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Received: 24 December 2024
Revised: 25 January 2025
Accepted: 31 January 2025
Published: 3 February 2025
Citation: Gracia, M.D.; Mar-Ortiz, J.;
Vargas, M. TruckAppointment
Scheduling: A Review of Models and
Algorithms. Mathematics 2025,13, 503.
https://doi.org/10.3390/
math13030503
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Review
Truck Appointment Scheduling: A Review of Models and Algorithms
Maria D. Gracia 1, Julio Mar-Ortiz 1,* and Manuel Vargas 2
1Faculty of Engineering Tampico, Universidad Autonoma de Tamaulipas, Tampico 89140, Mexico;
mgracia@docentes.uat.edu.mx
2Industrial Engineering Department, Universidad de Santiago de Chile, Santiago 9170124, Chile;
manuel.vargas@usach.cl
*Correspondence: jmar@docentes.uat.edu.mx
Abstract: This paper provides a comprehensive review of truck appointment schedul-
ing models and algorithms that support truck appointment systems (TASs) at container
terminals. TASs have become essential tools for minimizing congestion, reducing wait
times, and improving operational efficiency at the port and maritime industry. This review
systematically categorizes and evaluates existing models and optimization algorithms,
highlighting their strengths, limitations, and applicability in various operational contexts.
We explore deterministic, stochastic, and hybrid models, as well as exact, heuristic, and
metaheuristic algorithms. By synthesizing the latest advancements and identifying research
gaps, this paper offers valuable insights for academics and practitioners aiming to enhance
TAS efficiency and effectiveness. Future research directions and potential improvements in
model formulation are also discussed.
Keywords: truck appointment systems; port logistics; optimization models and algorithms;
truck appointment scheduling; port capacity planning and scheduling
MSC: 90B06
1. Introduction
In the mid-2000s, Truck Appointment Systems (TASs) emerged as a prevalent strategy
for reducing congestion and truck turnaround times at container terminals [
1
]. A TAS
aims to regulate truck arrivals throughout the day to minimize gate congestion, improve
operational planning, and reduce waiting times, thereby promoting efficiency and relia-
bility in container drayage. A well-designed TAS benefits both carriers, through shorter
waiting times, and container terminals, by enabling better resource planning. The benefits,
particularly in reducing waiting times and gate congestion, have been quantified (see the
work of Zhao and Goodchild [2]).
From a practical perspective, TASs are technological platforms designed to coordinate
and balance truck flows at ports and container terminals by planning and scheduling truck
arrivals. This ensures that truck arrival patterns are evenly distributed, reducing peak-hour
congestion [
3
]. The implementation of a TAS varies based on the specific conditions of
each container terminal, particularly in terms of flexibility and the role of truck carriers.
Consequently, tailoring TAS designs to the unique operational context of terminals is crucial
to achieving tangible benefits [4].
From early studies that examined the advantages and disadvantages of TASs [
4
] to
recent research addressing disruptions [
5
] and collaborative schemes [
6
,
7
], TAS design has
been widely studied. Modern TAS platforms incorporate several advanced features, such
as appointment scheduling systems that allow trucking companies to book specific time
Mathematics 2025,13, 503 https://doi.org/10.3390/math13030503
Mathematics 2025,13, 503 2 of 25
slots for container pickups or drop-offs. This smooths gate operations and prevents sudden
spikes in arrivals. These systems also integrate real-time data from terminal operations,
trucking schedules, and traffic conditions, enabling dynamic schedule adjustments. Addi-
tionally, a TAS enhances communication and collaboration among stakeholders, including
terminal operators, trucking companies, and shippers, by employing optimization algo-
rithms to allocate time slots efficiently and balance truck arrivals with terminal capacity.
The reader is referred to Huynh et al. [
1
] and Abdelmagid et al. [
8
] for previous reviews of
truck appointment systems.
In practice, port environments utilizing TASs require consignees to book specific
time slots in advance for picking up inbound containers. Similarly, customers delivering
outbound containers must schedule appointments ahead of time. From a mathematical
perspective, a critical aspect of TAS design involves determining the appointment quota,
which refers to the number of truck appointments to schedule per time slot [
9
]. Objec-
tive functions in existing models often aim to minimize truck turnaround time, delays,
emissions, and energy consumption while maximizing yard equipment utilization [
8
]. Mod-
eling approaches such as queuing theory, mathematical programming, and computer-aided
simulations are frequently employed.
This review focuses on modeling TASs, with particular attention to the components of
analytical models. This paper makes three key contributions to the literature: (i) it conducts
a comprehensive review, analyzing and discussing TAS features, objective functions, deci-
sions, constraints, and solution methods; (ii) it introduces a taxonomy that classifies various
aspects of TASs, offering a deeper understanding of the current state of the problem; and
(iii) it examines recent trends to provide guidance for future research directions.
The remainder of this paper is organized as follows: Section 2outlines the formulation
of a basic TAS model. Section 3details the methodology employed in this study. Section 4
examines TAS modeling approaches and variants in solution algorithms. Section 5discusses
the findings and highlights potential directions for future research. Finally, Section 6
presents the conclusions of this study.
2. A Basic TAS Model
In this section, we present the formulation of a baseline problem representing the
simplest variant of a TAS. The optimization model is designed to identify the optimal
assignment of arriving trucks to time slots at a container terminal, with the objective of
minimizing congestion.
Indices:
•t: time slots (t= 1, 2, . . ., T).
•i: trucks (i= 1, 2, . . ., N).
Parameters
•di: demand (number of trucks) from trucking company i.
•ct: capacity of the container terminal during time slot t.
•pt: penalty cost for exceeding terminal capacity at time slot t.
Decision variables
•xit ∈{0, 1}: 1 if truck iis assigned to time slot t, 0 otherwise.
•yt≥0: congestion (number of trucks in operation) at time slot t.
Objective function
min
T
∑
t=1
pt·max(0, yt−ct)(1)
Mathematics 2025,13, 503 3 of 25
Subject to:
T
∑
t=1
xit =1∀i=1, . . . , N(2)
N
∑
i=1
xit ≤ct∀t=1, . . . , T(3)
yt=
N
∑
i=1
xit ∀t=1, . . . , T(4)
xit ∈{0, 1}∀i=1, . . . , N;t=1, . . . , T(5)
yt≥0∀t=1, . . . , T(6)
The objective function (1) minimizes congestion, where
max(0, yt−ct)
represents the
exceeding terminal capacity at time slot t. Constraint (2) ensures that each truck is assigned
to exactly one time slot. Constraint (3) imposes a terminal capacity limit, stipulating
that the number of trucks assigned to any time slot cannot exceed the terminal’s capacity.
Constraint (4)
defines the congestion term, which measures the total number of trucks
scheduled for a given time slot. Finally, constraints (5) and (6) specify the nature of the
decision variables.
3. Methodological Framework
This study conducts a literature review to summarize the existing research on modeling
and solution approaches for TASs and to provide a comprehensive understanding of the
state of the art and research needs in this area. This research adopts a content analysis
methodology [10,11], guided by the following steps:
Material collection: To gather relevant publications related to TAS models and algorithms in
ports and container terminals, an extensive search was conducted across digital resources,
including databases and publishers such as Google Scholar, ScienceDirect, Emerald, Inder-
science, Springer, Hindawi, and Taylor & Francis. The search utilized keywords such as
truck appointment systems, truck appointment scheduling, gate appointment system, truck
scheduling, vehicle booking systems, and time slot assignment. To enhance the reliability
of the review process, the full text of each paper was screened and included in this review
only if it met the following criteria: (i) papers published in 2008–2024; (ii) papers written in
English; (iii) exclusive focus on TASs in ports and container terminals; (iv) papers including
a mathematical models for TASs; and (v) exclusion of “grey” literature items, such as
textbooks, conference papers, monographs, doctoral dissertations, and book chapters.
Category selection and material evaluation: To define the formal aspects of the materials
for evaluation and summarize the review findings, a set of questions was developed (as
presented in Table 1) across four structural dimensions: (1) journals and publication trends;
(2) context and scope; (3) modeling and solution approach; and (4) data integration and
validation. The collected papers were systematically analyzed according to these structural
dimensions, enabling the identification of relevant insights and trends in the literature.
Mathematics 2025,13, 503 4 of 25
Table 1. Category and selection of structural dimensions.
I. Journals and Publication Trends II. Context and Scope
(1) Trend: How is the distribution of publications across
the period 2008–2024?
(2)
Journals: In which journals are such articles mainly
published?
(3)
Research topics: Which are the main research topics
within the TAS literature?
(4)
Scope: Is the focus on terminal operators, trucking
companies, port authority, or collaborative?
(5)
Context: Does the study focus on a single terminal,
multiple terminals, or a broader port area?
(6)
Contribution of the paper: Which is the main
contribution of the paper?
III. Modeling and Solution Approach IV. Data Integration and Validation
(7)
Modeling: What type of modeling approach is
proposed (e.g., mixed-integer programming,
stochastic programming, dynamic programming,
simulation–optimization framework)?
(8)
Aims and Objectives: What is being optimized (e.g.,
minimizing waiting times, maximizing resource
utilization, reducing emissions)?
(9)
Decisions: Which are the main decisions to make
(e.g., assign trucks to time slots, reschedule truck
appointments)?
(10)
Constraints: What operational and regulatory
constraints are incorporated (e.g., time windows,
resource availability, truck capacities)?
(11)
Algorithms: Which exact, metaheuristic, or hybrid
method is used to solve the problem?
(12)
Data Sources: Are real-world data or simulated data
used for validation?
(13) Validation: Is the model validated using simulations,
real-world case studies, or both?
(14)
Dynamic Features: Are the data deterministic or
uncertain? Is the model static or dynamic? Does the
model account for real-time data (e.g., live traffic
conditions, truck GPS updates)?
4. TAS Models and Algorithms: State of the Art
The implementation of TASs to mitigate hinterland delays and enhance terminal
velocity was adopted by ports in Asia, the United States, and Europe around 2005 [
12
].
However, to the best of our knowledge, the first formal formulation of the truck appoint-
ment scheduling problem was introduced by Rashidi and Tsang in 2006 [
13
]. The earliest
formal publications on TASs appeared in 2007, notably, the work of Giuliano and O’Brien [
4
],
who analyzed the outcomes of legislation enabling terminals to adopt gate appointments
as a strategy to reduce truck queues at the gates of the Ports of Los Angeles and Long
Beach. The publication of research articles presenting mathematical models for the truck
appointment scheduling problem began in 2008. A comprehensive review of the literature
identified 65 articles published between 2008 and 2024.
The literature database is shown in Table A1 of Appendix A.
4.1. Descriptive Analysis of Published Literature
The study of TASs has presented a considerable increase in the number of research
works in the last 17 years (see Figure 1). This resulted in several models, algorithms and
solution approaches in multiple TAS variants.
The reviewed literature indicates that most contributions are journal articles spanning
various fields, including transportation, operation research and management science, engi-
neering, environmental studies, decision science, and computer science. The journals with
the highest volume of TAS-related works include Transportation Research Part E,Computers
and Industrial Engineering,Flexible Services and Manufacturing Journal,Sustainability,Annals
of Operations Research,European Journal of Operational Research,International Journal of Produc-
Mathematics 2025,13, 503 5 of 25
tion Economics,Logistics,Maritime Economics and Logistics, and The Asian Journal of Shipping
and Logistics.
Mathematics 2025, 13, x FOR PEER REVIEW 5 of 24
Figure 1. Trend in the publication of articles proposing truck appointment scheduling models.
The reviewed literature indicates that most contributions are journal articles span-
ning various fields, including transportation, operation research and management sci-
ence, engineering, environmental studies, decision science, and computer science. The
journals with the highest volume of TAS-related works include Transportation Research
Part E, Computers and Industrial Engineering, Flexible Services and Manufacturing Journal, Sus-
tainability, Annals of Operations Research, European Journal of Operational Research, Interna-
tional Journal of Production Economics, Logistics, Maritime Economics and Logistics, and The
Asian Journal of Shipping and Logistics.
Figure 2 illustrates the annual volume of TAS-related research published in these
journals. The width of the horizontal bars represents the number of papers published per
year and journal, while the total number of papers published in each journal between 2008
and 2024 is displayed on the right side of the figure. Additionally, 25 papers were pub-
lished across 20 other journals, including the Journal of Marine Science and Engineering, In-
ternational Journal of Modelling and Simulation, Transportation Research Part B and D, Trans-
portation Research Records, and Maritime Policy and Management. Notably, the past two years
have seen an expansion in the range of journals publishing TAS-related research, reflect-
ing a growing diversification in the dissemination of studies within this field.
Figure 2. Distribution of articles per journal.
Journal Total
Transp. Res. E Logist. Transp. Rev. || || || |||| || || || || |||| 11
Co mp u t. I nd . En g . || |||| || 4
Flex. Serv. Manuf. J. |||| || || 4
Sus ta i n a b i l i ty- Ba se l |||| || || 4
Ann. Op er. Res. |||| || 3
Eur . J. Oper . Res . || || || 3
Int. J. Prod. Econ. |||| || 3
Log i s ti c s |||| || 3
Marit. Econ. Logist. || || || 3
Asian J. Shipp. Logist. || || 2
Other Journals || || || |||| || |||| || |||||| || |||||| |||||||| |||||||||| 25
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 201 9 2020 2021 2022 2023 2024
65
Figure 1. Trend in the publication of articles proposing truck appointment scheduling models.
Figure 2illustrates the annual volume of TAS-related research published in these
journals. The width of the horizontal bars represents the number of papers published per
year and journal, while the total number of papers published in each journal between 2008
and 2024 is displayed on the right side of the figure. Additionally, 25 papers were published
across 20 other journals, including the Journal of Marine Science and Engineering,International
Journal of Modelling and Simulation,Transportation Research Part B and D,Transportation
Research Records, and Maritime Policy and Management. Notably, the past two years have
seen an expansion in the range of journals publishing TAS-related research, reflecting a
growing diversification in the dissemination of studies within this field.
Mathematics 2025, 13, x FOR PEER REVIEW 5 of 24
Figure 1. Trend in the publication of articles proposing truck appointment scheduling models.
The reviewed literature indicates that most contributions are journal articles span-
ning various fields, including transportation, operation research and management sci-
ence, engineering, environmental studies, decision science, and computer science. The
journals with the highest volume of TAS-related works include Transportation Research
Part E, Computers and Industrial Engineering, Flexible Services and Manufacturing Journal, Sus-
tainability, Annals of Operations Research, European Journal of Operational Research, Interna-
tional Journal of Production Economics, Logistics, Maritime Economics and Logistics, and The
Asian Journal of Shipping and Logistics.
Figure 2 illustrates the annual volume of TAS-related research published in these
journals. The width of the horizontal bars represents the number of papers published per
year and journal, while the total number of papers published in each journal between 2008
and 2024 is displayed on the right side of the figure. Additionally, 25 papers were pub-
lished across 20 other journals, including the Journal of Marine Science and Engineering, In-
ternational Journal of Modelling and Simulation, Transportation Research Part B and D, Trans-
portation Research Records, and Maritime Policy and Management. Notably, the past two years
have seen an expansion in the range of journals publishing TAS-related research, reflect-
ing a growing diversification in the dissemination of studies within this field.
Figure 2. Distribution of articles per journal.
Journal Total
Transp. Res. E Logist. Transp. Rev. || || || |||| || || || || |||| 11
Co mp u t. I nd . En g . || |||| || 4
Flex. Serv. Manuf. J. |||| || || 4
Sus ta i n a b i l i ty- Ba se l |||| || || 4
Ann. Op er. Res. |||| || 3
Eur . J. Oper . Res . || || || 3
Int. J. Prod. Econ. |||| || 3
Log i s ti c s |||| || 3
Marit. Econ. Logist. || || || 3
Asian J. Shipp. Logist. || || 2
Other Journals || || || |||| || |||| || |||||| || |||||| |||||||| |||||||||| 25
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 201 9 2020 2021 2022 2023 2024
65
Figure 2. Distribution of articles per journal.
4.2. Modeling and Solution Approaches
The various methods used in the literature to handle the truck appointment scheduling
problem can be grouped into four large categories: the queueing models, the optimization
models, the simulation-based models, and the hybrid models (see Figure 3).
Traditional queuing and mathematical programming approaches focus on gate and
yard optimization. Queuing models are used to model gate and yard congestion dynamics
and aim to minimize truck waiting times and service delays [
14
–
17
]. These models are usu-
ally integrated with cost optimization models. Optimization models are used to minimize
Mathematics 2025,13, 503 6 of 25
waiting times, emissions, or operational costs, and to balance yard workloads and optimize
crane scheduling [
9
,
18
,
19
]. Simulation-based models are used to evaluate system perfor-
mance under real-world variability, and to test the robustness of TAS designs [
3
,
20
–
24
].
Hybrid models combining queuing, simulation, and optimization techniques between them
and with data analytics techniques, have been proposed to handle complex constraints,
uncertainty, and multi-objective scenarios [
25
–
29
]. Collaborative systems are modeled as
decentralized and agent-based frameworks accommodating multiple actors [
30
]. Emerging
trends include AI-driven and IoT-enabled solutions for real-time and predictive scheduling.
Mathematics 2025, 13, x FOR PEER REVIEW 6 of 24
4.2. Modeling and Solution Approaches
The various methods used in the literature to handle the truck appointment schedul-
ing problem can be grouped into four large categories: the queueing models, the optimi-
zation models, the simulation-based models, and the hybrid models (see Figure 3).
Traditional queuing and mathematical programming approaches focus on gate and
yard optimization. Queuing models are used to model gate and yard congestion dynamics
and aim to minimize truck waiting times and service delays [14–17]. These models are
usually integrated with cost optimization models. Optimization models are used to min-
imize waiting times, emissions, or operational costs, and to balance yard workloads and
optimize crane scheduling [9,18,19]. Simulation-based models are used to evaluate system
performance under real-world variability, and to test the robustness of TAS designs [3,20–
24]. Hybrid models combining queuing, simulation, and optimization techniques between
them and with data analytics techniques, have been proposed to handle complex con-
straints, uncertainty, and multi-objective scenarios [25–29]. Collaborative systems are
modeled as decentralized and agent-based frameworks accommodating multiple actors
[30]. Emerging trends include AI-driven and IoT-enabled solutions for real-time and pre-
dictive scheduling.
Figure 3. TAS models.
From the analysis of the collected papers, 23 types of objective functions, 19 types of
decision, and 20 types of constraints were identified (see Figure 4), on which the complex-
ity of the TAS problem depends. These elements are explicitly analyzed in the following
sections.
Figure 3. TAS models.
From the analysis of the collected papers, 23 types of objective functions, 19 types of de-
cision, and 20 types of constraints were identified (see Figure 4), on which the complexity of
the TAS problem depends. These elements are explicitly analyzed in the
following sections
.
Mathematics 2025, 13, x FOR PEER REVIEW 7 of 24
Figure 4. Characteristics of TAS models.
4.2.1. Decisions
The decision variables for scheduling truck appointments can be categorized into
four primary groups (see Figure 5): (i) scheduling and routing, (ii) appointment quotas,
(ii) resource utilization, and (iv) gate and yard operations.
Figure 5. Decisions of TAS models.
Scheduling and routing decisions focus on allocating truck and container operations
to time slots to optimize arrivals and departures, reduce gate congestion, and minimize
idle times [31–33]. By balancing workloads across time windows, these decisions aim to
enhance service rates. Rescheduling often requires dynamic updates and real-time data
integration [31]. Additionally, integrating scheduling and routing decisions improves net-
work-wide efficiency by minimizing empty runs, maximizing resource utilization, and
coordinating internal and external movements across terminals and hinterlands.
Appointment quota decisions focus on regulating truck appointments through quo-
tas to manage demand and prevent overloading [34,35]. By balancing truck flow and ca-
pacity across time periods, these decisions aim to avoid bolenecks and implement de-
mand-side control mechanisms, such as auction-based quotas.
Resource utilization decisions involve the allocation and efficient use of terminal re-
sources such as gates, equipment, and yard cranes [36–38]. The primary objective is to
maximize equipment throughput while minimizing operational costs and energy
Figure 4. Characteristics of TAS models.
Mathematics 2025,13, 503 7 of 25
4.2.1. Decisions
The decision variables for scheduling truck appointments can be categorized into
four primary groups (see Figure 5): (i) scheduling and routing, (ii) appointment quotas,
(iii) resource utilization, and (iv) gate and yard operations.
Mathematics 2025, 13, x FOR PEER REVIEW 7 of 24
Figure 4. Characteristics of TAS models.
4.2.1. Decisions
The decision variables for scheduling truck appointments can be categorized into
four primary groups (see Figure 5): (i) scheduling and routing, (ii) appointment quotas,
(ii) resource utilization, and (iv) gate and yard operations.
Figure 5. Decisions of TAS models.
Scheduling and routing decisions focus on allocating truck and container operations
to time slots to optimize arrivals and departures, reduce gate congestion, and minimize
idle times [31–33]. By balancing workloads across time windows, these decisions aim to
enhance service rates. Rescheduling often requires dynamic updates and real-time data
integration [31]. Additionally, integrating scheduling and routing decisions improves net-
work-wide efficiency by minimizing empty runs, maximizing resource utilization, and
coordinating internal and external movements across terminals and hinterlands.
Appointment quota decisions focus on regulating truck appointments through quo-
tas to manage demand and prevent overloading [34,35]. By balancing truck flow and ca-
pacity across time periods, these decisions aim to avoid bolenecks and implement de-
mand-side control mechanisms, such as auction-based quotas.
Resource utilization decisions involve the allocation and efficient use of terminal re-
sources such as gates, equipment, and yard cranes [36–38]. The primary objective is to
maximize equipment throughput while minimizing operational costs and energy
Figure 5. Decisions of TAS models.
Scheduling and routing decisions focus on allocating truck and container operations
to time slots to optimize arrivals and departures, reduce gate congestion, and minimize
idle times [
31
–
33
]. By balancing workloads across time windows, these decisions aim to
enhance service rates. Rescheduling often requires dynamic updates and real-time data
integration [
31
]. Additionally, integrating scheduling and routing decisions improves
network-wide efficiency by minimizing empty runs, maximizing resource utilization, and
coordinating internal and external movements across terminals and hinterlands.
Appointment quota decisions focus on regulating truck appointments through quotas
to manage demand and prevent overloading [
34
,
35
]. By balancing truck flow and capacity
across time periods, these decisions aim to avoid bottlenecks and implement demand-side
control mechanisms, such as auction-based quotas.
Resource utilization decisions involve the allocation and efficient use of terminal
resources such as gates, equipment, and yard cranes [
36
–
38
]. The primary objective is to
maximize equipment throughput while minimizing operational costs and energy consump-
tion. Gate and yard operation decisions address operational priorities at terminal gates and
yards, with the aim of minimizing processing delays [
5
,
35
,
39
]. They focus on streamlining
operations at entry and exit points of the terminal and within the yard, reducing truck idle
time and container rehandling costs. These decisions typically involve sequencing and
priority-based rules to enhance efficiency.
4.2.2. Objective Functions
The objective functions for scheduling truck appointments can be categorized into
four main groups (see Figure 6): (i) efficiency-oriented objectives, (ii) congestion and
flow management objectives, (iii) environmental sustainability objectives, and (iv) cost
minimization objectives.
Efficiency-oriented objectives focus on reducing waiting queue times, improving
turnaround times, maximizing resource utilization to enhance operational flow, enhance
efficiency by reducing operational bottlenecks, and improve customer satisfaction by
minimizing delays [
35
,
40
]. Congestion and flow management aims to minimize traffic con-
gestion and deviations from preferred arrival times, ensuring smoother operations
[9,40,41]
.
Environmental sustainability targets reducing truck emissions, energy consumption, and
empty trips, emphasizing eco-friendly practices, reducing the environmental impact of
port operations, and supporting compliance with emission regulations and sustainability
Mathematics 2025,13, 503 8 of 25
targets [
42
,
43
]. Lastly, cost minimization seeks to lower transportation costs and eliminate
unnecessary travel, aligning financial efficiency with environmental benefits, achieving
cost efficiency while maintaining service quality, and addressing economic impacts on both
terminals and external stakeholders [
7
,
30
,
40
]. Multi-objective functions often integrate
environmental, economic, and operational goals [
36
,
44
]. These classifications align with
terminal goals to improve efficiency, sustainability, and cost effectiveness.
Mathematics 2025, 13, x FOR PEER REVIEW 8 of 24
consumption. Gate and yard operation decisions address operational priorities at terminal
gates and yards, with the aim of minimizing processing delays [5,35,39]. They focus on
streamlining operations at entry and exit points of the terminal and within the yard, re-
ducing truck idle time and container rehandling costs. These decisions typically involve
sequencing and priority-based rules to enhance efficiency.
4.2.2. Objective Functions
The objective functions for scheduling truck appointments can be categorized into
four main groups (see Figure 6): (i) efficiency-oriented objectives, (ii) congestion and flow
management objectives, (iii) environmental sustainability objectives, and (iv) cost mini-
mization objectives.
Figure 6. Objective functions of TAS models.
Efficiency-oriented objectives focus on reducing waiting queue times, improving
turnaround times, maximizing resource utilization to enhance operational flow, enhance
efficiency by reducing operational bolenecks, and improve customer satisfaction by min-
imizing delays [35,40]. Congestion and flow management aims to minimize traffic con-
gestion and deviations from preferred arrival times, ensuring smoother operations
[9,40,41]. Environmental sustainability targets reducing truck emissions, energy con-
sumption, and empty trips, emphasizing eco-friendly practices, reducing the environmen-
tal impact of port operations, and supporting compliance with emission regulations and
sustainability targets [42,43]. Lastly, cost minimization seeks to lower transportation costs
and eliminate unnecessary travel, aligning financial efficiency with environmental bene-
fits, achieving cost efficiency while maintaining service quality, and addressing economic
impacts on both terminals and external stakeholders [7,30,40]. Multi-objective functions
often integrate environmental, economic, and operational goals [36,44]. These classifica-
tions align with terminal goals to improve efficiency, sustainability, and cost effectiveness.
4.2.3. Constraints
The constraints for scheduling truck appointments can be categorized into four pri-
mary groups: (i) capacity constraints, (ii) operational constraints, (iii) fairness and collab-
oration constraints, and (iv) environmental and sustainability objectives (see Figure 7).
Figure 6. Objective functions of TAS models.
4.2.3. Constraints
The constraints for scheduling truck appointments can be categorized into four pri-
mary groups: (i) capacity constraints, (ii) operational constraints, (iii) fairness and collabo-
ration constraints, and (iv) environmental and sustainability objectives (see Figure 7).
Mathematics 2025, 13, x FOR PEER REVIEW 9 of 24
Figure 7. Constraints of TAS models.
Capacity constraints ensure that terminal operations remain within the physical and
operational limits of available resources [45,46]. Their primary aim is to prevent resource
overutilization, manage demand fluctuations, and maintain system stability. Typically
modeled as upper-bound constraints, they play a critical role in maintaining operational
efficiency. Operational constraints address the physical feasibility, resource limitations,
temporal alignment, and coordination requirements of truck appointment systems
[47,48]. The objective is to optimize terminal performance while ensuring operations are
practical, equitable, and efficient. Fairness and collaboration constraints focus on equitable
resource allocation and scheduling across stakeholders, including terminals, trucking
companies, and drayage firms [49,50]. The aim is to foster collaboration and ensure a fair
distribution of appointment slots and other resources. Environmental and sustainability
constraints align terminal operations with environmental goals and regulatory standards
[43,51,52]. The aim is to minimize the environmental footprint of terminal activities by
reducing emissions and ensuring compliance with sustainability regulations.
4.2.4. Input Parameters
The input parameters for scheduling truck appointments can be classified into four
main categories: (i) truck arrival parameters, (ii) terminal and resource capacity parame-
ters, (iii) environmental and emission parameters, and (iv) scheduling, time and cost pa-
rameters (see Figure 8).
Truck arrival parameters provide data on the timing, paerns, and preferences asso-
ciated with truck operations [53]. Their primary aim is to model and predict truck arrival
behaviors to optimize scheduling and balance truck inflow, thereby minimizing conges-
tion and waiting times. Terminal and resource capacity parameters reflect the physical
and operational capabilities of terminals [5,39]. Their objectives include assessing resource
limits, ensuring efficient alignment of resource allocation with demand, optimizing yard
operations and container handling, and enhancing stacking, retrieval, and container
movement efficiency. Environmental and emission parameters quantify the environmen-
tal impact of terminal and truck operations [54–56]. The aim is to evaluate and minimize
the environmental footprint of terminal activities while supporting compliance with sus-
tainability and regulatory requirements. Scheduling, time, and cost parameters focus on
optimizing cost efficiency while meeting operational constraints [29,57,58]. They aim to
ensure fair and balanced appointment slot allocation, support equitable decision-making,
enhance stakeholder satisfaction, and foster collaboration among terminals, trucking com-
panies, and other stakeholders.
Figure 7. Constraints of TAS models.
Capacity constraints ensure that terminal operations remain within the physical and
operational limits of available resources [
45
,
46
]. Their primary aim is to prevent resource
overutilization, manage demand fluctuations, and maintain system stability. Typically
modeled as upper-bound constraints, they play a critical role in maintaining operational
efficiency. Operational constraints address the physical feasibility, resource limitations,
temporal alignment, and coordination requirements of truck appointment systems [
47
,
48
].
The objective is to optimize terminal performance while ensuring operations are practical,
equitable, and efficient. Fairness and collaboration constraints focus on equitable resource
Mathematics 2025,13, 503 9 of 25
allocation and scheduling across stakeholders, including terminals, trucking companies,
and drayage firms [
49
,
50
]. The aim is to foster collaboration and ensure a fair distribution of
appointment slots and other resources. Environmental and sustainability constraints align
terminal operations with environmental goals and regulatory standards [
43
,
51
,
52
]. The aim
is to minimize the environmental footprint of terminal activities by reducing emissions and
ensuring compliance with sustainability regulations.
4.2.4. Input Parameters
The input parameters for scheduling truck appointments can be classified into four
main categories: (i) truck arrival parameters, (ii) terminal and resource capacity parameters,
(iii) environmental and emission parameters, and (iv) scheduling, time and cost parameters
(see Figure 8).
Mathematics 2025, 13, x FOR PEER REVIEW 10 of 24
Additionally, to enhance model robustness and improve resilience against disrup-
tions, published TAS models incorporate variability and uncertainty related to yard ca-
pacity, travel and loading times, no-show probabilities, and truck arrival paerns.
Figure 8. Input parameters of TAS models.
4.2.5. Solution Approaches
Initially, TAS models were predominantly solved using commercial optimization
solvers, and priority rule-based heuristics. However, the increasing complexity of these
problems and advancements in solution techniques led to the adoption of a broader range
of methodologies. Notable approaches include queuing-theory-based models for dynamic
arrival paerns [44], exact algorithms, and heuristic or metaheuristic solutions such as
genetic algorithms and auction-based mechanisms to handle dynamic and complex sce-
narios [59–61]. The integration of mathematical programming with non-stationary and
vacation queuing models has significantly improved the estimation of truck waiting times
and service rates, facilitating more responsive TAS designs [62]. Additionally, decentral-
ized systems utilizing agent-based approaches enable realistic simulations of interactions
between drayage and terminal operators [61,63,64].
Optimization models in TAS can be classified into exact and metaheuristic ap-
proaches. Exact methods include techniques such as the Frank–Wolfe method and branch-
and-price heuristics. Metaheuristic algorithms encompass Genetic Algorithms (GAs), hy-
brid GA-Simulated Annealing, Tabu Search (TS), Variable Neighborhood Search (VNS),
improved VNS (IVNS), and Hybrid GA-VNS combinations. Robust and stochastic opti-
mization models are tackled using two-stage robust optimization with column-and-row
generation algorithms or stochastic assignment heuristics integrated with discrete choice
modeling. Simulation-based optimization approaches embed simulation within heuristic
methods or combine discrete-event simulation with optimization algorithms like GA. Fur-
thermore, agent-based models employ auction-based mechanisms for decentralized
scheduling or simulate collaborative systems to evaluate interactions and performance.
5. Discussion and Further Research Directions
From the analysis of the reviewed literature, we observe that the modeling ap-
proaches for TAS optimization have evolved over the years, reflecting the increasing com-
plexity of port operations, the growing emphasis on environmental and operational effi-
ciency, and advancements in emerging technologies aimed at enhancing data integration
and automation. To provide a clearer understanding of these developments and their pro-
gression, we classify the TAS models into four distinct generations (see Table 2).
Figure 8. Input parameters of TAS models.
Truck arrival parameters provide data on the timing, patterns, and preferences associ-
ated with truck operations [
53
]. Their primary aim is to model and predict truck arrival
behaviors to optimize scheduling and balance truck inflow, thereby minimizing congestion
and waiting times. Terminal and resource capacity parameters reflect the physical and op-
erational capabilities of terminals [
5
,
39
]. Their objectives include assessing resource limits,
ensuring efficient alignment of resource allocation with demand, optimizing yard opera-
tions and container handling, and enhancing stacking, retrieval, and container movement
efficiency. Environmental and emission parameters quantify the environmental impact
of terminal and truck operations [
54
–
56
]. The aim is to evaluate and minimize the envi-
ronmental footprint of terminal activities while supporting compliance with sustainability
and regulatory requirements. Scheduling, time, and cost parameters focus on optimizing
cost efficiency while meeting operational constraints [
29
,
57
,
58
]. They aim to ensure fair
and balanced appointment slot allocation, support equitable decision-making, enhance
stakeholder satisfaction, and foster collaboration among terminals, trucking companies,
and other stakeholders.
Additionally, to enhance model robustness and improve resilience against disruptions,
published TAS models incorporate variability and uncertainty related to yard capacity,
travel and loading times, no-show probabilities, and truck arrival patterns.
4.2.5. Solution Approaches
Initially, TAS models were predominantly solved using commercial optimization
solvers, and priority rule-based heuristics. However, the increasing complexity of these
Mathematics 2025,13, 503 10 of 25
problems and advancements in solution techniques led to the adoption of a broader range
of methodologies. Notable approaches include queuing-theory-based models for dynamic
arrival patterns [
44
], exact algorithms, and heuristic or metaheuristic solutions such as
genetic algorithms and auction-based mechanisms to handle dynamic and complex sce-
narios [
59
–
61
]. The integration of mathematical programming with non-stationary and
vacation queuing models has significantly improved the estimation of truck waiting times
and service rates, facilitating more responsive TAS designs [
62
]. Additionally, decentral-
ized systems utilizing agent-based approaches enable realistic simulations of interactions
between drayage and terminal operators [61,63,64].
Optimization models in TAS can be classified into exact and metaheuristic approaches.
Exact methods include techniques such as the Frank–Wolfe method and branch-and-price
heuristics. Metaheuristic algorithms encompass Genetic Algorithms (GAs), hybrid GA-
Simulated Annealing, Tabu Search (TS), Variable Neighborhood Search (VNS), improved
VNS (IVNS), and Hybrid GA-VNS combinations. Robust and stochastic optimization
models are tackled using two-stage robust optimization with column-and-row generation
algorithms or stochastic assignment heuristics integrated with discrete choice modeling.
Simulation-based optimization approaches embed simulation within heuristic methods
or combine discrete-event simulation with optimization algorithms like GA. Furthermore,
agent-based models employ auction-based mechanisms for decentralized scheduling or
simulate collaborative systems to evaluate interactions and performance.
5. Discussion and Further Research Directions
From the analysis of the reviewed literature, we observe that the modeling approaches
for TAS optimization have evolved over the years, reflecting the increasing complexity of
port operations, the growing emphasis on environmental and operational efficiency, and
advancements in emerging technologies aimed at enhancing data integration and automa-
tion. To provide a clearer understanding of these developments and their progression, we
classify the TAS models into four distinct generations (see Table 2).
The earlier contributions, categorized as the first generation of TAS models, present
foundational approaches focused on optimizing truck turn times and crane utilization
using deterministic and queuing-based formulations. These formulations are characterized
by deterministic inputs, such as fixed arrival rates and static service times, with limited con-
sideration of variability. The models predominantly employed linear programming, integer
programming [
14
], and queuing theory [
15
,
18
] to minimize operational bottlenecks and
utilize simulations to validate and evaluate the impacts of appointment systems
[24,25,44]
.
These early models were relatively simple, often assuming static or deterministic inputs
and exhibiting limited ability to handle real-world uncertainties, such as late arrivals or
no-shows.
The second generation of TAS models demonstrates greater attention to integrating
environmental objectives [
28
,
57
], such as emission reduction, with traditional operational
goals; proposing collaborative frameworks [
48
,
49
] to promote coordination between ter-
minals and trucking companies for optimized scheduling; and expanding the scope of
TAS decisions to consider yard and drayage operations to coordinate truck arrivals with
container relocations and retrievals [
65
–
67
] and matching inbound and outbound contains
to facilitate double moves and minimize empty trips [
19
]. The complexity of the models
necessitated an increased use of heuristics and metaheuristics to solve complex problems.
However, the increased model complexity posed challenges for real-world implementation.
These models often lacked the ability to dynamically adapt to real-time changes in truck
arrivals or terminal operations. Furthermore, while collaboration was introduced, models
typically addressed yard and gate operations separately rather than holistically.
Mathematics 2025,13, 503 11 of 25
The third generation of TAS models addresses uncertainty in operational conditions,
such as dynamic truck arrivals, stochastic travel times, and real-time disruptions. These
models are characterized by the introduction of dynamic and stochastic approaches [
68
],
the use of agent-based simulations to explore decentralized and centralized scheduling [
30
],
and the incorporation of real-time decision-making capabilities [
51
]. This generation
accounted for uncertainties in truck arrivals, travel times, and service times, making the
models more realistic. Agent-based simulations enabled the exploration of decentralized
and centralized scheduling approaches, offering valuable new insights. Additionally,
this generation began to cohesively integrate yard operations, gate operations, and truck
appointment systems. Despite these advances, challenges persisted; for example, dynamic
and stochastic models required significant computational resources, limiting their scalability.
Furthermore, real-time deployment remained difficult due to the need for high-quality,
real-time data and advanced infrastructure, and the complexity of these models made them
less accessible to terminal operators without specialized expertise.
The fourth generation of TAS models leverages artificial intelligence, multi-agent
systems, and advanced optimization algorithms to handle large-scale, real-time, and decen-
tralized scenarios. These models capitalize on auction-based mechanisms and decentralized
coordination [
61
], the integration of machine learning algorithms for predictive and adap-
tive optimization [
31
,
69
], and advanced algorithms such as branch-and-price heuristics [
70
]
and robust optimization frameworks to handle uncertainty [
35
,
43
,
61
,
71
]. These models
achieve fully integrated gate, yard, and crane operations, addressing congestion, emis-
sions, and resource utilization simultaneously. However, these models rely heavily on
high-quality, real-time data, which may not be available in all terminal settings, and re-
quire advanced technological infrastructure, such as IoT devices and cloud-based systems,
for successful implementation. Additionally, the integration of intelligent systems and
decentralized approaches posed considerable challenges for practical deployment, and the
adoption of advanced technologies and infrastructure upgrades incurred high initial costs.
Table 2. Classification of TAS models.
Generation Characteristics Advantages Limitations Related Papers
First Generation Deterministic,
foundational models
for gate optimization.
Simple, foundational
models;
computationally
efficient; introduced
TAS concepts.
Deterministic; limited
scope; no real-time or
stochastic
considerations;
scalability issues.
Guan and Liu [14],
Namboothiri and
Erera [18], Huynh [20],
Zhao and
Goodchild [21],
Esmemr et al. [22],
Huynh and
Walton [25].
Second Generation
Emphasis on
environmental and
collaborative
optimization.
Integrated
environmental and
collaborative objectives;
advanced heuristics;
expanded scope.
Computational
complexity; limited
real-time adaptability;
partial yard–gate
integration.
Schulte et al. [7], Do
et al. [28], Zhang
et al. [44], Phan and
Kim [49], Chen and
Jiang [57], Torkjazi
et al. [63], Azab and
Morita [65].
Third Generation
Dynamic and stochastic
models with real-time
decision-making.
Dynamic and stochastic
models; real-time
adaptability;
agent-based
simulations;
synchronization.
High computational
demand;
implementation
barriers; complexity for
practitioners.
Li et al. [5], Riaventin
et al. [30], Xu et al. [51],
Stoop et al. [68].
Fourth Generation
Intelligent systems
leveraging AI, IoT, and
robust optimization.
Intelligent systems;
decentralized
coordination; robust
and holistic integration;
sustainability.
Data dependency; high
infrastructure
requirements; cost and
implementation
complexity.
da Silva et al. [31], Li
et al. [35], Hoxha
et al. [43], Wang
et al. [70], Wasesa
et al. [71].
Mathematics 2025,13, 503 12 of 25
The key elements that define the contribution and scope of a TAS model include
quotas and time slot considerations, yard and drayage operations, sustainability and envi-
ronmental objectives, uncertainty handling, collaborative and real-time decision-making
capabilities, appointment rescheduling, and the integration of advanced technologies.
The primary aim of TAS models is to optimize the allocation of time slots for ex-
ternal trucks to alleviate gate congestion [
3
,
40
]. Additionally, TAS models may consider
yard
[53,72]
and drayage operations [
16
,
36
,
70
], synchronizing external truck arrivals with
yard crane schedules to minimize truck delays and streamline terminal operations. Sus-
tainability is another feature considered in TAS models [
37
,
71
]. These models integrate
emission reduction a core objective, targeting CO
2
and other pollutants associated with
idling trucks and inefficient yard operations. Uncertainty handling is also a modeling
feature of TAS models [
35
]. These models address stochastic elements, including early
arrivals, no-shows, travel delays, and operational disruptions, to enhance scheduling ro-
bustness. Methods such as overbooking mechanisms and robust optimization approaches
are often employed to mitigate these uncertainties [
41
,
68
,
71
]. The option of collaborative
decision-making and the optimization of multiple objectives, such as minimizing costs,
emissions, and congestion while maximizing throughput and efficiency, are special features
considered in some TAS models. Finally, the integration of advanced technologies to predict
emissions, gather real-time data, and facilitate the dynamic rescheduling of appointments
and disruption management [
31
,
61
,
69
,
73
] represents a recent advancement in TAS model-
ing. Table 3provides a comparison of these specific modeling features, highlighting the
progression from foundational deterministic models to advanced intelligent systems.
Table 3. Comparison of modeling features within the four generations of TAS models.
Modeling Feature First Generation Second Generation Third Generation Fourth Generation
Quotas and Time Slot
Focused primarily on
static quotas and
deterministic time slots.
Early models lacked
flexibility in adjusting
quotas dynamically.
Introduced
time-window
adjustments for
improved scheduling
but remained mostly
static. Collaborative
quota adjustments
began emerging.
Time slots became
dynamic, with models
incorporating demand
variability and
operational constraints.
Quota adjustments
linked to real-time
conditions.
Fully dynamic quota
and time slot
management with
adaptive allocation
using AI and machine
learning for
optimization.
Auction-based systems
emerged.
Yard Operations
Minimal focus on yard
operations. Models
were limited to gate
optimization and truck
turn times.
Began integrating yard
operations, such as
crane scheduling, but
often addressed yard
and gate operations
separately.
Comprehensive
integration of yard and
gate operations,
including
synchronization of yard
crane and truck
movements.
Holistic yard and gate
integration. Advanced
algorithms handle
crane scheduling,
container relocations,
and yard throughput
optimization. IoT
enables real-time
updates.
Drayage Operations
Limited consideration
of drayage operations.
Focused on truck turn
times at the gate.
Introduced basic
collaboration between
terminals and trucking
companies to optimize
drayage schedules.
Significant focus on
drayage operations
with dynamic routing,
real-time truck
scheduling, and
decentralized systems.
Full integration of
drayage operations
with TAS, utilizing
multi-agent systems,
AI, and predictive
analytics for efficient
scheduling.
Mathematics 2025,13, 503 13 of 25
Table 3. Cont.
Modeling Feature First Generation Second Generation Third Generation Fourth Generation
Sustainability and
Environment
No explicit focus on
sustainability or
emissions reduction.
Introduced
sustainability
objectives, such as
emissions reduction,
alongside operational
goals.
Strong emphasis on
sustainability, with
models optimizing
truck arrival patterns to
reduce emissions and
idle times.
Sustainability is a
central focus, with
advanced systems
optimizing emissions,
energy consumption,
and overall
environmental impact.
Uncertainty
Deterministic models
with limited ability to
handle uncertainties
such as late arrivals or
no-shows.
Began addressing
uncertainty with
stochastic elements in a
few models, though
still limited in scope.
Comprehensive
treatment of
uncertainty in truck
arrivals, travel times,
and operational
disruptions using
stochastic and dynamic
models.
Advanced uncertainty
handling with robust
optimization,
predictive analytics,
and real-time
adjustments for
dynamic scenarios.
Collaborative Decisions
Models focused on
individual terminal
optimization.
Collaboration between
terminals and trucking
companies emerged,
focusing on schedule
coordination.
Enhanced
collaboration, with
agent-based systems
allowing for
decentralized
decision-making
among stakeholders.
Decentralized
collaboration is
supported by
multi-agent systems
and auction-based
frameworks, enabling
stakeholder alignment
and flexibility.
Real-Time Decisions No real-time
capabilities.
Limited real-time
adaptability. Few
models included
dynamic adjustments
based on near-term
data.
Real-time
decision-making
became a key feature,
enabled by dynamic
models and
agent-based systems.
Advanced real-time
capabilities using IoT,
cloud computing, and
AI for continuous
optimization and
decision-making.
Appointment
Rescheduling
No rescheduling
capabilities.
Appointments were
static and fixed once
scheduled.
Basic rescheduling
capabilities began to
emerge, often requiring
manual intervention.
Rescheduling became
dynamic, accounting
for real-time
disruptions and delays
using advanced
algorithms.
Fully dynamic
rescheduling based on
real-time data,
leveraging AI and IoT
to optimize changes
and minimize
disruptions.
Technology integration
Limited use of
technology. Relied on
traditional
optimization methods
(e.g., linear and integer
programming).
Early use of heuristics
and metaheuristics
(e.g., Genetic
Algorithms).
Adoption of
agent-based
simulations and
predictive analytics.
Advanced integration
of AI, machine learning,
IoT, and auction-based
systems. Real-time data
feeds and predictive
algorithms optimize
operations.
Despite significant progress, future research should address several critical areas.
Stakeholder integration is needed to create holistic frameworks that unify the perspectives
of terminal operators, drayage firms, and port authorities. Models must also enhance
scalability and real-time adaptability to manage high-traffic terminals and dynamic demand
conditions. The digital transformation of TASs using IoT, AI, and blockchain technologies
presents opportunities to enhance data integration and automation. Lastly, the exploration
of sustainability beyond emissions, such as noise pollution and community well-being,
remains an underexplored yet vital area for future work.
Mathematics 2025,13, 503 14 of 25
6. Conclusions
The development of advanced optimization models for truck appointment scheduling
has significantly enhanced container terminal operations by addressing efficiency, revenue
maximization, and risk management. Employing methodologies like robust optimization,
stochastic dynamic programming, mixed-integer programming, and hybrid heuristics,
these models effectively manage uncertainty and interdependent operational decisions.
Through real-world case studies and simulation-based evaluations, researchers have pro-
vided practical insights for terminal managers, demonstrating the potential to improve
operational efficiency, reduce costs, and mitigate risks. These efforts underscore the impor-
tance of combining mathematical modeling with empirical validation to meet the complex
demands of modern terminal operations.
Collectively, the state-of-the-art TAS models reflect substantial progress in address-
ing challenges such as disruptions, uncertainty, emissions, and dynamic scheduling. By
integrating truck scheduling with yard equipment allocation and employing innovative
frameworks, such as vessel-dependent time windows and advisory-based systems, recent
studies highlight strategies to optimize terminal performance. Furthermore, advancements
in TAS models emphasize multi-stakeholder collaboration, robust optimization techniques,
and sustainability-focused approaches to reduce congestion, emissions, and operational
costs while enhancing overall terminal efficiency.
The evolution of TAS modeling approaches reveals a clear progression in sophisti-
cation, scope, and technological integration. Early generations laid the foundation for
operational efficiency but lacked considerations such as uncertainty, real-time adaptability,
and environmental sustainability. Subsequent generations progressively addressed these
limitations by incorporating advanced features, including dynamic scheduling, collabora-
tive decision-making, and sustainability objectives. The fourth generation represents the
pinnacle of current advancements, leveraging artificial intelligence, the IoT, and robust
optimization frameworks to achieve holistic and sustainable terminal operations.
Looking ahead, the TAS literature presents significant opportunities for further in-
novation. Incorporating cutting-edge technologies such as AI, IoT, and blockchain could
enable real-time decision-making, enhance scalability, and improve system resilience. Fu-
ture research should prioritize the integration of multi-modal operations and adaptive
systems to address the growing complexity of port ecosystems. This paper provides a solid
foundation for a comprehensive understanding of TAS models, identifying critical gaps
and highlighting opportunities to expand the scope of TAS applications. Ultimately, these
advancements aim to foster efficiency, resilience, and environmental sustainability in global
terminal operations.
Author Contributions: Conceptualization, J.M.-O. and M.D.G.; methodology, J.M.-O., M.D.G. and
M.V.; formal analysis, J.M.-O. and M.D.G.; investigation, M.D.G. and M.V.; data curation, M.V.;
writing—original draft preparation, J.M.-O.; writing—review and editing, J.M.-O., M.D.G. and M.V.;
visualization, M.D.G. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: The raw data supporting the conclusions of this article will be made
available by the authors on request.
Conflicts of Interest: The authors declare no conflicts of interest.
Mathematics 2025,13, 503 15 of 25
Appendix A
Table A1. Selected research articles on truck appointment scheduling literature.
Author
Year
Model * Data Source Validation Framework Main Contribution
Huynh and
Walton [25]
2008
OPT + SIM
Not explicitly
provided but
references
terminals like
Evergreen Los
Angeles Terminal
and Long Beach
Simulations to test the
effectiveness of the
proposed system under
various arrival scenarios,
including late arrivals and
no-shows
Introduces a methodology
that combines a
mathematical model and
simulation to optimize truck
appointment systems
Namboothiri and
Erera [18]
2008
OPT
Simulated data
based on U.S. port
operations
Computational experiments
using test instances
designed to simulate
realistic drayage operations.
These tests explore the
impact of slot capacity
variations on fleet
productivity and customer
service levels
Develops an integer
programming-based
framework to optimize
drayage fleet operations
under appointment-based
port access control systems.
The study highlights how
increased slot capacities
improve fleet productivity,
providing insights into the
impact of appointment
systems on drayage firms
Guan and Liu [14]
2009
QUE U.S. marine
terminal data
Case study using field data
collected from marine
terminal gate operations.
Sensitivity analysis is
conducted to assess the
impact of appointment caps
and arrival rates on system
performance
Proposes a multi-server
queuing model to optimize
gate appointment systems,
balancing terminal
operating costs and truck
waiting costs. The study
demonstrates that
appointment systems
significantly reduce
congestion and associated
costs at terminal gates
Huynh [20]
2009
SIM
Simulated terminal
data
Evaluates different
scheduling rules under
various operational
scenarios, showing clear
improvements in resource
utilization and truck turn
times
The study provides
evidence that properly
designed appointment
systems improve yard crane
utilization and reduce truck
turn times in grounded
operations
Zhao and
Goodchild [21]
2010
SIM
Simulated data
based on container
yard setups
Simulation experiments to
model different levels of
truck arrival information
and container bay
configurations
Demonstrates how
improved truck arrival
information can reduce
container rehandling in
terminal yards, enhancing
crane productivity
Esmemr et al. [22]
2010
SIM Turkish port
Case study at a Turkish port
to analyze how varying the
number of terminal trucks
impacts environmental and
operational performance
Proposes a simulation-based
approach to optimize the
number of terminal trucks
required for operations,
integrating lean and green
concepts
Mathematics 2025,13, 503 16 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Kiani et al. [15]
2010
QUE Simulated data
Simulates various gate
configurations and arrival
patterns
Develops a queuing-based
simulation methodology to
address truck congestion
and reduce turnaround
times at marine terminal
gates. The study provides
practical insights into
improving gate operations
and mitigating queue
lengths
Huynh and
Walton [23]
2011
SIM
Simulated terminal
data
Simulation experiments to
evaluate the impact of
appointment caps and
scheduling rules on gate
throughput and resource
utilization
Analyze the effects of TAS
on gate throughput and
operational efficiency. The
paper introduces scheduling
rules and their impact on
reducing resource idling
and truck turn times
Sharif et al. [26]
2011
DAN + SIM --- Simulates experiments with
real-time data scenarios
Highlights how real-time
information, coupled with
predictive strategies by
truck dispatchers, can
stabilize truck arrivals and
reduce gate queuing
van Asperen
et al. [53]
2013
SIM An automated
container terminal
Testing different scenarios
of truck arrival
announcements,
quantifying crane idle time
and reshuffling efficiency
Demonstrates the TAS’s
ability to optimize yard
crane utilization, albeit with
challenges in
implementation
Dekker et al. [72]
2013
QUE
Rotterdam
Maasvlakte
terminals
A case study quantifying
waiting time and emission
reductions
Proposes a Chassis
Exchange Terminal concept
that mitigates gate
congestion and enhances
throughput, focusing on
operational off-peak hours
Zhao and
Goodchild [2]
2013
SIM + QUE ---
Analytical framework
demonstrating improved
efficiency in yard crane
productivity and reduced
truck delays
Validates the operational
benefits of using truck
arrival information to
optimize yard operations
Zhang et al., [55]
2013
OPT Tianjin terminal
Case study demonstrating
significant reductions in
turnaround times
Validates TAS as a viable
tool for congestion
management and reduce
truck turn time at container
terminals using optimized
appointment quotas
Chen et al. [59]
2013
OPT Northern China
terminal
Case study from a Northern
China terminal
Implement
vessel-dependent time
windows to control truck
arrivals and reduce
congestion at terminal gates
and highlight significant
reductions in gate
congestion and improved
resource allocation
Chen et al. [62]
2013
QUE Port of Vancouver Case study
Demonstrates dynamic TAS
improves flexibility and
reduces congestion
effectively
Mathematics 2025,13, 503 17 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Chen et al. [42]
2013
OPT + QUE --- Validated through
numerical examples
Proves that minor shifts in
truck arrivals can
significantly reduce
emissions and congestion
Islam et al. [54]
2013
OPT Port of New York
and New Jersey
Case study using publicly
available port operation
data
Reengineers the truck
hauling process at container
terminals by introducing a
truck-sharing arrangement
to minimize empty trips and
improve transport capacity
Nossack and
Pesch [60]
2013
OPT --- Computational experiments
on synthetic datasets
Highlights efficient
handling of pre- and
end-haulage to reduce
operational costs in
intermodal transportation
Zehendner and
Feillet [38]
2014
OPT ---
Real-world data
demonstrate reductions in
delays and improved
multimodal service quality
Evaluates the benefits of a
TAS on multimodal terminal
service quality, gained by
coordinating inland
transport and yard resource
allocation
Phan and Kim [6]
2015
OPT ---
Numerical simulations
validating system efficiency
under different scenarios
Develops a decentralized
negotiation process for
scheduling truck arrivals at
container terminals
Phan and Kim [49]
2016
OPT ---
Numerical experiments to
assess system robustness
under operational
uncertainties
Introduces a collaborative
truck appointment system,
integrating trucking
company operations with
terminal schedules
Chen and
Jiang [57]
2016
OPT Chinese container
terminals
Numerical experiments
with real-world scenarios
Demonstrates the
effectiveness of
vessel-dependent time
windows in reducing gate
congestion
Do et al. [28]
2016
SIM
Simulated terminal
data
Numerical experiments to
analyze emission reductions
Demonstrates the impact of
operational control
mechanisms on emission
reduction and efficiency
Schulte et al. [7]
2017
OPT ---
A real-world scenario,
demonstrating effective
reductions in emissions and
costs through collaboration
Advocates for collaborative
TAS designs, showing
significant environmental
and economic benefits for
ports and trucking
companies
Ramírez-Nafarrate
et al. [24]
2017
SIM Port of Arica Case study
Evaluates the impact of a
truck appointment system
(TAS) on yard efficiency in
port terminals
Gracia et al. [3]
2017
SIM Port of San
Antonio Case study
Demonstrates that lane
segmentation and optimal
booking levels significantly
reduce congestion and
emissions at the terminal
gates
Mathematics 2025,13, 503 18 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Torkjazi et al. [63]
2018
OPT U.S. container
terminals
Numerical analysis of
real-world scenarios
Proposes a TAS considering
drayage truck tours to
minimize costs for terminal
and drayage operations
Li et al. [5]
2018
SIM ---
Sensitivity analysis of
strategies under disruption
scenarios at container
terminals
Introduces practical
resilience strategies to
manage typical disruptions
effectively, improving
operational stability and
sustainability
Zhang et al. [44]
2019
QUE --- Numerical experiments
with sensitivity analysis
Improves service efficiency
by aligning truck arrivals
with crane operations,
reducing gate and yard
congestion
Yi et al. [32]
2019
OPT ---
Empirical data from a port
terminal are used for
validation, demonstrating
improved scheduling
efficiency
Effective in balancing
terminal workloads and
minimizing
congestion-related delays
Zeng et al. [39]
2019
OPT ---
Numerical experiments
validate the model, showing
significant reductions in
container rehandling
Provides tools for terminals
to enhance yard efficiency
and reduce delays by
optimizing container
rehandling and pickup
sequences using partial
truck arrival information
Fan et al. [58]
2019
OPT Chinese container
terminals Numerical examples
Addresses truck scheduling
under TAS to minimize
carbon emissions and
operational and proves
low-carbon scheduling
improves operational
efficiency and sustainability
Ma et al. [40]
2019
OPT Tianjin Port
Numerical experiments
demonstrating emission
reductions
Demonstrates the
effectiveness of
vessel-dependent time
windows in congestion and
emission management
Caballini et al. [19]
2020
DAN + OPT
PSA—Genova,
Italy and Altamira
terminal, Mexico
Case studies on two
real-world terminals, and an
experimental design using
factorial analysis to evaluate
the impacts of various
clustering and optimization
configurations
Offers a robust TAS
methodology combining
clustering and optimization
to minimize empty truck
trips and congestion,
applicable across terminals
globally
Mar-Ortiz et al. [9]
2020
OPT Mexican container
terminal
Real case study at a Mexican
container terminal
Proposes an
optimization-based DSS to
determine the appointment
quota for each time slot on a
one-day planning horizon,
within a container terminal
working on a TAS
environment
Mathematics 2025,13, 503 19 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Azab et al. [27]
2020
OPT + SIM
Alexandria
Container
Terminal
Validated against artificial
instances inspired by
real-world data
Develop a simulation-based
optimization approach for
collaborative scheduling of
external trucks in container
terminals and highlights the
importance of collaborative
scheduling and IoT-based
frameworks for improved
terminal performance
Li et al. [36]
2020
OPT Dalian Maritime
Terminal Numerical experiments
Highlights the efficiency of
integrated quota allocation
and crane scheduling in
reducing congestion
Im et al. [64]
2021
OPT Generic large-scale
container terminals
Simulated case study
highlighting cooperative
scenarios
Cooperation models
between transport
companies and terminal
operators reduce congestion
and improve scheduling
efficiency
Xu et al. [51]
2021
OPT ---
Simulation-based
experiments on real data
validate the model, showing
improved cost efficiency
over traditional TAS
approaches
Develops a multi-constraint
truck appointment system
considering truck
companies and terminals to
minimize operation costs
while considering urban
peak congestion and
queuing costs
Neagoe et al. [52]
2021
SIM Bulk cargo marine
terminal
Simulated using empirical
data from weighbridges and
geo-positioning systems
Compares congestion
management initiatives at
bulk cargo marine terminals
using discrete-event
simulation to assess truck
queuing and emissions
Wasesa et al. [71]
2021
SIM ---
Case studies focusing on
operational performance
under varying no-show
rates
Proposes overbooking
strategies to enhance
terminal productivity and
environmental performance
Azab and
Morita [50]
2022
OPT Japanese container
terminal
A case study demonstrating
significant reductions in
container relocations while
preserving scheduling
preferences
Integrates truck
appointments and yard
operations decisions to
reduce yard congestion and
enhanced terminal
efficiency
Xu et al. [66]
2022
OPT ---
Simulation experiments
demonstrate cost reductions
and improved adaptability
to arrival uncertainties.
Addresses dynamic
appointment rescheduling
under truck arrival
uncertainties to minimize
operating costs and
operational disruptions
Abdelmagid
et al. [33]
2022
OPT Port of Alexandria
Numerical experiments
based on instances from
literature
Improves workload
distribution and reduces
truck turnaround time,
leading to cost minimization
and enhanced terminal
efficiency
Azab and
Morita [65]
2022
OPT
Simulated terminal
data
Solved using instances from
literature
Highlights the benefits of
integrating appointment
scheduling with yard
operations
Mathematics 2025,13, 503 20 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Li et al. [16]
2022
OTP + QUE Shenzhen and
Dalian terminals
Simulation-based
experiments
Develops a queuing model
to optimize truck
appointments and yard
equipment use for dual
transaction systems
Ma et al. [37]
2022
OPT Dalian Maritime
Terminal Numerical experiments
Enhances yard efficiency by
integrating truck arrivals
with crane operations
Nadi et al. [56]
2022
SIM Port of Rotterdam Experimental analysis
Introduces an
advisory-based time slot
management system to
mitigate truck waiting times
at terminal gates and
highlights the benefits of
behavioral modeling in time
slot allocation for
congestion reduction
Sun et al. [41]
2022
OPT + DAN YT Port, China Numerical experiments
based on smart gate data
Reduces external truck
turnaround times and
emissions in ports using
data-driven optimization of
appointment quotas
Torkjazi et al. [45]
2022
OPT U.S. container
terminals
Simulated using
multi-player game scenarios
Models TAS as a
multi-player game between
terminals and drayage firms,
that outperform
single-player models in
balancing terminal and
drayage firm interests
da Silva et al. [69]
2023
SIM + DAN Brazilian port
terminal
A case study achieving a
90.4% reduction in waiting
times and reduced queue
sizes
Demonstrates the
effectiveness of integrating
smart technologies in truck
appointment systems to
improve port logistics
flexibility and visibility with
real-time data
Zhou [34]
2023
OPT + QUE ---
Real-world data
demonstrate reductions in
no-show impacts and
improved resource
utilization
Highlights overbooking
strategies to mitigate
disruptions in TAS
operations, and incorporate
no-show behaviors into
truck appointment
scheduling to minimize
terminal resource
inefficiencies and carbon
emissions
He et al. [47]
2023
OPT
Shanghai Maritime
University’s data
Sensitivity analysis on task
appointment strategies
Demonstrates that balancing
yard workload improves
efficiency and reduces truck
delays
Minh and Noi [46]
2023
OPT + QUE Ho Chi Minh City
Terminal
Case study validation with
comparison to observed
data
Develops a TAS to optimize
arrival management and
service gate allocation and
demonstrate cost and
congestion reductions
through optimized gate
management
Mathematics 2025,13, 503 21 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Abeysooriya
et al. [17]
2024
QUE + OPT
A major Asian port
Data-driven analysis based
on truck arrival and
emission patterns
Proposes a gate queuing
optimization model to
minimize greenhouse gas
emissions from idling trucks
Huang et al. [48]
2024
OPT ---
Extensive experiments
showing a 29.4% reduction
in total operating time
compared to traditional
approaches
Highlights the benefits of
integrating appointment
systems with efficient task
scheduling to enhance
operational efficiency in
drayage operations
Li et al. [35]
2024
OPT ---
A case study on real-world
terminal operation data,
showing robust
performance under
uncertain scenarios
Provides a practical
framework for gate
appointment design,
improving terminal
efficiency and mitigating
congestion under
uncertainty
Bett et al. [29]
2024
SIM + OPT Literature-derived
scenarios.
Numerical experiments
based on research data
Emphasizes the need for
dynamic scheduling and
resource optimization in the
face of uncertainties.
Optimize truck
appointment systems using
simulation-based methods
to account for yard
congestion and dynamic
scheduling
da Silva et al. [31]
2024
DAN + OPT Brazilian port
terminal
A case study to anticipate
disruptions and to actively
manage hinterland port
flows
Proposes a conceptual
model for flexible truck
appointment systems, able
to consider a continuous
stream of real-time data
from smart technologies to
identify disruptive events
and to dynamically
reschedule truck
appointments
Duan et al. [67]
2024
OPT
Simulated data
from Chinese
terminals
Numerical experiments
with sensitivity analysis
Integrates TAS with
container relocation
operations to enhance yard
crane efficiency and reduce
congestion while balancing
operational workloads
Hoxha et al. [43]
2024
DAN + OPT PSA Genova Case study
Demonstrates effective
emission reductions
through optimized arrival
scheduling
Riaventin et al. [
30
]
2024
SIM ---
Simulation with synthetic
data reflecting real-world
configurations
Investigates synchronization
between truck arrival and
yard crane scheduling
under centralized and
decentralized approaches to
reduce emissions
Stoop et al. [68]
2024
OPT Port of Antwerp Case study
Demonstrates robust
scheduling under
uncertainties of drayage
operations improve
efficiency and reduce delays
Mathematics 2025,13, 503 22 of 25
Table A1. Cont.
Author
Year
Model * Data Source Validation Framework Main Contribution
Wang et al. [70]
2024
OPT Tianjin Port Case study
Develops an optimization
model for scheduling
automated container
terminal robots and external
trucks in a parallel layout
Wasesa et al. [71]
2024
SIM Port of Rotterdam Case study
Designs an auction-based
truck appointment system
for automated container
terminals and demonstrate
enhanced operational
efficiency and sustainability
through market-driven
appointment allocation
* (OPT) optimization model, (SIM) simulation model, (QUE) queueing model, (DAN) data analytics.
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