅𝑐with preferred eco-labels from shippers. The pickup and delivery
terminals of request 𝑟∈𝑅𝑐are designated by 𝑝(𝑟)and 𝑑(𝑟). Request 𝑟∈𝑅𝑐must be picked up in time window [𝑎𝑝(𝑟), 𝑏𝑝(𝑟)]and needs
to be delivered in time window [𝑎𝑑(𝑟), 𝑏𝑑(𝑟)], but the delivery time can exceed 𝑏𝑑(𝑟)with a delay penalty. Further, we use 𝑒𝑙𝑟(A, B,
or C) to express the eco-label of request 𝑟, where emission rates per eco-label level 𝑒𝑙𝑟can be found in Fig. 2.
The transport network of a carrier 𝑐∈𝐶is defined as a directed graph 𝐺= (𝑁𝑐, 𝐴𝑐).𝑁𝑐=𝑃𝑐∪𝐷𝑐∪𝑂𝑐∪𝑇𝑐represents the set
of all vertices, where 𝑃𝑐, 𝐷𝑐, 𝑂𝑐, and 𝑇𝑐are pickup terminals, delivery terminals, depots of vehicles, and transshipment terminals,
respectively. 𝐴𝑐⊆(𝑖, 𝑗)|𝑖, 𝑗 ∈𝑁𝑐, 𝑖 ≠𝑗represents the set of arcs. The transport networks of different carriers may overlap with each
other. The nonnegative travel time 𝜏𝑘
𝑖𝑗 equals distance between 𝑖and 𝑗divided by speed of vehicle 𝑘. Note that distances are different
for different modes because they use different infrastructure between 𝑖and 𝑗. A vehicle 𝑘is allowed to wait at terminal 𝑖and a
request 𝑟is allowed to be stored temporarily at terminal 𝑖.
To provide more sustainable transport and better services, carriers collaborate by exchanging requests, i.e., horizontal collabo-
ration. Carriers only share requests when they cannot match requirements by themselves because they want to satisfy shippers and
gain additional profits. The shared requests can be served by any other carrier as long as the required eco-label is respected.
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Y. Zhang et al.
Fig. 3. Conceptional sketch of the considered problem.
4. Modeling and solution approach
This section presents the modeling and heuristic algorithm to solve the ITPP-SP together with a framework for the collaborative
planning approach. Firstly, we introduce how emissions are calculated and how to handle vague sustainability preferences by fuzzy
logic theory in Section 4.1. Then, the mathematical model for the ITPP-SP of an individual carrier is presented in Section 4.2 and
an ALNS heuristic is illustrated in Section 4.3. Finally, the collaborative planning framework is described in Section 4.4.
4.1. Emissions calculation and vague preferences
To analyze whether or not a request is shipped in accordance to its eco-label we have to measure the emissions that are emitted
while shipping the request from its origin to destination. For this, two kind of transport-related emissions need to be considered
for a request 𝑟: first, emissions from the vehicles that are transporting requests on the arcs (𝑒arcs
𝑟), and, second, emissions from
transshipment operations at the nodes that are required in an intermodal transport setting (𝑒nodes
𝑟).
Regarding emissions from the vehicles, several emission estimation models have been proposed in the literature. We refer
to Demir et al. (2011) and Heinold (2020) for studies comparing models for trucks and trains, respectively. Generally, the models
differ in the level of detail of the required input data, with microscopic models requiring granular data inputs (e.g., speed profiles)
and macroscopic models requiring only a few rough data inputs (e.g., average speed). For our purpose, we use a macroscopic
methodology proposed by the EcoTransIT World Initiative (2020), the so-called ETW model. The model provides calculation
procedures for all of our considered transport modes: trucks, trains, and barges. The model is further in accordance with the
European norm EN 16258 (European Committee for Standardization,2012) on the calculation of freight transport related greenhouse
gas emissions. Generally, the ETW method uses empirically-based functions that take the vehicle’s load 𝑞𝑘
𝑖𝑗 (in TEU) and traveled
distance 𝑑𝑘
𝑖𝑗 (in km) between terminals 𝑖and 𝑗as the main input to estimate emissions. Thereby, various sources are used to come up
with realistic functions like the average annual energy consumption of rail freight transport companies or surveys among transport
companies. With this, the model considers emissions from the driving of vehicles as well as from the idling of vehicles (e.g., Rahman
et al.,2013). In our problem, we consider emissions that relate to a regular 40-ton truck (Euro VI norm), a typical diesel train with
‘‘sgis’’ cars, and a standard European barge. We refer to EcoTransIT World Initiative (2020) for details on the model’s methodology
and data of the parameters that are used for these vehicle types. Further emission estimation model parameters are set as follows:
the empty trip factor is set to 0.2, the slope profile is set to 1, and the well-to-wheel emission factor is set to 3.90 (kgCO2e/kg)
for regular diesel and to 3.92 (kgCO2e/kg) for marine diesel (see European Committee for Standardization (2012)). With this, the
condensed formulas to calculate emissions 𝑒𝑘𝑖𝑗
𝑤(in kgCO2e) of vehicle 𝑘traveling between terminals 𝑖and 𝑗in one of the three
modes 𝑤∈ {truck, train, barge}are shown in Eqs. (1) to (3), respectively.
𝑒𝑘𝑖𝑗
𝑡𝑟𝑢𝑐𝑘 = 0.7233 ⋅𝑑𝑘
𝑖𝑗 + 0.1872 ⋅𝑑𝑘
𝑖𝑗
⋅𝑞𝑘
𝑖𝑗 (1)
𝑒𝑘𝑖𝑗
𝑡𝑟𝑎𝑖𝑛 = 22.6278 ⋅𝑑𝑘
𝑖𝑗
⋅𝑞𝑘
𝑖𝑗
⋅(123 + 13 ⋅𝑞𝑘
𝑖𝑗 + 23 ⋅⌈𝑞𝑘
𝑖𝑗
⋅13∕40⌉)−0.62 (2)
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Y. Zhang et al.
Table 2
Notations used in the paper.
Sets and indices:
𝐶Set of carriers indexed by 𝑐.
𝑊𝑐Set of modes owned by carrier 𝑐indexed by 𝑤.
𝑅𝑐Set of requests of carrier 𝑐indexed by 𝑟.
𝑁𝑐Set of terminals in carrier 𝑐’s transport network indexed by 𝑖and 𝑗.𝑃𝑐∕𝐷𝑐∕𝑇𝑐⊆ 𝑁𝑐, set of pickup/delivery/transshipment terminals.
𝑂𝑐∕𝑂𝑐⊆ 𝑁𝑐, set of depots/virtual depots.
𝐴𝑐Set of arcs in carrier 𝑐’s transport network. For 𝑖, 𝑗 ∈𝑁𝑐, the arc from 𝑖to 𝑗is denoted by (𝑖,𝑗 ) ∈ 𝐴𝑐.𝐴𝑐
𝑝∕𝐴𝑐
𝑑⊆ 𝐴𝑐represents the set of
pickup/delivery arcs. For (𝑖, 𝑗) ∈ 𝐴𝑐
𝑝,𝑖∈𝑃𝑐. For (𝑖, 𝑗) ∈ 𝐴𝑐
𝑑,𝑗∈𝐷𝑐.𝐴𝑐
𝑤⊆ 𝐴𝑐represents the set of arcs belonging to a specific mode 𝑤.
𝐴𝑘
fix ⊆ 𝐴𝑐represents the set of arcs for a fixed-route vehicle 𝑘∈𝐾𝑐
fix .
𝐾𝑐Set of vehicles owned by carrier 𝑐indexed by 𝑘and 𝑙.𝐾𝑐
b&t ⊆ 𝐾𝑐, set of barges and trains. 𝐾𝑐
truck ⊆ 𝐾 𝑐, set of trucks. 𝐾𝑐
𝑤⊆ 𝐾𝑐, set of
vehicles belonging to a specific mode 𝑤.𝐾𝑐
fix ⊆ 𝐾 𝑐, set of fixed-route vehicles. 𝐾𝑐
𝑟⊆ 𝐾𝑐, set of vehicles that can serve request 𝑟.
Parameters:
𝑢𝑘Capacity (TEU) of vehicle 𝑘.
𝑞𝑟Payload quantity (TEU) of request 𝑟.
𝜏𝑘
𝑖𝑗 The travel time (in hours) on arc (𝑖, 𝑗)for vehicle 𝑘.
[𝑎𝑝(𝑟), 𝑏𝑝(𝑟)]The pickup time window for request 𝑟.
[𝑎𝑑(𝑟), 𝑏𝑑(𝑟)]The delivery time window for request 𝑟.
𝑒𝑙𝑟The requested eco-label of request 𝑟.
[𝑎𝑘
𝑖, 𝑏𝑘
𝑖]The opening time window for fixed vehicle 𝑘at terminal 𝑖.
𝑡′′𝑘
𝑖The loading/unloading time (in hours) for vehicle 𝑘at terminal 𝑖.
𝑣𝑘Speed (km/h) of vehicle 𝑘.
𝑑𝑘
𝑖𝑗 Distance (km) between terminals 𝑖and 𝑗by vehicle 𝑘.
𝑒𝑘𝑙 The CO2e emissions (kg/TEU) of vehicle 𝑘during the transshipment between vehicles 𝑘and 𝑙.
𝑐𝑛
𝑘𝑐1
𝑘/𝑐1′
𝑘is unit cost (euro per TEU) of transportation per hour/km using vehicle 𝑘∈𝐾𝑐.𝑐2
𝑘is the loading/unloading cost per container. 𝑐3
𝑘
is the storage cost per container per hour. 𝑐4
𝑘is the carbon tax coefficient per ton. 𝑐5
𝑘is the cost per hour of waiting time.
𝑐delay
𝑟The delay penalty per container per hour of request 𝑟.
𝑆Satisfaction benchmark.
𝑀A large enough positive number.
Variables:
𝑥𝑘
𝑖𝑗 Binary variable; 1 if vehicle 𝑘uses arc (𝑖, 𝑗), 0 otherwise.
𝑦𝑘𝑟
𝑖𝑗 Binary variable; 1 if request 𝑟transported by vehicle 𝑘uses arc (𝑖, 𝑗), 0 otherwise.
𝑧𝑘
𝑖𝑗 Binary variable; 1 if terminal 𝑖precedes (not necessarily immediately) terminal 𝑗in the route of vehicle 𝑘, 0 otherwise.
𝑠𝑘𝑙
𝑖𝑟 Binary variable; 1 if request 𝑟is transferred from vehicle 𝑘to vehicle 𝑙≠𝑘at terminal 𝑖, 0 otherwise.
𝑡𝑘𝑟
𝑖∕𝑡′𝑘𝑟
𝑖∕𝑡𝑘𝑟
𝑖The arrival time/service start time/service finish time of request 𝑟served by vehicle 𝑘at terminal 𝑖.
𝑡𝑘
𝑖∕𝑡′𝑘
𝑖∕𝑡𝑘
𝑖The arrival time/last service start time/departure time of vehicle 𝑘at terminal 𝑖.
𝑡wait
𝑘𝑖 The waiting time of vehicle 𝑘at terminal 𝑖.
𝑡delay
𝑟The delay time of request 𝑟at delivery terminal.
𝑞𝑘
𝑖𝑗 The load of vehicle 𝑘between terminals 𝑖and 𝑗.
𝑒𝑘𝑖𝑗
𝑟The CO2e emissions (kg) of request 𝑟transported by vehicle 𝑘between terminals 𝑖and 𝑗.
𝑒𝑘
𝑟The CO2e emissions (kg) of request 𝑟transported by vehicle 𝑘.
𝑒𝑘𝑙
𝑟The CO2e emissions (kg) of request 𝑟during the transshipment between vehicles 𝑘and 𝑙.
𝑒′𝑟The unit CO2e emissions (kg) of request 𝑟per TEU per km.
𝑆𝑟Satisfaction value of request 𝑟.
𝑒𝑘𝑖𝑗
𝑏𝑎𝑟𝑔𝑒 = 35.9525 ⋅𝑑𝑘
𝑖𝑗 + 0.0819 ⋅𝑑𝑘
𝑖𝑗
⋅𝑞𝑘
𝑖𝑗 (3)
These emissions are then allocated among the requests based on each request’s contribution to a service’s overall load between
terminals 𝑖and 𝑗:
𝑒𝑘𝑖𝑗
𝑟=𝑒𝑘𝑖𝑗
𝑤⋅𝑞𝑟∕𝑞𝑘
𝑖𝑗 (4)
The emissions of request 𝑟using vehicle 𝑘is the sum of emissions of all trips served by 𝑘:
𝑒𝑘
𝑟=∑
(𝑖,𝑗)∈𝐴𝑐
𝑦𝑘𝑟
𝑖𝑗 𝑒𝑘𝑖𝑗
𝑟(5)
The total emissions on arcs of request 𝑟is:
𝑒arcs
𝑟=∑
𝑘∈𝐾𝑐
𝑟
𝑒𝑘
𝑟(6)
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Y. Zhang et al.
Regarding emissions from transshipment processes at ports (i.e., transshipments involving barge 𝑙), the values of 𝑒𝑘𝑙 are 6.3,
19.6, and 11.2 kgCO2e/TEU when vehicle 𝑘is a truck, a train, and a barge, respectively, as reported in an analysis of two container
terminals in the Port of Rotterdam (Geerlings and van Duin,2011). For all other transshipment operations (e.g., from truck to
train and vice versa), we assume the value of 𝑒𝑘𝑙 is 2.6 kgCO2e/TEU. This value is based on the energy consumption of such
processes as reported for the European intermodal rail/road network by Kim and van Wee (2009). The emissions of request 𝑟
during transshipment between vehicles 𝑘and 𝑙can be obtained by the following equation:
𝑒𝑘𝑙
𝑟=𝑞𝑟(𝑒𝑘𝑙 +𝑒𝑙𝑘)(7)
The total emissions at nodes of request 𝑟are:
𝑒nodes
𝑟=∑
𝑘,𝑙∈𝐾𝑐,𝑘≠𝑙
∑
𝑖∈𝑇𝑐
𝑠𝑘𝑙
𝑖𝑟 𝑒𝑘𝑙
𝑟(8)
The total emissions of request 𝑟are:
𝑒𝑟=𝑒arcs
𝑟+𝑒nodes
𝑟(9)
The unit emissions of request 𝑟are:
𝑒′𝑟=𝑒𝑟∕(𝑞𝑟∑
𝑘∈𝐾
∑
(𝑖,𝑗)∈𝐴
𝑑𝑘
𝑖𝑗 𝑦𝑘𝑟
𝑖𝑗 )(10)
Shippers’ sustainability preferences are usually vague, such as ‘‘around eco-label B is fine’’ or ‘‘eco-label C is enough’’, i.e., a
shipper’s satisfaction is still relatively high when the emission value does not perfectly match the required eco-label but is very close
to it. Therefore, simple rules like only accepting services with lower emissions than the eco-label are not necessarily appropriate
for the evaluation of shippers’ satisfaction. Instead, we use the fuzzy set theory to capture such vague preferences. Fuzzy set theory
is a methodology that does not express the ‘‘truthiness’’ in a discrete manner as either true or false but instead also allows for
partially true or partially false. Accordingly, whether an emission value belongs to a particular eco-label or not is also expressed as
(partially) true or false in our study. For this, emissions can be represented by a fuzzy variable, which has a predefined value range
and eco-labels are used to describe it. The value in the value range is called crisp value, which is how we think of the variable using
normal mathematics, e.g., 0.4 kgCO2e/(TEU km). Each eco-label has a membership function that defines the degree of truth of a
crisp value that belongs to the eco-label on a scale of 0 to 1. For example, 0.4 kgCO2e/(TEU km)’s membership to eco-label A and
eco-label B could be 0.8 and 0.2, respectively.
Based on request 𝑟’s actually caused unit emissions 𝑒′𝑟and the emission boundary 𝑒𝑙𝑟of the requested eco-label, the satisfaction
value 𝑆𝑟will be obtained by fuzzy set theory:
𝑆𝑟=𝐹 𝑢𝑧𝑧𝑦(𝑒′𝑟, 𝑒𝑙𝑟)(11)
where 𝐹 𝑢𝑧𝑧𝑦() represents the fuzzy set theory approach used in this study as is described next.
The membership function of emissions 𝑒′𝑟and satisfaction 𝑆𝑟are shown in Fig. 4. The trapezoidal and triangle fuzzy numbers
are used in the membership function, where the triangular membership function is a special trapezoidal membership function. The
trapezoidal membership function is given in Eq. (12) for the trapezoidal fuzzy number of 𝑒′𝑟involving scalar parameters 𝑎, 𝑏, 𝑐, 𝑑 ,
whereby 𝑎≤𝑏≤𝑐≤𝑑and 𝑏=𝑐for the triangular membership function. For the fuzzy number of 𝑆𝑟, we use the same type of
function.
𝜇(𝑒′𝑟) =
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
0, 𝑒′𝑟< 𝑎
(𝑒′𝑟−𝑎)
(𝑏−𝑎), 𝑎 ≤𝑒′𝑟≤𝑏
1, 𝑏 ≤𝑒′𝑟≤𝑐
(𝑑−𝑒′𝑟)
(𝑑−𝑐), 𝑐 ≤𝑒′𝑟≤𝑑
0, 𝑒′𝑟> 𝑑
(12)
Fuzzy variables for the emissions and satisfaction can be linked using a set of rules, which are IF-THEN statements that describe
how one variable relates to another. The used fuzzy rules are as follows:
1. When the shipper prefers eco-label A, IF the obtained eco-label equals/is worse than A, THEN the satisfaction will be high/low.
2. When the shipper prefers eco-label B, IF the obtained eco-label is better than/equals/is worse than B, THEN the satisfaction will
be high/medium/low.
3. When the shipper prefers eco-label C, IF the obtained eco-label is better than/equals C, THEN the satisfaction will be
high/medium.
After defining fuzzy variables and fuzzy rules, the satisfaction value 𝑆𝑟can be obtained using a defuzzification method, such as
Center of Gravity used in van Leekwijck and Kerre (1999). The same emissions may lead to different satisfaction because preferred
eco-labels are different for different shippers. For example, if shipper 1 prefers eco-label B and shipper 2 prefers eco-label C, shipper
2 will be more satisfied than shipper 1 when the actual eco-label is B.
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Y. Zhang et al.
Fig. 4. Membership functions for emissions and satisfaction.
4.2. Mathematical model for ITPP-SP
This section presents the mathematical model for one carrier 𝑐. In this model, we try to ensure shippers’ satisfaction while
minimizing the carrier’s costs. There are two levels of objectives. The upper-level objective (𝐹1) is to maximize the number of served
requests of the considered carrier 𝑐. The lower-level objective (𝐹2) is minimizing the carrier’s cost, which consists of transport cost,
transfer cost, storage cost, carbon tax, waiting cost, and delay penalty. For the lower-level objective (𝐹2), we refer to Guo et al.
(2020). In practice, it is important to serve as many requests as possible for long-term trust. Shippers will not opt for a less costly
service when it is not reliable. Therefore, the model will choose the solution with the highest objective value of 𝐹1. If several
solutions have the same optimal value for 𝐹1, the solution with a lower objective value of 𝐹2among these is selected. There are also
other ways to model the objective function, e.g., the objective (13) can be weighted by a penalty and added to objective function
(14). The results of this alternative approach are compared in Section 5.3.
The binary variables 𝑥𝑘
𝑖𝑗 and 𝑦𝑘𝑟
𝑖𝑗 decide whether vehicle 𝑘uses arc (𝑖, 𝑗)or not and whether vehicle 𝑘carries request 𝑟on arc
(𝑖, 𝑗)or not, respectively. The binary variable 𝑧𝑘
𝑖𝑗 is used for subtour elimination. We also have the binary variable 𝑠𝑘𝑙
𝑖𝑟 , which decides
whether request 𝑟is transferred from vehicle 𝑘to vehicle 𝑙at terminal 𝑖or not. Other variables related to time, emissions, load, and
satisfaction are shown in Table 2. For barge and train services, constraints for both vehicle flow (constraints related to variables
𝑥𝑘
𝑖𝑗 ) and request flow (constraints related to variables 𝑦𝑘𝑟
𝑖𝑗 ) are considered. Some constraints for vehicle flows do not apply to truck
services, because truck services in this study are truck fleets and trucks in a truck fleet may serve different requests with different
schedules.
Objective:
max 𝐹1=∑
𝑟∈𝑅𝑐
∑
𝑘∈𝐾𝑐
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑝(𝑟)𝑗(13)
min 𝐹2=∑
𝑘∈𝐾𝑐
∑
(𝑖,𝑗)∈𝐴𝑐
∑
𝑟∈𝑅𝑐
(𝑐1
𝑘𝜏𝑘
𝑖𝑗 +𝑐1′
𝑘𝑑𝑘
𝑖𝑗 )𝑞𝑟𝑦𝑘𝑟
𝑖𝑗 +∑
𝑘,𝑙∈𝐾𝑐,𝑘≠𝑙
∑
𝑟∈𝑅𝑐
∑
𝑖∈𝑇𝑐
(𝑐2
𝑘+𝑐2
𝑙)𝑞𝑟𝑠𝑘𝑙
𝑖𝑟
+∑
𝑘∈𝐾𝑐
∑
(𝑖,𝑗)∈𝐴𝑐
𝑝
∑
𝑟∈𝑅𝑐
𝑐2
𝑘𝑞𝑟𝑦𝑘𝑟
𝑖𝑗 +∑
𝑘∈𝐾𝑐
∑
(𝑖,𝑗)∈𝐴𝑐
𝑑
∑
𝑟∈𝑅𝑐
𝑐2
𝑘𝑞𝑟𝑦𝑘𝑟
𝑖𝑗 +∑
𝑘,𝑙∈𝐾𝑐,𝑘≠𝑙
∑
𝑟∈𝑅𝑐
∑
𝑖∈𝑇𝑐
𝑐3
𝑘𝑞𝑟𝑠𝑘𝑙
𝑖𝑟 (𝑡′𝑙𝑟
𝑖−𝑡𝑘𝑟
𝑖)
+∑
𝑘∈𝐾𝑐
∑
(𝑖,𝑗)∈𝐴𝑐
𝑝
∑
𝑟∈𝑅𝑐
𝑐3
𝑘𝑞𝑟𝑦𝑘𝑟
𝑖𝑗 (𝑡′𝑘𝑟
𝑖−𝑎𝑝(𝑟)) + ∑
𝑘∈𝐾𝑐
∑
𝑟∈𝑅𝑐
𝑐4
𝑘𝑒𝑘
𝑟
+∑
𝑘,𝑙∈𝐾𝑐,𝑘≠𝑙
∑
𝑟∈𝑅𝑐
∑
𝑖∈𝑇𝑐
𝑞𝑟𝑠𝑘𝑙
𝑖𝑟 (𝑐4
𝑘𝑒𝑘𝑙 +𝑐4
𝑙𝑒𝑙𝑘) + ∑
𝑘∈𝐾𝑐
b&t
∑
𝑖∈𝑁𝑐
𝑐5
𝑘𝑡wait
𝑘𝑖 +∑
𝑟∈𝑅𝑐
𝑐delay
𝑟𝑞𝑟𝑡delay
𝑟
(14)
Constraints (15)–(33) are the routing constraints. Constraints (15) and (16) ensure that a vehicle begins and ends at its
starting/ending depot, respectively. Some depots may be the same terminals as pickup/delivery terminals, which makes some
constraints of pickup/delivery terminals, such as time window constraints, also work on these depots when the related vehicle
does not serve the request. For this purpose, virtual depots 𝑜(𝑘)∕𝑜′(𝑘) ∈ 𝑂𝑐are introduced as additional nodes that have the same
location of starting/ending depot 𝑜(𝑘)∕𝑜′(𝑘) ∈ 𝑂𝑐but a distinct naming. Constraints (17) and (18) ensure that each request must be
picked and delivered at its pickup and delivery terminal, respectively.
∑
𝑗∈𝑁𝑐
𝑥𝑘
𝑜(𝑘)𝑗⩽1 ∀𝑘∈𝐾𝑐
b&t (15)
∑
𝑗∈𝑁𝑐
𝑥𝑘
𝑜(𝑘)𝑗=∑
𝑗∈𝑁𝑐
𝑥𝑘
𝑗𝑜′(𝑘)∀𝑘∈𝐾𝑐
b&t (16)
∑
𝑘∈𝐾𝑐
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑝(𝑟)𝑗⩽1 ∀𝑟∈𝑅𝑐(17)
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Y. Zhang et al.
∑
𝑘∈𝐾𝑐
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑗𝑑(𝑟)⩽1 ∀𝑟∈𝑅𝑐(18)
Constraints (19) represent flow conservation for vehicle flow and (20)–(23) represent flow conservation for request flow.
Constraints (20) are for regular terminals and Constraints (21) are for transshipment terminals. Constraints (22) and (23) ensure the
flow conservation of requests when request 𝑟is not transferred at terminal 𝑖∈𝑇𝑐but vehicle 𝑘passes terminal 𝑖due to operations
for other requests. Constraints (24) link 𝑦𝑘𝑟
𝑖𝑗 and 𝑥𝑘
𝑖𝑗 variables in order to guarantee that for a request to be transported by a vehicle,
that vehicle needs to traverse the associated arc.
∑
𝑗∈𝑁𝑐
𝑥𝑘
𝑖𝑗 −∑
𝑗∈𝑁𝑐
𝑥𝑘
𝑗𝑖 = 0 ∀𝑘∈𝐾𝑐
b&t,∀𝑖∈𝑁𝑐⧵𝑜(𝑘), 𝑜′(𝑘)(19)
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑖𝑗 −∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑗𝑖 = 0 ∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐,∀𝑖∈𝑁𝑐⧵𝑇𝑐, 𝑝(𝑟), 𝑑 (𝑟)(20)
∑
𝑘∈𝐾𝑐
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑖𝑗 −∑
𝑘∈𝐾𝑐
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑗𝑖 = 0 ∀𝑟∈𝑅𝑐,∀𝑖∈𝑇𝑐⧵𝑝(𝑟), 𝑑 (𝑟)(21)
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑖𝑗 −∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑗𝑖 ⩽∑
𝑙∈𝐾𝑐
𝑠𝑙𝑘
𝑖𝑟 ∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐,∀𝑖∈𝑇𝑐⧵𝑝(𝑟), 𝑑(𝑟)(22)
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑗𝑖 −∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑖𝑗 ⩽∑
𝑙∈𝐾𝑐
𝑠𝑘𝑙
𝑖𝑟 ∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐,∀𝑖∈𝑇𝑐⧵𝑝(𝑟), 𝑑(𝑟)(23)
𝑦𝑘𝑟
𝑖𝑗 ⩽𝑥𝑘
𝑖𝑗 ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐(24)
Constraints (25) and (26) facilitate transshipment. Constraints (25) ensure that the transshipment occurs only once per
transshipment terminal. Constraints (26) forbid transshipment between the same vehicle 𝑘.
∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑗𝑖 +∑
𝑗∈𝑁𝑐
𝑦𝑙𝑟
𝑖𝑗 ⩽𝑠𝑘𝑙
𝑖𝑟 + 1 ∀𝑟∈𝑅𝑐,∀𝑖∈𝑇𝑐,∀𝑘, 𝑙 ∈𝐾𝑐(25)
𝑠𝑘𝑘
𝑖𝑟 = 0 ∀𝑟∈𝑅𝑐,∀𝑖∈𝑇𝑐,∀𝑘∈𝐾𝑐(26)
Constraints (27)–(29) are the subtour elimination constraints (Öncan et al.,2009). Constraints (30) are the capacity constraints.
𝑥𝑘
𝑖𝑗 ⩽𝑧𝑘
𝑖𝑗 ∀𝑖, 𝑗 ∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t (27)
𝑧𝑘
𝑖𝑗 +𝑧𝑘
𝑗𝑖 = 1 ∀𝑖, 𝑗 ∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t (28)
𝑧𝑘
𝑖𝑗 +𝑧𝑘
𝑗𝑝 +𝑧𝑘
𝑝𝑖 ⩽2 ∀𝑖, 𝑗, 𝑝 ∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t (29)
∑
𝑟∈𝑅𝑐
𝑞𝑟𝑦𝑘𝑟
𝑖𝑗 ⩽𝑢𝑘𝑥𝑘
𝑖𝑗 ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐(30)
The characteristics of intermodal transport are considered in (31)–(33). Constraints (31) avoid vehicles running on unsuitable
routes, for example, trucks cannot run on inland waterways. Constraints (32) take care of predefined routes for certain vehicles,
for example, trains have fixed routes and terminals. Constraints (33) ensure the transshipment occurs in the right terminal because
some transshipment terminals (𝑇𝑤2
𝑤1) only allow the transshipment between two specific modes (𝑤1and 𝑤2).
𝑥𝑘
𝑖𝑗 = 0 ∀𝑘∈𝐾𝑐
𝑤,∀(𝑖, 𝑗) ∈ 𝐴𝑐⧵𝐴𝑐
𝑤,∀𝑤∈𝑊𝑐(31)
𝑥𝑘
𝑖𝑗 = 0 ∀𝑘∈𝐾𝑐
fix,∀(𝑖, 𝑗 ) ∈ 𝐴𝑐⧵𝐴𝑘
fix (32)
𝑠𝑘𝑙
𝑖𝑟 = 0 ∀𝑘∈𝐾𝑤1,∀𝑙∈𝐾𝑤2,∀𝑖∈𝑇𝑐⧵𝑇𝑤2
𝑤1,∀𝑟∈𝑅𝑐,∀𝑤1, 𝑤2∈𝑊𝑐(33)
Constraints (34)–(47) are temporal constraints. Constraints (34)–(38) are time constraints on services. Constraints (34) guarantee
that the service starts after the arrival of a request. Constraints (35) ensure that the service finishes after the service start time plus
the service time. Constraints (36) maintain that the departures of barges and trains happen only after all services are completed.
Constraints (37) ensure that the request’s arrival time cannot be earlier than the vehicle’s arrival time. Constraints (38) define the
vehicle’s last service start time.
𝑡𝑘𝑟
𝑖⩽𝑡′𝑘𝑟
𝑖∀𝑖∈𝑁𝑐,∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐(34)
𝑡′𝑘𝑟
𝑖+𝑡′′𝑘𝑟
𝑖∑
𝑗∈𝑁𝑐
𝑦𝑘𝑟
𝑖𝑗 ⩽𝑡𝑘𝑟
𝑖∀𝑖∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t,∀𝑟∈𝑅𝑐(35)
𝑡𝑘
𝑖⩾𝑡𝑘𝑟
𝑖∀𝑖∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t,∀𝑟∈𝑅𝑐(36)
𝑡𝑘
𝑖⩽𝑡𝑘𝑟
𝑖∀𝑖∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t,∀𝑟∈𝑅𝑐(37)
𝑡′𝑘
𝑖⩾𝑡′𝑘𝑟
𝑖∀𝑖∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t,∀𝑟∈𝑅𝑐(38)
Constraints (39) and (40) ensure that the time on route of barges and trains is consistent with the distance traveled and speed,
and Constraints (41) and (42) ensure the time on route of trucks. Constraints (43) and (44) take care of the time windows for pickup
terminals and fixed terminals, respectively.
𝑡𝑘
𝑖+𝜏𝑘
𝑖𝑗 −𝑡𝑘
𝑗⩽𝑀(1 − 𝑥𝑘
𝑖𝑗 ) ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐
b&t (39)
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𝑡𝑘
𝑖+𝜏𝑘
𝑖𝑗 −𝑡𝑘
𝑗⩾−𝑀(1 − 𝑥𝑘
𝑖𝑗 ) ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐
b&t (40)
𝑡𝑘𝑟
𝑖+𝜏𝑘
𝑖𝑗 −𝑡𝑘𝑟
𝑗⩽𝑀(1 − 𝑦𝑘𝑟
𝑖𝑗 ) ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐
truck (41)
𝑡𝑘𝑟
𝑖+𝜏𝑘
𝑖𝑗 −𝑡𝑘𝑟
𝑗⩾−𝑀(1 − 𝑦𝑘𝑟
𝑖𝑗 ) ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐
truck (42)
𝑡′𝑘𝑟
𝑝(𝑟)⩾𝑎𝑝(𝑟)𝑦𝑘𝑟
𝑖𝑗 , 𝑡𝑘𝑟
𝑝(𝑟)⩽𝑏𝑝(𝑟)+𝑀(1 − 𝑦𝑘𝑟
𝑖𝑗 ) ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑟∈𝑅𝑐,∀𝑘∈𝐾𝑐(43)
𝑡𝑘𝑟
𝑖⩾𝑎𝑘
𝑖𝑦𝑘𝑟
𝑖𝑗 ,𝑡𝑘𝑟
𝑖⩽𝑏𝑘
𝑖+𝑀(1 − 𝑦𝑘𝑟
𝑖𝑗 ) ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑟∈𝑅𝑐,∀𝑘∈𝐾𝑐
fix (44)
Constraints (45) are time constraints for transshipment. If there is a transshipment from vehicle 𝑘to vehicle 𝑙, but vehicle 𝑙arrives
before vehicle 𝑘departs, vehicle 𝑙can wait until vehicle 𝑘completes its unloading. Constraints (46) and (47) calculate waiting time
and delay time, respectively.
𝑡𝑘𝑟
𝑖−𝑡′𝑙𝑟
𝑖⩽𝑀(1 − 𝑠𝑘𝑙
𝑖𝑟 ) ∀𝑟∈𝑅𝑐,∀𝑖∈𝑇𝑐,∀𝑘, 𝑙 ∈𝐾𝑐, 𝑘 ≠𝑙(45)
𝑡wait
𝑘𝑖 ⩾𝑡′𝑘
𝑖−𝑡𝑘
𝑖∀𝑖∈𝑁𝑐,∀𝑘∈𝐾𝑐
b&t (46)
𝑡delay
𝑟⩾(𝑡𝑘𝑟
𝑑(𝑟)−𝑏𝑑(𝑟))∑
𝑖∈𝑁𝑐
𝑦𝑘𝑟
𝑖𝑑(𝑟)∀𝑟∈𝑅𝑐,∀𝑘∈𝐾𝑐(47)
Constraints (48) and (49) define the binary variables.
𝑥𝑘
𝑖𝑗 ∈ {0,1} ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐(48)
𝑦𝑘𝑟
𝑖𝑗 ∈ {0,1} ∀(𝑖, 𝑗) ∈ 𝐴𝑐,∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐(49)
Constraints (50) ensure that preferences are respected. 𝑆is a preset satisfaction benchmark. It is set as 50 in our experiments,
which means ‘‘medium satisfaction’’. Only when the satisfaction value 𝑆𝑟reaches satisfaction benchmark 𝑆, the solution for request
𝑟is considered acceptable.
𝑆𝑟⩾𝑆∀𝑟∈𝑅𝑐(50)
4.3. ALNS for ITPP-SP
ALNS is a powerful and well-suited algorithm for Vehicle Routing Problems and has been further developed since its introduction
by Ropke and Pisinger (2006). Using the insertion and removal operators iteratively, ALNS achieves the exploration and exploitation
in the search space and finds (near) optimal solutions. Different types of ALNS operators, such as greedy, random, and regret
operators, can be customized according to the characteristics of the problem. ALNS adapts to different problem instances because it
selects operators according to their historical performance during the search. ALNS has been applied to similar problems successfully,
such as the pickup and delivery problem with transshipment (Qu and Bard,2012;Masson et al.,2013) and synchromodal transport
planning problems (Zhang et al.,2022b,c). As verified in Zhang et al. (2022c), solving a similar problem to optimality using an
exact approach (Gurobi) is more computationally expensive than ALNS and the exact approach is unable to provide the optimal
solution for large instances due to the complexity. Zhang et al. (2022b) verify that ALNS produces high-quality solutions with low
computation time and performs well on large-scale instances in intermodal transport. Therefore, we use ALNS to solve the ITPP-SP
in this study. The pseudocode of the developed ALNS is shown in Appendix A. The operators and adaptive mechanism of ALNS are
illustrated in detail in the literature (Ropke and Pisinger,2006) and our previous papers (Zhang et al.,2022a,b). As these papers
did not involve eco-labels, we briefly sketch here how this feature is incorporated into the ALNS.
The emissions in this study are load-dependent, which means the load of barges/trains will influence the emissions allocated to
a transported request. Therefore, it is difficult for ALNS to ‘‘predict’’ which vehicle is more suitable to reduce the emissions because
the final load of the vehicle is not yet known while constructing a solution. For example, when ALNS inserts a new request to a route
of an empty barge, it will obtain a very high emission. But later in the solution process, this barge may serve many requests with a
high load factor, and the emissions allocated to a single request are then much lower. To alleviate the impact of the load-dependent
emissions, we expect large capacity vehicles will be utilized at the end and set the load factors of trains and barges as 60% during
each iteration of ALNS when computing emissions. By doing so, requests may be added to these large-capacity vehicles already
when these vehicles are quite empty. After each iteration, the preference Constraints (50) are then rechecked using the actual load,
and requests will be removed when Constraints (50) cannot be satisfied due to a too low load factor.
4.4. Collaborative planning approach
In the following, we consider three approaches of a (non-)collaboration of the carriers in set 𝐶, namely: (a) a centralized
approach, (b) an auction-based collaborative approach, and (c) a non-collaborative approach. Since carriers do not want to reveal
private information (such as costs) to their competitors, we assume there is a neutral coordinator in approaches (a) and (b). In reality,
the coordinator could be a collaborative planning platform in intermodal transport. In approach (a), the coordinator conducts the
routing and scheduling for carriers. In approach (b), carriers make decisions by themselves and the coordinator only plays a role in
connecting carriers and providing request and bid pools.
More precisely, in the approach (a), shippers send requests, including lanes (origin–destination pairs), time windows, amounts of
containers, and requested eco-labels, to carriers which then forward this information to the coordinator. Furthermore, carriers send
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Fig. 5. Collaboration approaches (a) and (b), which are centralized approach and auction-based collaborative approach, respectively.
their transport network information including terminals, vehicle fleets, and associated parameters to the coordinator, as shown in
Fig. 5(a). The coordinator solves a single holistic ITPP-SP and optimizes the overall intermodal network based on this information,
then assigns requests to carriers and reports costs to shippers either directly or via the carriers.
In approach (b), when a carrier has unserved requests, they will be exchanged with others via the coordinator as shown in
Fig. 5(b). This is done through an auction as is explained later in this section. In approach (c), carriers receive requests from
shippers and do not share them with others. Each carrier solves an ITPP-SP and optimizes schedules only using their own services,
and some requests might be rejected when their requirements cannot be met by the carrier who received these requests.
In approaches (a) and (c), solutions are obtained by the ALNS directly where approach (a) optimizes schedules based on requests
and resources of all carriers 𝐶, i.e., 𝑋𝐶
best,𝑅𝐶
pool =𝐴𝐿𝑁𝑆 (𝐾𝐶,𝑅𝐶,𝑁𝐶,𝐴𝐶,𝑋𝐶
best) and approach (c) optimizes the operations
individually for each carrier 𝑐∈𝐶. For approach (b), a request exchanging mechanism is needed and an auction-based approach is
adopted in this study because auctions can respect the preferences of participants by bidding (Li et al.,2015b;Gansterer and Hartl,
2018). For example, consider two carriers A and B that bid for requests in an auction pool. The bidding of carrier A is based on costs
and the bidding of carrier B is based on both costs and emissions. The auction will then reveal the carriers’ preferences as they only
place a bid if it is reasonable to add a request to the current routing with respect to their individual criteria. Specifically, we use a
sealed-bid first-price iterative auction, where bidders submit sealed bids and the bidder submitting the lowest cost wins the request
and charges this cost to the shipper. In an iterative auction, there are multiple rounds until a stopping criterion is reached and
bidders can adapt their bids during the iterative process. The flowchart of the iterative auction procedure in collaborative planning
is shown in Fig. 6.
In an auction round, there are three steps for each carrier 𝑐:
1. Obtain an initial solution: Based on the 𝐾𝑐,𝑁𝑐,𝐴𝑐, and the carrier’s own requests 𝑅𝑐, each carrier solves an ITPP-SP and the
routes are optimized by the ALNS. Then, the carrier sends unserved requests 𝑅𝑐
pool to the coordinator.
2. Try and bid: The carrier obtains requests 𝐶𝑃 𝑅𝐶⧵𝑐
pool shared by other carriers from the coordinator and sets 𝐶𝑃 𝑅𝐶⧵𝑐
pool as 𝑅𝑐
pool.
Then the carrier tries to insert these requests into its routes by Algorithm 1. If the carrier can serve requests 𝑅𝑐
try =𝐶𝑃 𝑅𝐶⧵𝑐
pool ⧵𝑅𝑐
pool
and finds a better solution than before, the carrier submits bids 𝐵𝑖𝑑𝑐to the coordinator with costs of these requests 𝑅𝑐
try.
3. Insert new requests: For those bids 𝐵𝑖𝑑𝑐
win ⊆ 𝐵𝑖𝑑𝑐that carrier 𝑐won through the auction, requests in 𝐵𝑖𝑑𝑐
win are set as 𝑅𝑐
pool
and the carrier inserts these requests into its routes by Algorithm 1. It is worth noting that maybe a request 𝑟that can be served in
Step 2 cannot be served in Step 3, because it can only be served in combination with some other requests in the failed bids. In this
case, 𝑟will be added to 𝑅𝑐
pool and considered in the next round of the auction. Finally, the carrier sends the information of served
new requests 𝑅new to the coordinator.
Algorithm 1: Re-planning with shared requests.
Input: 𝐾𝑐,𝑅𝑐
pool,𝑁𝑐,𝐴𝑐,𝑋𝑐
best;Output:𝑋𝑐
best;
Obtain served requests 𝑅𝑐
serve in 𝑋𝑐
best;
Combine 𝑅𝑐
pool and 𝑅𝑐
serve as a set of requests 𝑅𝑐;
𝑅𝑐
pool,𝑋𝑐
best =𝐴𝐿𝑁𝑆 (𝐾𝑐,𝑅𝑐,𝑁𝑐,𝐴𝑐,𝑋𝑐
best)
return 𝑅𝑐
pool,𝑋𝑐
best;
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Fig. 6. Flowchart of the iterative auction procedure in the collaborative planning. Dashed arrows represent exchange of information between carriers and the
coordinator.
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Fig. 7. Transport networks of EGS, Contargo, and HSL.
From the perspective of the coordinator, the procedure is as follows: The coordinator operates two pools, i.e., a collaborative
planning request pool (𝐶𝑃 𝑅pool ) and a bids pool (𝐵𝑖𝑑pool ). The coordinator adds or deletes requests in 𝐶𝑃 𝑅pool when receiving
related information from carriers. Before an auction starts, the coordinator sets these two pools as empty and then receives unserved
requests 𝑅𝑐
pool of each carrier 𝑐∈𝐶. Request 𝑟∈𝑅𝑐
pool will be added in 𝐶𝑃 𝑅pool if 𝑟∉𝐶 𝑃 𝑅pool. After receiving all carriers’ 𝑅𝑐
pool
and updating 𝐶𝑃 𝑅pool , the coordinator sends unserved requests of other carriers 𝐶 𝑃 𝑅𝐶⧵𝑐
pool to each carrier 𝑐and waits for bids. After
receiving bids from carriers, the coordinator groups bids according to requests and ranks them depending on the cost. Then, the
coordinator sends winning bids to carriers and waits for the final optimization of carriers. Finally, the served requests are removed
from 𝐶𝑃 𝑅pool and 𝐵 𝑖𝑑pool is set empty to prepare for the next round of the auction.
The auction will stop either when no carrier wants to exchange further requests or a predefined number of rounds is reached.
This mechanism aims to provide carriers enough chances to share requests.
5. Case study
A network with three carriers along the European Rhine-Alpine corridor is considered as a real-world case to test the proposed
model. The Rhine-Alpine corridor constitutes one of the busiest freight routes in Europe. Around 138 billion tonne-kilometers of
freight is transported along this corridor annually, accounting for 19% of total GDP of the EU. The three carriers are European
Gateway Services (EGS), Contargo, as well as Haeger & Schmidt Logistics (HSL) which are all intermodal transport carriers that
provide barge, train, and truck services from sea ports (Rotterdam and Antwerp) to inland terminals. Fig. 7 presents the transport
networks of these carriers. In this case study, EGS, Contargo, and HSL provide services among 10, 20, and 15 terminals/ports,
respectively. A total of 11 terminals are shared by two or three carriers (there are multiple terminals in the sea port). The
three carriers can share their requests in the overlapping transport network. Services’ information is obtained from schedules on
their websites (EGS,2021;Contargo,2021;HSL,2021), and EGS, Contargo, and HSL operate 49/33/34, 38/23/95, and 41/8/70
barge/train/truck services, respectively, according to this data. For the distances between terminals of different modes, we use the
same data sources as in Shobayo et al. (2021).
The origins and destinations of requests are distributed randomly among deep-sea terminals and inland terminals, respectively.
The container volumes of requests are drawn independently from a uniform distribution with range [10, 30] (unit: TEU). According
to services of EGS/Contargo/HSL, the earliest pickup time 𝑎𝑝(𝑟)of requests is drawn independently from a uniform distribution with
range [1, 120]/[1, 140]/[1, 140]; the latest delivery time 𝑏𝑑(𝑟)=𝑎𝑝(𝑟)+𝐿𝐷𝑟, where 𝐿𝐷𝑟is the lead time and it is independently and
identically distributed among 24, 48, 72 (unit: hours) with probabilities 0.15, 0.6, 0.25. Moreover, to define pickup and delivery
time windows, we set 𝑏𝑝(𝑟)and 𝑎𝑑(𝑟)equal to 𝑏𝑑(𝑟)and 𝑎𝑝(𝑟), respectively. Parameters for vehicles are taken from the literature and
shown in Table 3. In the objective function (13), the transport cost is a linear function of the travel time 𝜏𝑘
𝑖𝑗 and distance 𝑑𝑘
𝑖𝑗 . We
use different unit costs 𝑐1
𝑘and 𝑐1′
𝑘for 𝜏𝑘
𝑖𝑗 and 𝑑𝑘
𝑖𝑗 , which makes it possible to handle differences in the speed of vehicles. For trucks
and trains, as reported in Li et al. (2015a), we set 𝑐1
truck/𝑐1′
truck as 30.98 euros/(TEU h)/0.2758 euro/(TEU km) and 7.54 euros/(TEU
h)/0.0635 euro/(TEU km). According to the used type of barges and the database of an inland shipping community (Association of
the inland shipping,2010), the parameters of the Large Rhine Vessel (Va class) are used. Considering the labor, capital, maintenance,
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Table 3
Vehicle parameters used in the paper.
Parameter Value Parameter Value Parameter Value
𝑐1
truck 30.98 𝑐1
train 7.54 𝑐1
barge 0.6122
𝑐1′
truck 0.2758 𝑐1′
train 0.0635 𝑐1′
barge 0.0213
𝑐2
truck 3𝑐2
train 18 𝑐2
barge 18
𝑐3
𝑘1𝑐4
𝑘8𝑐5
𝑘1
Fig. 8. Transport network of EGS.
total sailing hours in a year, and occupancy rate, the time-related cost for barges 𝑐1
barge is set as 0.6122 euro/(TEU h). Based on
the fuel consumption, the distance related cost unit 𝑐1′
barge is set as 0.0213 euro/(TEU km). According to Sun and Lang (2015), the
loading/unloading costs 𝑐2
𝑘for trucks, trains, and barges are set as 3, 18, and 18 euros/(TEU h). The CO2e is converted into carbon
tax using a price 𝑐4
𝑘of 8 euros per ton, based on the price of the EU emission allowance (Riessen et al.,2015). As reported in Guo
et al. (2020) and Zhang et al. (2022b), the vehicle can wait for containers with a waiting fee, and containers can be stored in the
terminal with a storage fee. We use the same storage and waiting unit costs 𝑐3
𝑘and 𝑐5
𝑘of 1 euro/(TEU h).
We generate six instances for each carrier with 5, 10, 20, 30, 50, and 100 requests, respectively. Each instance contains three
sub-instances with homogeneous preferences, i.e., all shippers prefer the same eco-label (A, B, or C), and one sub-instance with
heterogeneous preferences (labeled as H), i.e., shippers have different preferred eco-labels. Under heterogeneous preferences, the
eco-label for each request is obtained randomly from a uniform distribution over eco-labels A, B, and C.
We consider two scenarios of collaborative planning. Scenario 1 is the collaboration among unimodal transport carriers and
each carrier operates one of three modes (inland waterway, railway, and road). Scenario 2 is the collaboration among intermodal
transport carriers and each carrier offers services in all three modes. In scenario 1, services of unimodal transport carriers are based
on the transport network of EGS, as shown in Fig. 8 with varying total number of requests [5, 10, 20, 30, 50, 100] across instances.
In scenario 2, the intermodal transport carriers are EGS, Contargo, and HSL and the total number of requests are [15, 30, 60, 90,
150, 300]. To ensure the accuracy of experimental results, all experiments are repeated five times and the results are averaged. The
detailed results are presented in Appendix B.
5.1. Results analysis
Table 4 shows the average computation time of instances with different numbers of requests under centralized, collaborative,
and non-collaborative approaches with preferences (a, b, c) and without (a∗, b∗, c∗) preferences. The computation time in scenario
2 is shorter than the computation time in scenario 1, because scenario 2 has more requests, more vehicles, and a larger transport
network. Due to the communication time used in collaboration, approach (b)/(b∗) needs more computation time than approach
(a)/(a∗) in most cases. On some exceptionally large instances, such as the instance with 300 requests in scenario 2, approach
(b)/(b∗) uses less computation time than approach (a)/(a∗), because the collaborative approach (b)/(b∗) saves computation time
by parallel computation which compensates the communication time. The computation time with preferences is usually larger since
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Table 4
Computation time (s).
Approach Scenario 1 Scenario 2
5 10 20 30 50 100 15 30 60 90 150 300
a 2.3 13.6 52.4 135.5 434.8 3041.1 36.0 534.1 1824.8 3976.5 6145.3 34 646.2
a∗0.7 3.3 12.3 14.3 92.2 604.1 17.7 119.8 2299.0 4247.0 7065.0 22 697.7
b 284.4 399.7 906.6 1767.5 2467.2 7667.3 801.5 1192.3 3129.9 4467.0 12309.3 13282.7
b∗178.4 172.8 324.4 513.3 711.5 1544.7 182.4 184.6 276.6 495.3 603.3 2225.8
c 0.3 0.9 1.9 3.1 27.7 92.2 4.5 55.2 162.4 505.7 1897.0 5385.4
c∗0.2 0.6 1.4 1.7 31.9 68.2 3.4 3.4 23.4 364.9 1004.7 3188.4
Fig. 9. Emissions comparison across approaches and eco-labels.
it is harder to find feasible solutions when preferences are incorporated. In most cases, the computation time is less than 2 h even
on large instances.
Fig. 9 shows the resulting emissions across different approaches, scenarios and eco-label settings. Under eco-label A, no requests
are served in the instances with 5/15 requests because the sustainability requirement is high and load factors of sustainable vehicles
are still too low to reach the requirement. For the instances with more requests, the average unit emissions for eco-label A, B, C, and
H under scenario 1/2 are 0.29/0.24, 0.47/0.47, 0.92/0.84, 0.86/0.62 kgCO2e/(TEU km), respectively. The corresponding solutions
meet the requested eco-labels and it is observed that higher requirements on eco-labels indeed lead to lower average emissions. The
emissions under eco-label A are reduced around 70% compared with eco-label C. Under eco-label C, more requests lead to lower
emissions due to the high load factor of vehicles, but they still cannot reach the same level as of eco-labels B and A. Scenario 2 has
a better performance compared with scenario 1 under the same eco-label due to the additional services.
Fig. 10 shows a cost comparison across approaches and eco-labels. We compare solutions based on cost per TEU km rather
than total cost as the number of served requests may differ in the solutions, which means that their total cost cannot be compared
suitably with each other. In scenario 1, the average unit costs under eco-labels A, B, C, and H (heterogeneous preferences) are 0.85,
0.88, 0.93, and 0.74 euro/(TEU km), respectively. In scenario 2, these average unit costs are 0.95, 0.62, 0.51, and 0.69 euro/(TEU
km), respectively. From eco-labels A to C, the emissions restriction decreases, while costs under scenario 1 increase. Scenario 2
shows the opposite trend. The truck carrier will keep requests when sustainability requirements are low, and requests will only
be shared with train and barge unimodal carriers under high sustainability requirements. Therefore, for unimodal carriers under
scenario 1, higher eco-labels could decrease costs because more low-cost vehicles are used due to emissions constraints. However,
for intermodal carriers with all three modes, costs will be minimized and barges will be used as much as possible when they do
not consider sustainability preferences, therefore cost under eco-label C is the lowest. When sustainability requirements are high,
more requests will be served by trains, which is more expensive than barges, hence costs increase. In some cases, the cost under the
centralized approach is higher than the collaborative approach because the served requests are different under these two approaches,
and the transshipment and storage costs vary for different requests. In some other cases, the collaborative approach has higher costs
which happen more in scenario 1. The reason behind is that truck carriers in scenario 1 serve requests by themselves with a high
cost when the eco-label requirement is not high, such as the instance with 30 requests under eco-label B and instances with 20,
30, 50, and 100 requests under eco-label C. Therefore, unimodal carriers, especially truck carriers, need to share more requests in
collaborative planning to reduce the overall cost and achieve a similar performance as centralized planning.
Fig. 11 shows the share of transport modes under both scenarios. Under eco-label A, trains dominate, especially in scenario 1,
because using unimodal truck transport cannot reach the requirement of eco-label A and barges are sustainable only when the load
factor is high. Under eco-label B, trucks serve more requests than trains and the reason behind is different for scenarios 1 and 2.
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Fig. 10. Costs comparison across approaches and eco-labels.
Fig. 11. Mode share comparison across approaches and eco-labels. There are three bars (left, middle, and right) for each instance, which represents mode shares
under approaches (a), (b) and (c), respectively.
In scenario 1, emissions of trucks with full truckload reach the requirement of eco-label B, hence part of the requests are served by
trucks from which the load factors of trains become low. Then, trains are used less due to higher emissions than trucks. In scenario
2, trucks can not only transport containers by unimodal transport but also be combined with trains in intermodal transports to
reach a lower cost. Therefore, the share of trucks is also higher than trains in scenario 2 under eco-label B. Under eco-labels C
and H, more barges are used to serve requests because barges are sustainable and have a lower cost when the load factor is high.
Furthermore, Fig. 12 shows the proportions of served requests by carriers in scenario 2. Compared with HSL, EGS and Contargo
serve more requests under eco-label A, because they operate more trains than HSL. Under eco-labels B, C, and H, the proportions
are similar.
Fig. 13 shows proportions of served requests, requests that satisfy fuzzy constraints, and requests that satisfy hard constraints
under approaches with environmental preferences (a, b, c) and without preferences (a∗, b∗, c∗). For the results without preferences,
the eco-labels are ignored, i.e., Constraints (50) are not considered. The higher the sustainability requirement is, the less the
proportion of served requests is. Almost all requests can be served when sustainability preferences are not considered. The proportion
of requests that satisfy fuzzy or hard constraints is in most cases higher when considering preferences compared to the approaches
that ignore preferences. In some others, e.g., in scenario 2 under eco-label A, more requests satisfy fuzzy or hard constraints when
preferences are not considered because more requests are served and load factors of sustainable vehicles are high. However, this
relies on the sacrifice of requests that have high emissions. Using fuzzy constraints, the number of served requests is increased
by an average of 10% compared with using hard constraints since the fuzzy constraints give the model flexibility to find a more
suitable solution. For unimodal carriers (scenario 1), centralized and collaborative approaches increase the number of served requests
significantly compared with non-collaboration, because unimodal carriers need the services of others to satisfy emission preferences,
especially under high sustainability requirements. Compared with the non-collaborative approach, the proportion in the collaborative
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Fig. 12. Proportions of served requests by carriers in scenario 2. There are three bars (left, middle, and right) for each instance, which represents mode shares
under approaches (a), (b), and (c), respectively.
Fig. 13. Proportions of served requests, requests that satisfy fuzzy constraints, and requests that satisfy hard constraints.
approach is increased by an average of 65%, 53%, 33%, and 41% under eco-labels A, B, C, and H, respectively. For intermodal
carriers (scenario 2), such an increase is not significant under eco-labels B, C, and H, because carriers own enough services. However,
the increase is still significant under eco-label A (29%). In both scenarios, the proportions of served requests of centralized and
collaborative approaches are similar.
Fig. 14 shows satisfaction values 𝑆𝑟across approaches with and without respecting preferences, i.e. with and without Con-
straint (50) for the satisfaction benchmark. As expected, considering preferences in the planning improves the satisfaction
significantly, especially under eco-label A. However, under eco-label C, satisfaction is slightly better when preferences are ignored
since more requests can be served, which increases the load factors and in turn reduces the emissions. In Figs. 14(b) and (d), the
satisfaction under eco-label B is lower than under eco-label A because more trucks are used due to reasons mentioned in the analyses
of Fig. 11.
5.2. Sensitivity analysis and convergence of the ALNS
Due to the different infrastructure in terminals and types of vehicles, the costs may be different. Advances in technology may also
change the structure of the costs across different modes. Therefore, a sensitivity analysis is needed for the parameters presented in
Table 3 to evaluate the influence of potential changes on the benefit of our proposed approach. We varied the values of all parameters
in Table 3 under the instance with 20 requests (EGS carrier) and the consistency of the results under varying parameters are presented
in Appendix C. We also conduct sensitivity analysis comparing centralized, collaborative, and non-collaborative approaches to check
whether the obtained insights still hold when the parameter values vary. The costs per km may be different for vehicles with different
loads and types and the carbon tax may differ in different countries/regions, therefore distance cost 𝑐1′
barge and carbon tax 𝑐4
𝑘are
interesting parameters to conduct the sensitivity analysis. The worst case of 𝑐1′
barge relates to the possibility of having higher cost than
the truck distance cost with very low load on the barge. When it comes to 𝑐4
𝑘, according to Yan et al. (2021), carbon tax will increase
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Fig. 14. Satisfaction 𝑆𝑟comparison across approaches with and without preferences.
to 80 euros per ton by 2030 and this could be higher to reach net zero emissions by 2050. Considering the best- and worst-case
scenarios, we vary 𝑐1′
barge and 𝑐4
𝑘in [0, 0.32] and [0, 128], respectively. The results are displayed in Fig. 15 and as expected, when
𝑐1′
barge or 𝑐4
𝑘increases, the costs under all approaches rise. However, the cost gaps between different approaches stay similar due to
the nature of approaches. The centralized approach obtains the lowest cost and the collaborative approach has better cost than the
non-collaborative approach. The emission gaps of these approaches are similar in most cases, while they change in extreme cases,
e.g., the carbon tax is 128 euros per ton, where all approaches have to reduce emissions as much as possible to minimize the total
cost. The number of served requests does not change for all approaches. The centralized and collaborative approaches can serve all
requests, while one quarter of requests cannot be served in the non-collaborative approach. Therefore, the proposed model is robust
and the obtained insights still hold under reasonable changes in parameters.
We use instances with different numbers of requests to illustrate the convergence of the ALNS heuristic. Fig. 16 shows the costs
and emissions of the best solution over 200 iterations. The cost could increase when there are more served requests and the cost
is minimized when the number of served requests is stable. Fig. 16 shows that ALNS clearly converges before terminating it on all
instances. For small instances (R =5, 10, and 20), ALNS converges rapidly in early iterations. For large instances (R =30, 50, and
100), no better solutions are found in the final 90 iterations.
5.3. Results under different objectives and preferences
In practice, the transportation cost and time are important for shippers, and there are two methods to consider preferences on
cost and time, i.e., (a) incorporate them as part of the objective function together with the number of served requests, (b) consider
these preferences in a similar way as eco-labels.
In method (a), we minimize 𝐹3, which is the sum of the costs 𝐹2and the penalty for unserved requests:
min 𝐹3=𝐹2+∑
𝑟∈𝑅𝑐
(1 − 𝑔𝑟)𝜆𝑟𝐹𝑟
truck,(51)
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Fig. 15. Sensitivity analysis on distance cost 𝑐1′
barge and carbon tax 𝑐4
𝑘under different approaches.
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Fig. 16. Convergence of ALNS on instances with preferences.
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Table 5
Results under different preferences.
Objective N Cost Time Emissions Barge Train Truck S T
Low-cost transport (cost-label A)
𝐹1, 𝐹216 0.48 1.18 0.43 28.57 38.10 33.33 77 70
Fast transport (time-label A)
𝐹1, 𝐹228 0.83 0.53 0.78 0.00 21.62 78.38 80 126
Sustainable transport (eco-label A)
𝐹1, 𝐹218 0.52 1.33 0.44 20.00 44.00 36.00 78 85
N: number of served requests; Cost: average cost of shipping one TEU one km; Time: average time ratio; Emissions: average
emissions per TEU per km; Barge/Train/Truck: mode share of used barges/trains/trucks; S: average satisfaction value; T: Times
of using objective function 𝐹2in total 200 iterations.
where 𝑔𝑟is a binary variable indicating whether request 𝑟is served or not and 𝜆𝑟is a parameter that controls the size of the penalty
for each unserved request 𝑟. The variable 𝑔𝑟respects the following constraints:
𝑔𝑟⩾∑
(𝑖,𝑗)∈𝐴𝑐
𝑦𝑘𝑟
𝑖𝑗 ∀𝑘∈𝐾𝑐,∀𝑟∈𝑅𝑐,(52)
𝑔𝑟∈ {0,1} ∀𝑟∈𝑅𝑐.(53)
When a request cannot be served by available vehicles, spot-market trucks can usually be used. Therefore, the penalty is calculated
by 𝐹𝑟
truck, which is the cost of transporting request 𝑟using trucks:
𝐹𝑟
truck = (𝑐1
truck𝜏truck
𝑝(𝑟)𝑑(𝑟)+𝑐1′
truck𝑑truck
𝑝(𝑟)𝑑(𝑟))𝑞𝑟+ 2𝑐2
truck𝑞𝑟+𝑐4
truck𝑒truck
𝑟.(54)
Fig. 17 shows results for the instance with 30 requests. Similar insights are obtained from results of other instances, as shown in
Appendix D. The size of the penalty needs to be set according to the importance of requests. We vary it from 0 to 100 to evaluate
the performance of method (a) in different scenarios. In the extreme case of 𝜆𝑟= 0, serving requests is not important and the carrier
only cares about minimizing cost 𝐹2. The number of served requests is then significantly less than in other cases. Compared to using
objectives 𝐹1and 𝐹2hierarchically as proposed in this paper, minimizing 𝐹3could obtain solutions with lower unit cost or emissions
by not serving requests with high cost/emissions in some scenarios, such as results when 𝜆𝑟= 0.5,𝜆𝑟= 1, and 𝜆𝑟= 2 in Fig. 17(b).
Nevertheless, in order to reach those results, one needs to tune the penalty term thoroughly for each instance with different number
of requests, problem parameters, etc. When the penalty 𝜆𝑟is large, i.e., 𝜆𝑟= 5,𝜆𝑟= 10, and 𝜆𝑟= 100, the number of served requests
is the same as the proposed approach with similar costs and emissions. Except for the scenario in which 𝜆𝑟= 0, these two ways
of modeling the objective function have similar performance when eco-label preferences are ignored, because all requests can be
served and the objective is essentially translated into the minimization of costs (𝐹2).
For method (b), the proposed model can be extended easily to consider cost-label and time-label. For the cost-label, the unit cost
of shipping one TEU for request 𝑟is calculated by:
𝑐′𝑟=𝐹𝑟
2∕(𝑞𝑟∑
𝑘∈𝐾
∑
(𝑖,𝑗)∈𝐴
𝑑𝑘
𝑖𝑗 𝑦𝑘𝑟
𝑖𝑗 )(55)
where 𝐹𝑟
2is the overall cost of request 𝑟and the calculation of 𝐹𝑟
2is similar to objective (14).
For the time-label, we use the ratio of actual time to expected time to evaluate how fast the transportation is, calculated by:
𝑡′𝑟=𝑡𝑟∕(𝑑average
𝑝(𝑟)𝑑(𝑟)∕𝑣average),(56)
where 𝑑average
𝑝(𝑟)𝑑(𝑟)/𝑣average is the average travel distance/speed of all vehicles and 𝑡𝑟is the actual travel time:
𝑡𝑟=max{𝑡𝑘𝑟
𝑖𝑦𝑘𝑟
𝑖𝑗 ∶ ∀(𝑖, 𝑗) ∈ 𝐴, ∀𝑘∈𝐾} − min{𝑡′𝑘𝑟
𝑖𝑦𝑘𝑟
𝑖𝑗 ∶ ∀(𝑖, 𝑗) ∈ 𝐴, ∀𝑘∈𝐾}.(57)
The rates of cost-label/time-label A, B, and C are set as 0.6/0.8, 0.9/1.1, and 1.2/1.4, respectively. Then, we can adopt a similar
method as in Section 4.1 to obtain the satisfaction value 𝑆𝑟and set constraints for 𝑆𝑟to ensure that the solutions are in line with
cost or time preferences of shippers.
Table 5 shows the results under different preferences on the instance with 30 requests, where the related cost, time, or emission
of the obtained solution is reduced according to the required labels. For example, when shippers prefer low-cost transport, the cost
is the lowest and the mode shares of low-cost modes (barges and trains) are the largest compared with other solutions. Column T
shows the frequency of using objective function 𝐹2, and it is used on average in 47% iterations out of 200 iterations when both
objective functions 𝐹1and 𝐹2are considered. Therefore, 𝐹2plays an important role in the optimization and the model finds solutions
with the same number of served requests frequently.
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Fig. 17. Comparison of results with different objectives (R = 30).
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6. Conclusions
In this paper, we have proposed a collaborative planning model for carriers in intermodal transport. It opens up a way to route
more shipments in accordance to their requested eco-label and, ultimately, to achieve a more sustainable overall transport solution.
The eco-labels requested by shippers are considered in the optimization of carriers, and carriers exchange requests that cannot be
served by themselves. An auction mechanism is proposed for collaborative planning. Three approaches are compared using realistic
transport networks and schedules. The experimental results show that collaboration can lead to 48%/11% increases of proportions
of served requests for unimodal/intermodal carriers, and the highest/mixed eco-labels reduce 70%/15% emissions compared with
ignoring preferences. Based on the experimental results, the following managerial insights are obtained: (a) Considering eco-label
preferences reduces emissions significantly. (b) Compared with the scheme without eco-label preferences, considering eco-labels
reduces the emissions at the expense of decreasing the number of served requests. (c) For collaboration among unimodal carriers,
high eco-labels reduce more costs than schemes with low eco-labels or ignoring eco-labels because requests of the truck carrier
will be served by train and barge carriers, who can provide both low-emissions and low-cost services. For collaboration among
intermodal carriers, satisfying high eco-labels requires more trains, and ignoring eco-labels increases barge use. Therefore, higher
eco-labels cause more costs as using trains is more expensive than barges. (d) When minimizing the sum of costs and penalty of
unserved requests, high-cost/-emissions requests cannot be served with a low penalty. Whereas, the solutions