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Hinterland intermodal transportation is the movement of containers between deep-sea ports and inland terminals by using trucks, trains, barges, or any combination of them. Synchromodal transportation, as an extension of intermodal transportation, refers to transport systems with dynamic updating of plans by incorporating real-time information. The trend towards spot markets and digitalization in hinterland intermodal transportation gives rise to online synchromodal transportation problems. This paper investigates a dynamic shipment matching problem in which a centralized platform provides online matches between shipment requests and transport services. We propose a rolling horizon approach to handle newly arrived shipment requests and develop a heuristic algorithm to generate timely solutions at each decision epoch. The experiment results demonstrate the solution accuracy and computational efficiency of the heuristic algorithm in comparison to an exact algorithm. The proposed rolling horizon approach outperforms a greedy approach from practice in total costs under various scenarios of the system.
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A dynamic shipment matching problem in hinterland
synchromodal transportation
Wenjing Guo
, Bilge Atasoy, Wouter Beelaerts van Blokland, Rudy R.
Negenborn
Department of Maritime and Transport Technology, Delft University of Technology,
Mekelweg 2, 2628CD Delft, the Netherlands
Abstract
Hinterland intermodal transportation is the movement of containers between
deep-sea ports and inland terminals by using trucks, trains, barges, or any
combination of them. Synchromodal transportation, as an extension of inter-
modal transportation, refers to transport systems with dynamic updating of
plans by incorporating real-time information. The trend towards spot mar-
kets and digitalization in hinterland intermodal transportation gives rise to
online synchromodal transportation problems. This paper investigates a dy-
namic shipment matching problem in which a centralized platform provides
online matches between shipment requests and transport services. We pro-
pose a rolling horizon approach to handle newly arrived shipment requests
and develop a heuristic algorithm to generate timely solutions at each deci-
sion epoch. The experiment results demonstrate the solution accuracy and
computational efficiency of the heuristic algorithm in comparison to an ex-
act algorithm. The proposed rolling horizon approach outperforms a greedy
approach from practice in total costs under various scenarios of the system.
Corresponding author
Email addresses: W.Guo-2@tudelft.nl (Wenjing Guo ), B.Atasoy@tudelft.nl
(Bilge Atasoy), W.W.A.BeelaertsvanBlokland@tudelft.nl (Wouter Beelaerts van
Blokland), R.R.Negenborn@tudelft.nl (Rudy R. Negenborn)
Preprint submitted to Decision Support Systems March 25, 2020
Keywords: Hinterland synchromodal transportation, Dynamic shipment
matching, Rolling horizon approach, Heuristic algorithm
1. Introduction
Hinterland intermodal transportation is the movement of containers be-
tween deep-sea ports and inland terminals by using trucks, trains, barges, or
any combination of them [17]. Compared with unimodal transportation, in-
termodal transportation has the flexibility to use different modes considering
the specific characteristics of containers and in turn achieves better perfor-
mance in costs, delays, and emissions [6]. However, due to the utilization of
multiple modes, operating an intermodal transportation system is very com-
plex. In intermodal transportation, barge and train services normally follow
fixed time schedules and have limited free capacity [6]. Conversely, truck
services are usually not scheduled and have time-dependent travel times as
a result of road traffic congestion [18]. Therefore, constraints such as time
compatibility between different services and capacity limitations of barge and
train services need to be considered in intermodal transport planning.
Synchromodal transportation, as an extension of intermodal transporta-
tion, refers to transport systems with dynamic updating of planning by incor-
porating real-time information [9]. The trend towards spot markets and digi-
talization in hinterland intermodal transportation increases the need for such
online synchromodal transportation problems. In the literature, most of the
existing studies assume that container shipments are only collected from large
shippers based on long-term contracts. These contractual shipment requests
are often fixed and known over a given planning period. Recently, quite a
few studies [e.g., 21, 22] have pointed out the trend towards spot markets
2
in container transportation. Different from the former contracted requests,
spot shipment requests arrive in real-time and require receiving transport so-
lutions as soon as possible. Thanks to the development of digitalization and
advanced information and communication technologies in logistic industries,
information can be collected in real-time, and decisions can be made online
[14]. Nevertheless, these new trends also introduce complexity in intermodal
transport planning, unveiling the need for decision support systems adapted
to dynamic contexts.
In this paper, we investigate a dynamic shipment matching (DSM) prob-
lem in which a platform provides online matches between shipment requests
and transport services. We consider an online synchromodal matching plat-
form that receives contractual and spot shipment requests from shippers,
and receives transport services from carriers, as shown in Figure 1. Shippers
are the entities that are searching for services to transport their shipments.
Examples of shippers include freight forwarders and ocean carriers. Carri-
ers are the entities that provide transport services. Carriers could be truck,
train or barge companies. We consider a network operator as the owner of
the platform. A network operator could be a logistics service provider or an
alliance formed by multiple carriers. The recent developments in information
technologies such as cloud computing and Internet of Things allow real-time
information sharing and container tracking, which facilitates the adoption of
such a platform in practice.
The objective of the platform is to minimize the total cost of match-
ing shipment requests and transport services over a given planning horizon.
Due to the capacity limitation of barge and train services, decisions made
for current requests may influence the decisions for future requests. There-
3
Online synchromodal matching platform
Contractual
shipment
requests
Spot
shipment
requests Truck
services
Rolling horizon approach
Train
services
Barge
services
Shippers
Inform shippers the
transport services
Carriers
Book capacity on
matched services
Matching decisions
Heuristic algorithm
Network operator
Figure 1: Illustration of an online synchromodal matching platform. The platform provides
online matches between shipment requests received from shippers and transport services
received from carriers thanks to the developed rolling horizon approach.
fore, dynamic approaches that create online matching decisions for current
requests are required. In this paper, we design a rolling horizon approach
to handle dynamically revealed shipment requests and develop a heuristic
algorithm to solve the DSM problem in a computationally efficient way.
The remainder of this paper is structured as follows. We discuss the
relevant literature in Section 2. In Section 3, we formally describe the DSM
problem. In Section 4, we explain the implementation of dynamic approaches.
In Section 5, we present optimization algorithms. In Section 6, we describe
the generation of instances and present the experiment results. Finally, in
Section 7, we provide concluding remarks and directions for future research.
2. Literature review
Over the past decades, different freight transport concepts have been
proposed in the literature and in the industry: multimodality, intermodal-
ity, co-modality, and synchromodality [9]. Although these concepts are often
4
used interchangeably, there are subtle differences between these terms: multi-
modality focuses on the utilization of multiple modes; intermodality empha-
sizes the integration between different modes by using standard loading units;
co-modality aims to have efficient utilization of resources; synchromodality,
as an extension of intermodality, adds dynamic updating of transport plans
over a network to benefit from real-time information [1]. In this section, the
studies related to the DSM problem have been divided into two categories:
hinterland intermodal transportation and synchromodality.
2.1. Hinterland intermodal transportation
Hinterland intermodal transportation is the provision of efficient, reliable,
and sustainable services through integrated strategic and tactical planning
at a network level. Strategic planning concerns the design of transporta-
tion network topologies, such as direct link, corridor, or hub-and-spoke [5].
Konings et al. [10] investigate the benefits of a hub-and-spoke network for
hinterland transportation in turnaround times, waiting times, and the relia-
bility of barge services. Containers at a seaport terminal that have different
destinations in the hinterland would be transported together to the hub and
after being regrouped and bundled with containers originate from other sea-
port terminals would continue their trip to their inland destination.
Tactical planning refers to optimally utilizing the given network by choos-
ing transportation services, allocating their capacity to customer demands,
and planning their itineraries and frequency [17]. Bhattacharya et al. [3]
propose a mixed integer programming model to optimize schedules for an
intermodal transport network by taking into account the road traffic flow
estimation. Zuidwijk and Veenstra [23] propose a single period model to al-
locate containers to a truck or barge and schedule the barge departure time
5
considering container release time uncertainty and service transit time un-
certainty. Crainic et al. [4] propose a service network design model to decide
the optimal schedules for the services operated by a fleet of shuttles on the
railway network connecting seaport terminals and inland terminals. Demir
et al. [6] investigate a service network design problem with travel time un-
certainty to decide on the routing of containers and the departure time of
transport services.
2.2. Synchromodality
While intermodality focuses on offline planning in which all forms of in-
put information are required in advance and decisions are made before the
start of transportation, synchromodality emphasizes online planning in which
real-time information about the current state of the transport system can be
taken into account in online planning processes [7]. Specifically, synchro-
modal transport planning deals with dynamic events that are not explicitly
addressed in intermodal transportation, including the representation of real-
time data, decisions, and system states [5]. The most common dynamic
events are the arrival of new shipment requests, but container flows and
travel times are possible dynamics as well.
In the literature, Fazi et al. [8] develop a decision support system for the
optimal allocation of import containers to a heterogeneous fleet composed of
barges and trucks. van Riessen et al. [19] design a decision tree to derive real-
time decision rules for suitable allocation of containers to services. Rivera and
Mes [16] propose an algorithm based on approximate dynamic programming
to assign newly arrived containers to either a barge or a truck. Although
the above studies considered the utilization of multiple modes, none of them
take into account the transshipment operations between different services.
6
Research that models transshipment in synchromodal transportation, such
as Li et al. [11] and Qu et al. [15], are usually designed for container flows.
However, in practice, shippers would like to receive their shipments as a
whole. Therefore, in this paper, we investigate the DSM problem from ship-
ment requests’ perspective, namely, decisions are designed as binary variables
indicating the allocation of a specific shipment request to a specific service.
Mes and Iacob [12] propose a greedy approach to select the cheapest services
for dynamically arrived shipment requests but without the consideration of
road traffic congestions. Due to the limited capacity of road infrastructures,
traffic congestions exist during several periods of a day [18]. The variation
of road travel times has been well investigated in the literature and therefore
can be incorporated in the online synchromodal matching process.
2.3. Contributions
In the literature, the work most similar to our work is Li et al. [11], which
proposes a rolling horizon approach to control container flows in a hinterland
intermodal network by considering time-dependent truck travel times and
time-schedules for trains and barges. In contrast to our work, Li et al. [11]
focuses on aggregated container flows instead of specific shipment requests
with time windows, and therefore uses the value of time instead of delay costs
in the objective function to push containers move to their destinations.
The main contributions of this paper are as follows. First, we propose
a rolling horizon approach to handle newly arrived shipment requests. The
implementation of the rolling horizon approach relies on an optimization
algorithm that can generate timely matching decisions at each decision epoch.
In particular, we develop a heuristic algorithm to solve the DSM problem.
Third, we conduct extensive experiments to assess the performance of the
7
heuristic algorithm in comparison to an exact algorithm, and the performance
of the rolling horizon approach in comparison to a greedy approach from
practice. Briefly, we design, operationalize and validate an online matching
platform in the context of synchromodal transportation.
3. Problem description
Let Rbe the set of shipment requests. Each shipment request rRis
characterized by its announce time Γannounce
r(i.e., the time when the platform
receives the request), release time Γrelease
r(i.e., the time when the shipment
is available for hinterland transportation) at origin terminal or, due time
Γdue
r(i.e., the time that the shipment needs to be delivered) at destination
terminal dr, and container volume qr(i.e., the number of containers). Delay
in delivery is available but with a delay cost coefficient per container per
hour overdue cdelay
r. The lead time of shipment request ris represented as,
LDr= Γdue
rΓrelease
r.
Shipment requests can be divided into two groups: contractual requests
Rcontract and spot requests Rspot. For a contractual request rRcontract,
the network operator has long-term contracts with shippers. Therefore,
the announce time of contractual request ris, Γannounce
r= 0. All the in-
formation {or, dr, qr,Γrelease
r,Γdue
r, cdelay
r}is known in a given planning hori-
zon. Conversely, for a spot request rRspot, the platform receives the
request from spot markets in real-time. The information of the spot request
{or, dr, qr,Γrelease
r,Γdue
r, cdelay
r}is unknown before its announce time.
Let Sbe the set of transportation services. According to the type of
modes, services can be divided into two groups: time-scheduled barge and
train services, and departure time flexible truck services.
8
Travel time
truck
s
t
truck
s
t
truck
s
t
2
b
3
b
4
b
5
b
6
b
7
b
8
b
9
b
10
b
Departure
time
Figure 2: Time-dependent travel times of truck services.
Barge and train services have limited capacity and fixed time schedules
but can help generating economies of scale. Each barge or train service s
Sbarge Strain is characterized by its origin terminal os, destination terminal
ds, free capacity in terms of loading units (i.e., containers) Qs, departure
time (at origin terminal) T Ds, arrival time (at destination terminal) T As,
transport cost cs, and generation of carbon emissions es.
Truck services have unlimited capacity, flexible departure times, and time-
dependent travel times ttruck
s(γ) = θm
sγ+ηm
s,γTm, as shown in Figure 2.
Here, we let γbe the departure time of truck services, and Trepresents the
set of time periods within a day. A time period TmTcan be defined by two
consecutive breakpoints. Let ttruck
sbe the travel time at non-peak periods, α
and βbe traffic congestion coefficients. For time period T2= [b2, b3], given
the values b2, b3, ttruck
s, αttruck
s, we can calculate the slope θof the function
and the intersection ηwith the y-axis. Each truck service sStruck is
characterized by its origin os, destination ds, time-dependent travel time
ttruck
s(γ), transport cost cs, and generation of carbon emissions es.
As spot shipment requests arrive in real-time, the platform provides online
matches between shipment requests and transport services. A match is de-
fined as a combination of a shipment and a service, which means the shipment
9
1
s6
2
5
3
s4
6
4
s1
s3
s4
s2
s5
s6
s7
r1
r2
r3
r4
s1
s3
s2
s7
s5
r2
r3
r2
r2
r1
r4
r3
r3
Barge services
s1 Feasible matches Matching decisions
Truck services Train services
r1
1
Shipment requests
Terminals
Services
Figure 3: Illustrative example of shipment matching in synchromdoal transportation.
will be transported by the service from the service’s origin to the service’s
destination. Each shipment might be matched with multiple services, each
service might be matched with multiple shipments. An illustrative example
of shipment matching in synchromodal transportation is shown in Figure 3.
Matching decision hr1, s4imeans shipment r1 will be transported by service
s4 from terminal 1 to terminal 5; matching decision hr2, s1i,hr2, s3i,hr2, s7i
means shipment r2 will be transported by service combination [s1, s3, s7]
from terminal 1 to terminal 6.
To model this problem, we make the following five assumptions. First, we
assume the platform is centralized and the contracts among carriers, shippers,
terminal operators, and the network operator have been made. Therefore,
we do not consider fairness, pricing, and contracting strategies among play-
ers. Second, we do not model the accept/reject decisions and consider only
the accepted spot requests by the platform. Third, we assume that ship-
pers require their shipments to be transported as a whole, thus shipments
are unsplittable. Fourth, we assume shippers require to receive matching
decisions before the release time of shipments. Therefore, the response time
10
of request ris ∆Γr= Γrelease
rΓannounce
r. Fifth, we assume the capacity of
truck services is unlimited. Therefore, the synchromodal matching system
always has feasible matches for newly arrived shipment requests. Last, we
do not consider stochasticity of travel times in this paper. Instead, we use
deterministic travel times for all services, and consider time-dependent travel
times for trucks, since the road traffic patterns have been well investigated
in the literature [18].
4. Dynamic approaches
To handle newly arrived shipment requests, we need to design method-
ologies that can update the decisions based on dynamically revealed informa-
tion. This paper proposes a rolling horizon approach for the DSM problem
and uses a greedy approach as the benchmark. While the greedy approach
makes matching decisions for each newly arrived shipment request and the
decisions are fixed once they are made, the rolling horizon approach makes
decisions at fixed time points for all active requests including newly received
requests at the current time interval and the requests received at previous
time intervals which have not expired yet, and the decisions are fixed only
when the response for the request cannot be further postponed, namely, the
request will expire before the next decision epoch.
4.1. Benchmark: greedy approach
Greedy approach (GA) is a simple, intuitive algorithm that makes fixed
decisions at each step. In practice, a GA is often used for container trans-
port planning [19]. By using the GA, a shipment request is assigned to the
cheapest feasible service at the time of request arrival. Figure 4 presents the
flow chart of the GA applied in dynamic shipment matching. Specifically, the
11
Optimization algorithm: generate
matching plan for all contractual
requests
Initialization Yes
End of the planning horizon?
Book all the services matched with
contractual requests
Update free capacity of barge and
train services
No
Optimization algorithm: generate
matching plan for the new request
Book all the services matched with
the request
Update free capacity of barge and
train services
Arrival of a new shipment request
Start
End
Figure 4: Flow chart of the greedy approach.
platform provides matches for all the contractual requests received before the
planning horizon. After that, the platform books all the services matched
with the contractual requests and updates the free capacity of barges and
trains. A dynamic event, that is the arrival of a spot shipment request before
the end of the planning horizon, triggers a new optimization process. After
that, the platform books all the services matched with the spot shipment
request, and updates the free capacity of barges and trains.
4.2. Rolling horizon approach
Rolling horizon approach (RHA) is a periodic reoptimization approach,
which has been applied in many research fields, such as ride-sharing problems
[13] and parcel delivery problems [2]. Under a RHA, the system is optimized
periodically at pre-specified points in time called optimization times. The
length between two consecutive optimization times is called the optimization
interval,h. The RHA is therefore executed at a given set of time points
{0, h, 2h, ..., T }. Here, Tis the length of the planning horizon.
12
End of the planning horizon?
Arrival of shipment requests in time
period (t-h,t]
Update the set of active requests
Optimization algorithm: generate
matching plan for all active requests
Expire before the next
decision epoch?
List all active requests; r=1
Book all the services matched with request r
Update free capacity of barge and train services
r=r+1
Yes
No
Checked all active requests?
No
Yes
t=t+h
Yes
No
End
Start
Initialization: decision epoch t=0; empty
the set of active requests
Figure 5: Flow chart of the rolling horizon approach.
Under the RHA, plans are made using all known information within a
planning horizon, but decisions are not finalized until necessitated by a dead-
line. Re-optimizing the system allows for enhancing the reliability of the
system and improving its performance by incorporating the latest informa-
tion. The flow chart of the RHA applied in the DSM problem is presented
in Figure 5. At each decision epoch, the system determines the matches for
all active shipments. At time point t, shipment ris active if its announce
time is earlier than t, and its release time is later than t. The matching plan
for active shipment rmade at time point tis fixed only if its release time is
earlier than t+h, namely, the shipment request will expire before the next
decision epoch. Thus, the system books all the services matched with this
request, and updates the free capacity of barge and train services.
13
5. Optimization algorithms
In this section, we present two optimization algorithms to solve the DSM
problem: an exact algorithm and a heuristic algorithm. While the exact algo-
rithm aims to generate optimal solutions, the heuristic algorithm is designed
to generate timely solutions. The notations used in this paper are shown in
Table 1.
Table 1: Notations used in this paper.
Sets:
NTerminals
RShipment requests
STransport services, S=Sbarge Strain Struck
S+
iTransport services depart at terminal iN,S+
i=Sbarge
i+Strain
i+Struck
i+
S
iTransport services arrive at terminal iN,S
i=Sbarge
iStrain
iStruck
i
Parameters
orOrigin terminal of shipment request rR
drDestination terminal of shipment request rR
qrContainer volume of shipment request rR
Γannounce
rAnnounce time of shipment request rR
Γrelease
rRelease time of shipment request rR
Γdue
rDue time of shipment request rR
cdelay
rDelay cost coefficient of request rRper container per hour overdue
osOrigin terminal of service sS
dsDestination terminal of service sS
QsFree capacity of service sSbarge Strain
T DsDeparture time of service sSbarge Strain
T AsArrival time of service sSbarge Strain
ttruck
sTravel time of truck service sStruck at non-peak periods
α, β Road traffic congestion coefficients
bkThe kth breakpoint of time-dependent travel time functions of truck
services, k={1,2, ..., K}
TmThe mth time period within a day, Tm= [bm, bm+1], m={1,2, ..., K 1}
θm
sThe slope of the travel time function of truck service sfor time period Tm
ηm
sThe intersection of the travel time function of truck service sStruck for
time period Tm
esCarbon emissions of service sSper container
csTransport cost of service sSper container
lcbarge Loading/unloading cost of barge services
ltbarge Loading/unloading time of barge services
lctrain Loading/unloading cost of train services
14
lttrain Loading/unloading time of train services
lctruck Loading/unloading cost of truck services
lttruck Loading/unloading time of truck services
cstorage Storage cost coefficient at terminals per container per hour
cemission carbon tax coefficient per ton
MLarge (enough) numbers used for binary constraints
Variables
xrs A binary variable equal to 1 if request rRis matched with service sS,
0 otherwise
Ari Arrival time of request rRat terminal iN
f+
ri Loading cost of request rRat terminal iNper container
f
ri Unloading cost of request rRat terminal iNper container
wri Storage time of request rRat terminal iN
Γdelay
rDelay of request rRat destination terminal dr
t0
rs Travel time of truck service sStruck with request rR
τrs Departure time of truck service sStruck with request rR
τ0
rs Normalized departure time of truck service sStruck with request rR,
0τ0
rs 24
nrs An integer variable used for normalizing departure time of truck service
sStruck with request rR
ζk
rs A continuous variable used for linearizing the time-dependent travel time
function of truck service sStruck, 0 ζk
rs 1
ξm
rs A binary variable used for linearizing the time-dependent travel time
function of truck service sStruck
5.1. Exact algorithm
In this section, we present a mixed integer linear programming model
(MILP) for the DSM problem. The MILP model is solved by an exact al-
gorithm which is the CPLEX solver. The objective function (1) minimizes
the total costs for the matching of all shipments with services. The total
costs consist of transport costs (including transit costs, transfer costs, and
storage costs), delay costs, and carbon tax. We include delay costs to address
the level of services (i.e., delayed deliveries). Considering carbon tax follows
the trend towards sustainability in the transport industry. In the literature,
there exist several models for calculating emission charges. However, most of
the models require detailed input data (e.g., the mass of the vehicle, air, and
15
rolling resistance) which is in many cases not available. As an alternative,
the activity-based method that multiplies the number of containers with the
CO2emission factor yields better feasibility in transportation practice and
has been applied in many studies [6, 18]. Therefore, this paper uses the
activity-based method to charge CO2emissions.
Minimize
X
rRX
sS
xrsqrcs+X
rRX
iNf+
ri +f
ri qr+X
rRX
iN
wriqrcstorage
+X
rR
Γdelay
rqrcdelay
r
+X
rRX
sS
xrsesqrcemission
(1)
subject to
X
sS+
or
xrs = 1,rR, (2)
X
sS
dr
xrs = 1,rR, (3)
X
sS+
i
xrs =X
sS
i
xrs,rR, i N\{or, dr},(4)
X
rR
xrsqrQs,sSbarge Strain ,(5)
f+
ri =X
sSbarge
i+
xrslcbarge +X
sStrain
i+
xrslctrain +X
sStruck
i+
xrslctruck,rR, i N\{dr},
(6)
f
ri =X
sSbarge
i
xrslcbarge +X
sStrain
i
xrslctrain +X
sStruck
i
xrslctruck,rR, i N\{or},
(7)
Aror= Γrelease
r,rR, (8)
Ari T As+ltbarge xrs +M(1 xrs ),rR, i N\{or}, s Sbarge
i,(9)
Ari T As+ltbarge xrs +M(xrs 1) ,rR, i N\{or}, s Sbarge
i,(10)
Ari T As+lttrain xrs +M(1 xrs ),rR, i N\{or}, s Strain
i,(11)
16
Ari T As+lttrain xrs +M(xrs 1) ,rR, i N\{or}, s Strain
i,(12)
Ari τrs +t
0
rs +lttruckxr s +M(1 xrs),rR, i N\{or}, s Struck
i,(13)
Ari τrs +t
0
rs +lttruckxr s + 2M(xrs 1) ,rR, i N\{or}, s Struck
i,(14)
Ari T Dsltbarge xrs +M(1 xrs ),rR, i N\{dr}, s Sbarge
i+,(15)
Ari T Dslttrain xrs +M(1 xrs ),rR, i N\{dr}, s Strain
i+,(16)
Ari τrs lttruck xrs +M(1 xrs ),rR, i N\{dr}, s Struck
i+,(17)
τ
0
rs =τrs 24nrs ,rR, s Struck,(18)
τ
0
rs =X
k
ζk
rsbk,rR, s Struck,(19)
X
k
ζk
rs = 1,rR, s Struck,(20)
t
0
rs =X
k
ζk
rs (θm
sbk+ηm
s),rR, s Struck,(21)
X
m
ξm
rs = 1,rR, s Struck,(22)
ζ1
rs ξ1
rs,rR, s Struck,(23)
ζk
rs ξk1
rs +ξk
rs,rR, s Struck, k ∈ {2,3, ...K 1},(24)
ζK
rs ξK1
rs ,rR, s Struck,(25)
wri T Dsltbarge xrs Ari ,rR, i N\{dr}, s Sbarge
i+,(26)
wri T Dslttrain xrs Ari ,rR, i N\{dr}, s Strain
i+,(27)
wri τrs lttruck xrs +M(xrs 1) Ari ,rR, i N\{dr}, s Struck
i+,(28)
Γdelay
rArdrΓdue
r,rR. (29)
Constraints (2)-(4) manage the inflow of shipments at their origin termi-
nal, outflow at destination terminal, and flow conservation at transshipment
terminal. Constraints (5) ensure that the total container volumes of ship-
ments carried by service sSbarge Strain do not exceed its free capacity.
Constraints (6)-(7) represent the loading and unloading cost of request rper
container generated at terminal i. Constraints (8) assume that the arrival
time of request rat origin terminal is the release time. Constraints (9)-(12)
ensure that the arrival time of request rat terminal iis the arrival time of
service sSbarge Strain plus unloading time, if request ris transported
17
by service sentering terminal i. Constraints (13)-(14) ensure that the ar-
rival time of request rat terminal iis the sum of departure time of service
sStruck with request rat terminal os, travel time of truck service s, and
unloading time, if request ris transported by truck service sentering termi-
nal i. In constraints (14), we use 2Minstead of Min the right-hand side
to make sure the value of Ar i will not be influenced by the constraints when
xrs = 0 and τrs =M. Constraints (15-17) ensure that the arrival time of
request rat terminal iis earlier than the departure time of service sS
minus loading time, if request ris transported by service sleaving terminal
i. Constraints (18)-(25) are imposed to linearize the time-dependent travel
time functions of truck services. Constraints (26)-(28) ensure that the stor-
age time of request rat terminal iis the departure time of service sminus
the arrival time of request rat terminal iand minus loading time, if request
ris transported by service sleaving terminal i. Constraints (29) are imposed
to calculate the late deliveries of request rat destination terminal dr. We do
not penalize earlier deliveries but only late deliveries.
5.2. Heuristic algorithm
Due to the computational complexity of the matching problem, the exact
algorithm proposed in Section 5.1 cannot generate feasible solutions for realis-
tic instances. Therefore, this paper proposes a preprocessing-based heuristic
algorithm to reduce the computational complexity. The algorithm consists
of three steps: preprocessing of path generation in which no request-specific
characteristics are taken into account, preprocessing of feasible matches in
which request-specific characteristics (i.e., release time and due time) are
considered, and binary integer programming to generate ‘optimal’ solutions.
18
5.2.1. Preprocessing of path generation
We define a path as a combination of services. A path pcan consist of
a single service or multiple services. For example, a path pconsists of a
barge service s1and a truck service s2, thus, p= [s1, s2]. We define Las the
largest number of services in a path. Due to fixed schedules of barge and
train services, some of the service combinations are infeasible. Let Pl
ij be the
set of feasible paths with lservices that depart at terminal iNand arrive
at terminal jN,l∈ {1, ..., L}. A path pPl
ij is feasible only if all the
services in path p= [s1, ..., sl] satisfies spatial and time compatibility: for
service sn, sn+1 p, n ∈ {1, ..., l 1}, the destination terminal of service sn
should be the same as the origin terminal of service sn+1; the arrival time of
snplus unloading and loading time at the transshipment terminal should be
earlier than the departure time of service sn+1.
Based on the above principles, feasible paths with maximum Lservices
are generated by using the offline preprocessing algorithm presented in Algo-
rithm 1. The algorithm starts with determining the feasible paths for each
origin-destination pair with just one service, and subsequently combines these
paths with a single service to create feasible paths with two services, three
services, and so on. For each feasible path, we record the virtual departure
and arrival time points of all the services in the path by calling the AUX-
ILIARYTIMEPOINTS as described in Algorithm 2. The virtual departure
(arrival) time points of barge and train services are the departure (arrival)
time of these services minus (plus) loading (unloading) time. Instead of de-
termining the departure time of truck services to avoid traffic congestion,
we define the virtual departure time points of truck services as the virtual
arrival time points of their previous services to reduce computational com-
19
Algorithm 1 Path generation algorithm.
Input: Set of transportation services S, set of terminals N, the largest number of services
in a path L, index l∈ {1,2, ..., L}.
Output: Set of feasible paths P=P1...P l...P L,Pl
ij Plrepresents the set of feasible
paths with lservices that depart at node i, and arrive at node j. Auxiliary time points
M T l
p=hM T l1
p, ..., M T l(2l)
pi.
Initialize: Let P← ∅, M T l
p[0] , l 1.
1: for node iN, node jNdo
2: for service sSdo
3: if origin os=iand destination ds=jthen
4: p[s]
5: Pl
ij Pl
ij ∪ {p}
6: M T l
pAUXILIARYTIMEPOINTS(p)
7: ll+ 1
8: while lLdo
9: for node iN, node jNdo
10: for service sSdo
11: if origin os6=iand destination ds=jthen
12: for feasible path p[s1, ..., sl1]Pl1
iosdo
13: if TIMECOMPATIBLE1(p, s)=1then
14: p0= [s1, ..., sl1, s]
15: Pl
ij Pl
ij ∪ {p0}
16: M T l
p0AUXILIARYTIMEPOINTS(p0)
17: ll+ 1
plexity. The time-dependent travel time of truck services is calculated based
on the virtual departure time point plus loading time. To examine whether
a path p0= [s1, ..., sl1, s]Pl
ij is feasible, we check the time compatibility
between path p= [s1, ..., sl1]Pl1
iosand service sS
jby calling the
TIMECOMPATIBLE1 as described in Algorithm 3.
5.2.2. Preprocessing of feasible matches
A match hr, piis defined as a combination of shipment rRand path
p= [s1, ..., sl], pP, which means shipment rwill be transported by the
services included in path p. The match hr, piis feasible only if it satisfies
spatial and time compatibility: the origin of shipment rshould be the same
20
Algorithm 2 AUXILIARYTIMEPOINTS.
Input: Feasible path p= [s1, ..., sl].
Output: Auxiliary time points M T l
p=hM T l1
p, ..., M T l(2n)
p, ..., M T l(2l)
pi, n ∈ {1, ..., l}.
Initialize: Let M T l
p[0] , n 1.
1: while nldo
2: if snStruck then
3: if n= 1 then
4: M T l(2n1)
p0
5: else
6: M T l(2n1)
pM T l(2n2)
p
7: Travel time of truck service sncalculate time-dependent travel time function
of truck service sn
8: M T l(2n)
pM T l(2n1)
pplus loading time plus travel time of truck service snplus
unloading time
9: else
10: M T l(2n1)
pdeparture time of service snSbarge Strain minus loading time
11: M T l(2n)
parrival time of service snSbarge Strain plus unloading time
12: nn+ 1
Algorithm 3 TIMECOMPATIBLE1.
Input: node iN, service sS\S+
i, feasible path p= [s1, ..., sl1]Pl1
ios.
Output: z, equal to 1 if path pand service sis time compatible, 0 otherwise.
Initialize: Let z0.
1: if sSbarge Strain then
2: if M T 2(l1)
pdeparture time of service sminus loading time then
3: z1, return z
4: else
5: z1, return z
as the origin of service s1, the destination of shipment rshould be the same
as the destination of service sl; the release time of shipment rshould be
earlier than the virtual departure time point of service s1.
We define Φ as the set of feasible matches, crp as the cost of matching ship-
ment rwith path p. Algorithm 4 is designed to create the feasible matches.
For shipment rand path p= [s1, ..., sl]Pl
ordr, the time compatibility be-
tween rand pis checked by calling TIMECOMPATIBLE2, as presented in
Algorithm 5. If s1, ..., snare truck services, the virtual departure and arrival
21
Algorithm 4 Feasible match generation algorithm.
Input: Set of feasible paths P, set of shipment requests R, the largest number of services
in a path L, index l∈ {1,2, ..., L}, set of auxiliary time points M T , objective function (1).
Output: Set of feasible matches Φ = Φ1Φ2... Φr... ΦR.
Initialize: Let Φ ← ∅, l 1.
1: for shipment request rRdo
2: for l∈ {1,2, ..., L}do
3: for feasible path p= [s1, s2, ..., sl]Pl
ordrdo
4: if TIMECOMPATIBLE2(r, p)=1then
5: ΦrΦr∪ {p}
6: crp Calculate the objective function
time points of these truck services need to be updated sequentially. After
the updating, if the virtual arrival time point of snis less than the virtual
departure time point of service sn+1 Sbarge Strain, match hr, piis feasible.
If s1is a barge or train service, and the release time of shipment ris less than
the virtual departure time point of service s1, then match hr, piis feasible.
5.2.3. Binary integer programming
Based on the above preprocessing procedures, the objective function is
updated to minimize the total costs for the matching of shipments with
feasible paths. Let yrp be a binary decision variable equal to 1 if shipment
ris matched with path p, and 0 otherwise. The mathematical formulation
translates into a binary integer programming (BIP) model:
Minimize
X
rRX
pΦr
crpyr p (30)
subject to
X
pΦr
yrp = 1,rR, (31)
X
rRX
pΦrs
yrpqrQs,sSbarge Strain ,(32)
yrp ∈ {0,1},rR, p Φr,(33)
22
Algorithm 5 TIMECOMPATIBLE2.
Input: shipment request rR, feasible path p= [s1, ..., sl]Pl
ordr, auxiliary time points
M T l
p=hM T l1
p, ..., M T l(2n)
p, ..., M T l(2l)
pi, n ∈ {1, ..., l}.
Output: z, equal to 1 if rand pis time compatible, 0 otherwise.
Initialize: Let z0, n 2.
1: if s1Struck then
2: update M T l1
prelease time of shipment request r
3: update travel time of truck service s1calculate time-dependent travel time func-
tion truck service s1
4: update M T l2
pM T l1
pplus loading time plus travel time of truck service s1plus
unloading time
5: while nldo
6: if snStruck then
7: update M T l(2n1)
pM T l(2n2)
p
8: update travel time of truck service sncalculate time-dependent travel time
function truck service sn
9: update M T l(2n)
pM T l(2n1)
pplus loading time plus travel time of truck service
snplus unloading time
10: else
11: if M T l(2n2)
pM T l(2n1)
pthen
12: z1, return z
13: else
14: return z
15: nn+ 1
16: else
17: if release time of shipment request rM T l1
pthen
18: z1, return z
where Φrs ={pΦr|sp}.
Constraints (31) ensure that only one feasible path will be assigned to
each shipment. Constraints (32) ensure that the total volume of shipments
assigned to service sSbarge Strain does not exceed its free capacity.
6. Numerical experiments
In this section, we first evaluate the performance of the optimization algo-
rithms and compare the GA with the RHA. Then, we investigate the impact
of different objective functions and optimization intervals. All algorithms
23
were implemented in MATLAB R2017a, and all experiments were performed
on a computer with 2.50 GHz Intel Core i5-7200U CPU and 8 GB RAM.
CPLEX 12.6.3 was used as an IP solver.
6.1. Generation of test instances
In practice, different companies have different network sizes. For exam-
ple, Combi Terminal Twente (https://www.ctt-twente.nl/en/, accessed:
2020-03-16) provides container transports from the port of Rotterdam to 3
inland terminals in the Netherlands and Germany with 7 barges, 3 trains
and 40 trucks per week. European Gateway Services (EGS, https://www.
europeangatewayservices.com/en, accessed: 2020-03-16) offers above 40
trains and 30 barges per week between the Ports of Rotterdam and Antwerp
and 11 inland terminals in the Netherlands, Belgium, Germany, and Austria.
Every year, approximately 1000000 TEU is transported within the EGS net-
work. To show the application of the model, we consider a hinterland inter-
modal network in Europe to carry out the numerical experiments, as shown
in Figure 6. The network consists of three deep-sea terminals (nodes 1, 2, 3)
and seven inland terminals (nodes 4, 5, 6, 7, 8, 9, 10) which are connected
by 116 transport services, including 49 barges, 33 trains, and 34 trucks. The
length of the planning horizon was set to one week. The coefficients used in
the experiments were derived from van Riessen et al. [20] and Li et al. [11],
as shown in Table 2. Here, the transit cost of services is a linear function of
the transit time tand distance d.
We generated several instances to represent different characteristics of
shipments within the given network. We use EU n1n2to represent an
instance with n1contractual requests and n2spot requests. The average con-
tainer volume of contractual requests is 20 TEU, and the average container
24
5
5
1
1
7
7
6
6
Rail services
Barge services
Inland terminals
Deep-sea terminals
2
2
3
3
4
4
Truck services
Port of Rotterdam
9
9
8
8
10
10
Node
Terminal
1
Delta
2
Euromax
3
HOME
4
Moerdijk
5
Venlo
6
Duisburg
7
Willebroek
8
Neuss
9
Dortmund
10
Nuremberg
Figure 6: The topology of an intermodal network in Europe.
Table 2: Experimental setting.
Coefficient Truck Barge Train
Transit cost (e/TEU-km-h) 30.98t+0.2758d 0.6122t+0.0213d 7.54t+0.0635d
Carbon emission (kg/TEU-km) 0.8866 0.2288 0.3146
Loading/unloading cost (e/TEU) 3 18 18
Loading/unloading time (h) 0 1 1
Carbon tax (e/ton) 8 8 8
Storage cost (e/TEU-h) 1 1 1
volume of spot requests is 5 TEU. We set the arrival frequency to 20, 10, 6 and
4 minutes for instances with 400, 800, 1200 and 1600 spot requests, respec-
tively. Regarding the time-dependent travel times, we set b1= 0, b2= 5, b3=
7, b4= 9, b5= 13, b6= 17, b7= 19, b8= 21, b9= 24, α = 2, β = 1.5. The
detailed information of services and instances used in this paper is available
at https://surfdrive.surf.nl/files/index.php/s/cCrpmO1dy8ls7if.
6.2. Performance of the heuristic algorithm
To compare the performance of the heuristic algorithm presented in Sec-
tion 5.2 with the exact algorithm presented in Section 5.1, we generated 8
instances of the DSM problem with different numbers of shipment requests.
25
Table 3: Number of variables and constraints for the instances under different algorithms.
Instances Exact algorithm Heuristic-1 Heuristic-2 Heuristic-3 Heuristic-4
N.var N.con N.var N.con N.var N.con N.var N.con N.var N.con
EU-5-0 4185 4221 26 18 54 25 66 25 68 25
EU-10-0 8370 8408 28 24 209 63 684 82 944 82
EU-20-0 16740 16676 84 61 428 85 1125 91 1488 91
EU-30-0 25110 24963 112 66 564 104 1646 105 2235 105
EU-700-0 585900 580996 2504 767 13725 780 36449 781 56777 781
EU-1000-0 837000 829916 3279 1067 18108 1082 49908 1082 79805 1082
EU-1300-0 1088100 1079016 4473 1367 25377 1380 69202 1381 109758 1381
EU-1600-0 1339200 1327942 6032 1667 33742 1680 91020 1681 143859 1681
In the exact algorithm, we set the large enough number Mto 168. In the
heuristic setting, we let the largest number of services in a path Lbe 1, 2, 3
and 4, respectively. We use heuristic-Lto represent the heuristic algorithm
with setting L. The number of variables (i.e., N.var) and constraints (i.e.,
N.con) for the instances under different algorithms is presented in Table 3.
We consider two performance indicators: total costs (obj: e) and compu-
tation time (CPU: seconds). The computation time of heuristics includes the
time of generating feasible matches and the time of solving the BIP model.
We use ‘gap’ to represent the %gaps in total costs between different algo-
rithms, which is given by (objective value - benchmark value)*100/benchmark
value. Table 4 summarizes the performance for all instances. It shows that
the small instances with up to 30 contractual requests are still solvable by
using the exact algorithm. However, the computation time increases dramat-
ically from 27 to 5647 seconds. In comparison, extending Lfrom 1 to 3, the
gaps in total cost between the heuristic algorithm and the exact algorithm
decreases to 0.00%. The computation time of the heuristic algorithm with a
maximum of 3 services in a path (Heuristic-3) is no more than 1 second.
For instances with above 700 total requests, we cannot obtain feasible
solutions with the exact algorithm. The limitation in these instances is not
the computation time but rather the memory since the size of the problems
26
Table 4: Performance of the heuristic algorithm with different L.
Instances Exact algorithm Heuristic-1 Heuristic-2 Heuristic-3 Heuristic-4
obj CPU %gap CPU %gap CPU %gap CPU obj %gap CPU
EU-5-0 4386 27.01 0.00 0.05 0.00 0.15 0.00 0.60 4386 0.00 0.28
EU-10-0 25988 213.06 32.89 0.03 0.00 0.11 0.00 0.45 25988 0.00 0.80
EU-20-0 44198 1704.98 29.56 0.02 0.05 0.13 0.00 0.43 44198 0.00 0.65
EU-30-0 65126 5647.03 28.52 0.02 0.00 0.13 0.00 0.60 65126 0.00 0.94
EU-700-0
Out of memory
17.49 1.37 0.17 8.21 0.00 25.47 1060077 38.43
EU-1000-0 18.37 2.60 0.25 16.46 0.00 45.22 1017669 78.94
EU-1300-0 19.03 6.12 0.42 34.15 0.00 94.62 1042481 158.57
EU-1600-0 18.36 10.55 0.17 63.22 0.00 176.24 1020075 302.41
becomes too large to read. In contrast, all these large instances can be
solved by using the heuristic algorithm with a maximum of 3 services in a
path within 176.24 seconds, and the gaps in total costs between heuristic-3
and heuristic-4 are 0.00%.
6.3. Performance of the dynamic approaches
In this section, we aim to compare the performance of two dynamic ap-
proaches: the GA and the RHA. Both of them work with Heuristic-3. We
set the length of the optimization interval under the RHA to 1 hour.
We generated 4 groups of instances with different demand densities repre-
sented by the ratio between demand and supply: EU-100-400 (40%), EU-200-
800 (80%), EU-300-1200 (120%), and EU-400-1600 (160%). Here, demand
is the total container volumes of shipments, supply is the total free capac-
ity of barge and train services. Each group includes 10 instances with the
same ratio between demand and supply. We use the GA as the benchmark.
Figure 7 (a) shows that the RHA has lower total costs in all the groups of
instances, and the reduction in total costs increases with the demand den-
sity. The reason is that the higher the ratio between demand and supply,
the competition between shipment requests is higher. The proposed RHA
better allocates limited barge and train capacity to more suitable shipment
requests which might arrive later in the system.
27
(a)
(c)
(b)
(d)
Figure 7: Comparison between the rolling horizon approach and the greedy approach.
We generated another 4 groups of instances with different degrees of dy-
namism (DOD). In this paper, we define the DOD as the ratio between the
number of spot containers and the number of total containers. Thus, the
DOD for instance EU-300-400 is (400 5) /(300 20 + 400 5) = 25%. The
DOD for instance EU-300-400, EU-200-800, EU-100-1200, EU-0-1600 are
therefore 25%, 50%, 75% and 100% respectively. Each group includes 10 in-
stances with the same DOD. Figure 7 (b) shows that the RHA also has better
performance in all the groups of instances compared to the GA, and the im-
provement is increasing further with a higher DOD. Interestingly, when the
matching system is 100% dynamic, the variance of the performance of the
RHA becomes the largest. The reason is when the system is fully dynamic,
the performance of the reoptimization-based RHA becomes uncertain.
To investigate the performance of the GA and the RHA under different
lead time scenarios, we generated 3 groups of instances with different lead
28
times of spot requests: EU-100-1200 (24), EU-100-1200 (48), and EU-100-
1200 (72). Each group consists of 10 instances with the same lead time
setting. Figure 7 (c) shows that the RHA has better performance than the
GA in terms of total costs for all groups of instances and the improvement
is larger for longer lead times. Longer lead times provide more flexibility for
the RHA to re-optimize the decisions as new requests are received and the
capacity can be allocated more effectively.
Similarly, we varied the response time of shipment requests from 1 hour
to 24 hours for 3 groups of instances: EU-100-1200 (1), EU-100-1200 (12),
and EU-100-1200 (24). Figure 7 (d) shows that the larger the response time,
the better the performance of the RHA is in reducing total costs since it has
more time to update decisions for all requests until their release times.
6.4. Impact of different objective functions and optimization intervals
In this section, we use the RHA and Heuristic-3 to investigate the impact
of different objective functions and the length of the optimization interval.
6.4.1. Impact of different objective functions
We investigate the impact of different objective functions under instance
EU-1000-0. The utilization of barges and trains is defined as the ratio be-
tween the utilized capacity of barge and train services multiplied by cor-
responding transit distances and the utilized total capacity of all services
multiplied by corresponding distances. Table 5 shows that different objec-
tive functions generate different matching solutions. Comparing case 11 with
cases 1 to 10, we observe that the total cost is the lowest when the objective
function includes all elements. When we minimize the transit cost (case 1)
or the carbon tax (case 5), the utilization of barges and trains is favored
29
Table 5: Impact of different objective functions
Case Carbon
tax co-
efficient
(e/ton)
Objective
function1
(Min.)
Total
cost (e)
OF1 (e) OF2 (e) OF3 (e) OF4 (e) OF5 (e) Delay
(TEU-h)
Carbon
emission
(kg)
Utilization
of barges
and trains
(%)
Utilization
of trucks
(%)
1
8
OF1 4478714 598864 328458 137798 3406214 7379 39170 922429 71.47 28.53
2 OF2 1473382 1411229 47622 0 0 14530 0 1816311 0.00 100.00
3 OF3 1618747 1499961 103374 00 15412 0 1926482 0.04 99.96
4 OF4 1617409 1495824 105960 245 015379 0 1922413 0.42 99.58
5 OF5 4432293 601621 324498 144863 3353948 7364 40167 920491 72.06 27.94
6 OF2,3,4,5 1473382 1411229 47622 0 0 14530 0 1816311 0.00 100.00
7 OF1,3,4,5 1042644 648402 313266 72066 1112 7799 11 974863 67.96 32.04
8 OF1,2,4,5 1028388 668393 270732 80338 972 7953 10 994084 65.78 34.22
9 OF1,2,3,5 1803565 656501 260772 69829 808619 7844 8624 980454 66.71 33.29
10 OF1,2,3,4 1017693 695156 252702 60783 880 8172 9 1021544 63.76 36.24
11 Total cost 1017675 692118 254448 62114 850 8145 9 1018154 64.05 35.95
12 100 Total cost 1110869 684140 260790 64039 972 100929 10 1009287 64.78 35.22
13 500 Total cost 1507925 658359 284862 72431 1162 491111 12 982222 66.94 33.06
14 1000 Total cost 1995063 643700 298386 78945 8159 965872 88 965872 68.48 31.52
1OF1: Transit cost; OF2: Transfer cost; OF3: Storage cost; OF4: Delay cost; OF5: Carbon tax; OF2,3,4,5: Transfer cost + Storage cost + Delay cost + Carbon
tax; OF1,3,4,5: Transit cost + Storage cost + Delay cost + Carbon tax; OF1,2,4,5: Transit cost + Transfer cost + Delay cost + Carbon tax; OF1,2,3,5: Transit
cost + Transfer cost + Storage cost + Carbon tax; OF1,2,3,4: Transit cost + Transfer cost + Storage cost + Delay cost
as they are cheaper and environmental friendlier than trucks. On the other
hand, minimizing the transfer (case 2), storage (case 3) or delay (case 4)
cost favors the utilization of trucks as they are faster in general and have
flexible departure times. Comparing case 11 with cases 6 to 10, we see that
the transit cost has the largest influence on the matching decisions while
carbon tax has the smallest impact. However, it is predictable that the car-
bon tax coefficient will increase in the near future because of the increasing
environmental issues and the enforced regulations. Under a restrict emission
policy, such as case 14, including the carbon tax in the objective function
can greatly affect the utilization of barges and trains. It is also interesting
to observe that there is a clear trade-off between delay and carbon emissions
as it is what is happening in real life.
6.4.2. Impact of the length of the optimization interval
To test the impact of the length of the optimization interval in the RHA,
we used 4 instances with different DOD: EU-300-400 (25%), EU-200-800
(50%), EU-100-1200 (75%) and EU-0-1600 (100%). For each instance, we
vary the length of the optimization interval hfrom 0.1 to 10 hours.
30
-0.50%
0.00%
0.50%
1.00%
1.50%
0.1 0.5 1 2 3 4 5 6 7 8 9 10
Gaps in total costs
The length of the optimization intervals (hours)
EU-300-400
EU-200-800
EU-100-1200
EU-0-1600
Figure 8: Impact of the length of the optimization interval.
We use optimization intervals of 1 hour as the benchmark. Figure 8 shows
that reducing hallows the system to react more quickly to new information,
which in turn leads to improved solutions. This is especially the case for
instances with a high DOD. However, excessively reducing hdoes not improve
the performance of the RHA. It is seen that below 1 hour of optimization
intervals does not bring values as expected since the response times are set as
a minimum of 1 hour. Therefore, decision makers can improve the matching
quality by choosing a proper h-value.
7. Conclusion and future research
In this paper, we introduced an online synchromdoal matching problem
in which a platform aims to provide optimal matches between shipment re-
quests and transport services. We proposed a rolling horizon approach and
a heuristic algorithm to support the online decision-making process. We
validated the heuristic algorithm and the rolling horizon approach on an
intermodal network in Europe. The results indicate that the heuristic algo-
rithm is efficient in large instances of the matching problem, and can be used
under dynamic contexts. The rolling horizon approach has been proved to
outperform a greedy approach in reducing total costs under various scenarios.
31
In conclusion, the proposed online matching platform will support deci-
sion makers to optimize the matching of shipments and services considering
the trade-off between transport cost, delay, and carbon emissions thanks to
the developed rolling horizon approach. In other words, with the proposed
approach, the use of barges, trains, and trucks can be managed more effec-
tively taking into account their impact on transport time, cost and emissions
together with different time sensitivities of shipments.
This work can be extended in several directions. During the day, the
number of trucks available to the matching platform is quite dynamic. There-
fore, combining the dynamics of truck services in the synchromodal matching
model is a further research direction. Considering the multiple uncertainties
that exist in synchromodal transportation, future research can be carried out
on stochastic and dynamic shipment matching. Furthermore, the origins and
destinations of containers are usually located in different countries. Thus,
looking into models with an integrated network combining international and
inland transport is a promising research direction. Besides, in this paper,
the online matching platform is controlled in a centralized way. However,
in practice, multiple operators are present and they may not all be willing
to give authority to a central platform. The coordination mechanism among
them and incentives to stimulate cooperation are part of future research.
Acknowledgments
This research is financially supported by the China Scholarship Council
under Grant 201606950003 and the project “Complexity Methods for Predic-
tive Synchromodality” (project 439.16.120) of the Netherlands Organisation
for Scientific Research (NWO).
32
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... However, road flexibility that enables truck departure time planning and speed optimization has not been fully formulated in intermodal routing. Zhang et al. [16], Sun et al. [51] and Guo et al. [59] separately explored an intermodal routing problem with timedependent travel times and considered truck departure time planning in the routing optimization to strengthen the efficiency of transshipment. However, road traffic restrictions were not included in the above relevant studies when planning truck departure times. ...
... Feasibility robustness minimizes the difference between the worst-case value ( 1 ) of the fuzzy capacity and its chance constraint value ( • 1 + (1 − ) • 2 ). This term determines the value of confidence level in Equation (59). In this term, is the penalty for violating the chance constraint. ...
... For example, the container block train running from Huinong to Xingang yielded a service time window [5,11] at Huinong in its first period. In the second period, this train was treated as a different rail service with a service time window [53,59] at Huinong. ...
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This study investigates a road-rail intermodal routing problem in a hub-and-spoke network. Carbon cap-and-trade policy is accommodated with the routing to reduce carbon dioxide emissions. Multiple time windows are employed to enhance customer flexibility and achieve on-time pickup and delivery services. Road service flexibility and resulting truck operations optimization are explored by combining truck departure time planning under traffic restrictions and speed optimization with the routing. To enhance the feasibility and optimality of the problem optimization, the routing problem is formulated in a fuzzy environment where capacity and carbon trading price rate are trapezoidal fuzzy parameters. Based on the customer-centric objective setting, a fuzzy nonlinear optimization model and its linear reformation are given to formulate the proposed routing problem that combines distribution route design, time window selection and truck operations optimization. A robust possibilistic programming approach is developed to optimize the routing problem by obtaining its robust solutions. A case study is presented to demonstrate the feasibility of the proposed approaches. The results show that the multiple time windows and truck operations optimization can lower the total costs, enhance the optimality robustness and reduce carbon dioxide emissions of the routing optimization. The sensitivity analysis finds that increasing the lower bound of the confidence level in the robust possibilistic programming model improve the robustness and environmental sustainability; however, worsen the economy of the routing optimization.
... The work on co-planning takes outset in the restricted information which can be communicated between the agents and a clear limits to their responsibilities. It is discussed further in Chapter 6. [5] x x Unclear [9] x x Unclear [10] x x [16] x [30] x [31] x x [36] x x [56] x [58] x [57] reject x [70] x [85] x x [88] x [92] x [105] x [112] x 5) x [110] x x [111] x [121] x [137] x Barge [126] x x [136] Truck [139] x [130] x x [134] x [165] x [164] x [175] x [178] x [184] x Terminal ...
... Decisions All Reconsider [80] Change [164] Infeasible Update [56] Handle exception [130] The real-time aspects of synchromodal transport is in many of the published methods used to allow for replanning. This can be either periodically at regular intervals (denounced rolling in this section) or when needed, e.g., because new demand needs planning for or disturbances render an existing plan infeasible. ...
... In [36] synchromodal transport is considered as part of a supply chain, so here stock is part of the operational costs, while most papers focus on the transport costs, e.g., [178]. In .e.g., [137] only the transit cost is considered, while ,e.g., [56] also consider the cost of changing modes and storing containers. Most methods consider time as part of the objective, either directly as travel time, i.e. aims at the fastest possible delivery, or as a penalty for containers that arrive too late. ...
Thesis
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Under the synchromodal transport paradigm, transport providers decide how freight is transported. Thereby, real-time information on the transport system can be used to integrate the routing decisions of both freight and vehicles to utilize the transport capacity well between multiple stakeholders. This dissertation proposes co-planning, where consciously chosen information is exchanged between cooperating partners that plan individually towards shared goals. In the dissertation multiple routing methods based on model predictive control are presented. The conclusions illustrate that co-planning can contribute to make freight transport more efficient and thereby alleviate the environmental impacts.
... There are two objectives. One objective ( 1 ) is to maximize the number of served requests, and another objective ( 2 ) is minimizing cost, which consists of transport cost, transfer cost, storage cost, carbon tax, waiting cost, and delay penalty (Guo et al., 2020). The emissions are calculated using an activity-based method by Demir et al. (2016) and the amount of emissions is related to vehicle type, distance, and amount of containers. ...
... EGS network is located at Rhine-Alpine corridor, which constitutes one of the busiest freight routes in Europe, around 138 billion tonne-kilometers freight is transported along this corridor annually, accounting for 19% of total GDP of the EU. Fig. 7 presents the overall network of this study (Guo et al., 2020). It contains three terminals in the Port of Rotterdam and seven inland terminals in the Netherlands, Belgium, and Germany. ...
... Moreover, we set ( ) and ( ) equal to ( ) and ( ) , respectively. Detailed information on how the instances are generated can be found in Guo et al. (2020). Specific parameters are shown in Table 4. ...
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In synchromodal transport, a freight forwarder usually serves multiple shippers with heterogeneous and vague preferences, such as low-cost, fast, or reliable transport. Ignoring shippers’ preferences will negatively impact the satisfaction of shippers and lead to the loss of them in the longer run. In order to incorporate these preferences, a Synchromodal Transport Planning Problem with Heterogeneous and Vague Preferences (STPP-HVP) is proposed and formulated as a mathematical model. Heterogeneous and Vague Preferences (HVP) are modeled through Multiple Attribute Decision Making approaches that integrate fuzzy set theory. The proposed model has two objectives, i.e., maximizing the number of served requests and minimizing the transportation cost. Preferences of shippers are set as constraints such that the freight forwarder needs to satisfy the preferred levels for each attribute. A heuristic algorithm (Adaptive Large Neighborhood Search) is proposed to find (near) optimal solutions. The case study in the European Rhine–Alpine corridor demonstrates that the proposed model can provide more attractive solutions to shippers compared with optimization which ignores preferences. Under various scenarios, the attributes, such as cost, time, emissions, reliability, and risk of damage, are analyzed and the (near) optimal modes and routes are suggested according to HVP. Moreover, the results show that the conflicts among attributes, conflicts among shippers, and conflicts between the freight forwarder and shippers are resolved by making one actor more satisfied without compromising any other actor’s preferences.
... However, the majority of the existing models in ST, e.g., Demir et al. (2016) and Guo et al. (2020), only consider services with fixed routes and schedules. The flexible services are not considered mainly due to the following reasons: (a) providing flexible services needs the development of various technologies, such as digital platform, information and communication technologies, and physical internet (Ambra et al., 2019;Giusti et al., 2019); (b) achieving flexible services needs to consider transshipment and synchronization of operations (Giusti et al., 2019); (c) tackling the optimization problem with flexible services needs customized, sophisticated and efficient algorithms due to computational complexity (Wolfinger, 2021). ...
... Flexible routing and scheduling need a vehicle routing component, which is often addressed by coarse approximations in the existing models that cannot be applied to ST with flexible services (Drexl, 2012). For example, the links or paths are used to ''transport'' containers in the literature (Van Riessen et al., 2013;Demir et al., 2016;Guo et al., 2020). When considering flexible routing and scheduling at the operational level, the transport operator needs to take the capacity and speed of each vehicle into account and decide which vehicle will be used to serve requests. ...
... In the literature, containers in ST are moved by vehicles with fixed schedules (Guo et al., 2020;Agamez-Arias and Moyano-Fuentes, 2017;SteadieSeifi et al., 2014). These models can be divided into two groups: Minimum Cost Network Flow model (MCNF) and Path-based Network Design model (PBND) (Van Riessen et al., 2013). ...
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As a critical feature of synchromodal transport (ST), service flexibility plays an important role in improving the utilization of resources to reduce costs, emissions, congestions, and delays. However, none of the existing studies considered flexible services under the framework of synchromodality. This paper develops a Mixed Integer Linear Programming (MILP) model to formulate service flexibility in ST planning. In the MILP model, vehicles with flexible services as well as fixed services are both considered, and vehicle routes and request routes are planned simultaneously. Due to the computational complexity, an Adaptive Large Neighborhood Search heuristic is designed to solve the problem. Several customized operators are designed based on the characteristics of the studied problem. The proposed model is compared with the models developed in a highly-cited paper and a newly published paper that do not consider service flexibility. Case studies on small instances verified that the proposed model with flexibility performs better on all scenarios, including scenarios with different weights for the individual objectives, scenarios under congestion,and dynamic optimization scenarios. On large instances (up to 1600 shipment requests), the proposed model with flexibility reduces the cost by 14% on average compared with the existing models in the literature.
... The model realizes the dynamic adjustment of transportation mode of transit terminals in intermodal transport networks to cope with the change of transportation time of channels in the network. Guo's paper [20] proposed an online matching platform for transport demand and transport services, and a hybrid algorithm based on the rolling horizon method and the heuristic method is used to deal with the matching process. Based on the platform, the research team also developed a hybrid stochastic approach to handle the uncertainty information of requests and travel times [21]. ...
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The cooperative planning in intermodal transport networks can obtain the global optimal decision under the premise of ensuring the data privacy of each role in the cooperation and avoiding massive data transmission. For the control of container flow in intermodal transport networks, the distributed model predictive control (DMPC) method can effectively realize cooperative planning, but the convergence speed of the existing DMPC methods is slow. Therefore, this study attempts to construct faster DMPC methods for cooperative planning. The Jacobi proximal distributed model predictive control (JP‐DMPC) and dual consensus distributed model predictive control (DC‐DMPC) methods are constructed for container flow control based on two variants of alternating direction method of multipliers (ADMM). The simulation experiments prove that the convergence speed of JP‐DMPC and DC‐DMPC methods is higher than that of the state‐of‐the‐art method on the premise that the time cost and interaction data volume of each iteration do not change much, and the DC‐DMPC method improves planning speed particularly significantly. This study provides new methods for intermodal transport cooperative planning and has significance for the development of synchromodal transport.
... The same authors also propose a method for simultaneous and real-time planning of container transport and vehicle routes using model predictive control (Larsen et al., 2021). Guo et al. (2020) investigates a dynamic shipment matching problem using a rolling horizon approach to handle newly arrived shipment requests. Most closely related to our work in the area of synchromodal transport planning is the work of Yee et al. (2021), who explicitly includes future real-time information, also by modelling the problem as an MDP. ...
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We study the problem of scheduling container transport in synchromodal networks considering stochastic demand. In synchromodal networks, the transportation modes can be selected dynamically given the actual circumstances and performance is measured over the entire network and over time. We model this problem as a Markov Decision Process and propose a heuristic solution based on Approximate Dynamic Programming (ADP). Due to the multi-period nature of the problem, the one-step look-ahead perspective of the traditional approximate value-iteration approach can make the heuristic flounder and end in a local-optimum. To tackle this, we study the inclusion of Bayesian exploration using the Value of Perfect Information (VPI). In a series of numerical experiments, we show how VPI significantly improves a traditional ADP algorithm. Furthermore, we show how our proposed ADP–VPI combination achieves significant gains over common practice heuristics.
... Original reasons for port digitalization are in traditional efficiency optimization and in enhancement of material (cargo) flow (e.g. [9,27]. As ports evolved from load and offload points to genuinely intermodal logistical service hubs, the importance of efficient information flows increased (also [4]. ...
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Chapter
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Hinterland networks for container transportation require planning methods in order to increase efficiency and reliability of the inland road, rail and waterway connections. In this paper we aim to derive real-time decision rules for suitable allocations of containers to inland services by analysing the solution structure of a centralised optimisation method used offline on historic data. The decision tree can be used in a decision support system (DSS) for instantaneously allocating incoming orders to suitable services, without the need for continuous planning updates. Such a DSS is beneficial, as it is easy to implement in the current practice of container transportation. Earlier proposed centralised methods can find the optimal solution for the intermodal inland transportation problem in retrospect, but are not suitable when information becomes gradually available. The main contributions are threefold: firstly, a structured method for creating decision trees from optimal solutions is proposed. Secondly, an innovative method is used for obtaining multiple equivalent optimal solutions to prevent overfitting of the decision tree. And finally, a structured analysis of three error types is presented for assessing the quality of an obtained tree. A case study illustrates the method͛s purpose by comparing the quality of the resulting plan with alternative methods.