83
1 INTRODUCTION
The increasing complexity of global trade has
significantly altered the role of container terminals,
which have evolved into crucial nodes in the
international logistics network. These infrastructures,
far beyond their initial purpose as transfer points, now
serve a crucial role in enhancing the fluidity, speed,
and reliability of global goods flows.
Contemporary container terminals function as
intricate, well-integrated systems, merging different
logistical, technological, and operational processes.
The handling of container movements depends on
accurate synchronization among various kinds of
specialized machinery. Key components include
quayside cranes, which transfer containers to and from
ships and the terminal; yard cranes (or yard gantry
cranes), utilized for organizing and accessing
containers from storage zones; and internal transport
vehicles, like port tractors or Automatic Guided
Vehicles (AGVs), which move containers horizontally
between the yard and quayside. Figure 1 shows the
operational and spatial arrangement of this apparatus
within a terminal.
Enhancing Container Handling Operations in Maritime
Terminals Using the Ant Colony Optimization
E.K. Adam, S. Youness, J. Kamelia, H. Hanaa & E.M. Chakib
Ibn Tofaïl University, Kénitra, Morocco
ABSTRACT: Numerous studies have underscored the significance of scheduling and optimization challenges
within maritime terminals. This dissertation examines how to optimize container movements specifically for
export operations, simultaneously taking into account the operating sequences of yard cranes and trucks. It also
considers any potential interference that may arise among yard cranes. A survey of existing literature on yard
crane scheduling indicates a lack of work addressing both unproductive crane moves and possible crane-to-crane
interferences at the same time, which constitutes an innovative element in our study. Initially, the container
loading scheduling task is formulated as a mixed-integer linear program, where the objective function aims to
minimize the overall handling time required by the yard cranes. The mathematical model incorporates various
assumptions that address interference effects and non-productive movements. In order to tackle this problem, an
Adaptive Large Neighborhood Search (ALNS) heuristic is introduced. This strategy proves effective in managing
optimization issues in container terminals, regardless of the size of the problem—whether it involves 10, 20, or
even 100 containers. The data utilized for validating the method are intentionally generated, allowing for
differences in both the number of containers and the amount of accessible handling equipment. Extensive testing
verified the ALNS algorithm’s usefulness. Various situations were tested by combining various removal and
insertion strategies, and the results demonstrated the ALNS method’s robustness.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 20
Number 1
March 2026
DOI: 10.12716/1001.20.01.10
84
Figure 1. The different constituents of a block (Zhang et al.,
2002)
The effectiveness of port activities relies on the
seamless and strict synchronization of all the human
and material resources involved. In a container
terminal, this coordination is crucial to ensure a steady
and efficient flow of goods, while reducing waiting
periods and operational expenses. A minor error in the
sequence of operations can lead to significant delays,
influence the logistics chain downstream, and
negatively affect the port’s competitiveness.
In general, a container terminal is divided into two
primary functional zones, with the connections
between them influencing the system’s overall
efficiency: the quay side and the yardside.
The quay side serves as the direct connection
between the vessels and the terminal. Here is where
quay gantry cranes are utilized for loading and
unloading containers. This region faces significant time
limitations because of the requirement to shorten the
duration of ship calls.
Conversely, the yard area is essential for the
temporary storage, arrangement, and readiness of
containers for their journey, whether it’s transportation
to another port or land delivery (by truck or train). It
includes different kinds of handling machinery, like
gantry cranes and forklifts.
Figure 2 demonstrates the functional separation
between the two regions and emphasizes the
significance of their dynamic interaction. Effective
handling of container movement between the quay
and the yard is crucial to prevent bottlenecks, enhance
productivity, and maintain the flow of port activities in
an environment frequently faced with intricate
logistical challenges.
Figure 2. Schematic view of a terminal (Vis and Koster, 2003)
Vehicles serve as shuttles between these zones. The
containers are stored in structured blocks made up of
bays, rows, and tiers, where the location of each
container is precisely defined (see Figure 3).
Figure 3. Container handling equipment (yard and quay
cranes)
The stack height is constrained by the type of
handling equipment available at the terminal
(Steenken et al., 2004; Chen & Langevin, 2011). Despite
technological advances, terminals face persistent
challenges such as congestion, high operational costs,
and the need for continuous reorganization of
containers. These issues arise mainly due to the
inefficient coordination between handling equipment,
especially between yard cranes and transport vehicles.
Traditional planning methods are often inadequate in
addressing the dynamic nature of terminal operations.
Interference, idle movements, and excessive waiting
times all contribute to performance degradation. Each
container handling operation can be viewed as a task
with a total completion time known as the makespan
(see Figure 4).
Figure 4. The container unloading process cycle (Lee et al.
2009a)
In the case of imports, tasks involve a sequence of
actions including waiting, transferring, unloading, and
empty returns. The export process mirrors this flow.
The role of transport vehicles, including Automated
Guided Vehicles (AGVs) and Straddle Carriers (SCs),
is essential to shuttle containers between quay and
yard zones (see Figure 5).
Figure 5. Means of transport (AGV LGV) in a terminal
(Steenken et al., 2004)
These vehicles differ significantly in terms of
flexibility, automation, and cost. This study proposes
an integrated optimization model for jointly
scheduling yard cranes and transport vehicles. We use
mixedinteger linear programming (MILP) formulation
combined with an adaptive large neighborhood search
(ALNS) heuristic to solve large problem instances
85
efficiently. The goal is to minimize the makespan of
export operations while mitigating crane interference
and reducing non-productive container movements.
The article is organized into three major sections.
The first section describes the operating background of
maritime container terminals, including critical
equipment and coordination requirements. The second
component is a literature study that focuses on
scheduling concerns with yard cranes and transport
vehicles, as well as crane interference and container re-
handling. The final section provides a comprehensive
optimization strategy that combines a Mixed-Integer
Linear Programming (MILP) model with an Ant
Colony Optimization (ACO) metaheuristic, and
validates the model by implementing it in AMPL
Studio with a genuine case study.
2 LITERATURE REVIEW
Container terminals possess numerous operational
issues, particularly in handling equipment planning
and scheduling, such as quay cranes, yard cranes, and
transportation trucks. These terminals are efficient,
depending largely on the careful planning of these
resources within a constraint set and minimizing
delays and redundant operations.
A substantial amount of literature has been devoted
to the scheduling of yard cranes. Early contributions by
Young & Hwan(1997 and 1999) introduced
optimization techniques and mixed-integer
programming models for determining crane routing
and bay visitation orders for export operations.
Additional research conducted by Linn & Zhang (2003)
introduced methods aimed at enhancing crane
efficiency using Lagrangian relaxation and heuristic
approaches. Ng et al.(2005) and Horng et al. (2007)
developed mathematical models to reduce crane
interference and container loading activities, while Gu
et al. (2008) demonstrated how real-time information
may improve yard crane productivity. These findings
highlight the complexities of crane operations and the
importance of flexible and speedy scheduling choices.
At the same time, research on the scheduling of
transport vehicles has highlighted the significance of
AGVs and ALVs in enabling smooth container
movement between the yard and the quay. Evers et al.
(1996) were among the first to model AGV traffic using
control systems grounded in simulation. Ebru (2003)
proposed two-stage vehicle assignment and container
allocation by using list scheduling heuristics. Other
researchers, such as those conducted by Vis and
Harika(2004) and Kim and Bae(2004), experimented on
the effect of equipment selection and traffic control on
terminal capacity.Huynh(2009) also addressed truck
scheduling and fleet management with genetic
algorithms and hybrid mathematical-simulation
approaches in pursuit of higher utilization and shorter
turnaround time. Aside from crane or truck
management on its own, coordinated scheduling has
recently gained popularity. Huynh et al.(2004) and Ng
and Ge (2006) proposed detailed models for yard crane
operations and truck scheduling to reduce overall
service time and vessel delays. These models usually
employ tabu search or fuzzy heuristics to handle the
complexity of resource interactions. Zhang and Jiang
(2008) designed multi-device coordination techniques,
focusing on equipment synchronization to improve
overall terminal performance. Cao et al.(2010)
conducted further studies by providing a
decomposition-based optimization platform for the
simultaneous scheduling of yard cranes and trucks,
with encouraging performance results for export
activities. Another significant cause of inefficiency is
rehandling, or pointless container moves. To solve
increasingly complicated optimization challenges,
academics have used a wide range of innovative
techniques.
Metaheuristic methods such as reinforcement
learning and ant colony optimization (ACO) have
gained fast momentum over the past couple of years
because they are readily adaptable to dynamic and
unpredictable scenarios. For example, ACO has been
successfully utilized to optimize energy-efficient
scheduling in smart manufacturing systems and
recorded dramatic increases in performance and
resource consumption (Eswaran et al., 2015). Similarly,
Tabu Search has also shown satisfactory performance
in proactive scheduling of projects, particularly under
flexible resource allocation and skill matching
conditions(Kellenbrink & Helber,2023). Hybrid
heuristics that combine greedy and insertion-based
approaches have also demonstrated robustness in
tough scheduling settings. The majority of current
research assumes static environments, limiting its
application in real-world scenarios where equipment
availability and task priorities can change
unexpectedly.
3 METHODOLOGY
The process of handling containers in maritime
terminals is a complex and highly dynamic operation,
comprising various interacting elements like yard
cranes (YCs), trucks (YTs), and quay cranes (QCs). In
this research, we aim to enhance the loading operations
of export containers by optimizing the coordination of
yard cranes and trucks while considering interference
and rehandling limitations. This part outlines the
approach used to model and enhance these operations
through an Ant Colony Optimization (ACO)
metaheuristic.
First, we represent the export container loading
issue by integrating multiple operational assumptions
and limitations. Every container has an established
location in the yard and a specified endpoint on the
quay. Yard cranes can only shift once between blocks
and might experience interference when several cranes
function in neighboring bays within the same block.
Trucks are expected to transport a single container at a
time and adhere to fixed travel durations between the
yard and quay. Additionally, container handling
encompasses not just the loading duration but also
extra time for any unproductive rehandling operations
necessary to reach containers that are situated under
others in the stack. The issue is illustrated as a directed
graph, with each node representing a container
handling task, while edges indicate possible transitions
between tasks for trucks and cranes. The goal is to
identify the best sequences and assignments that
reduce the total makespan.
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To address this scheduling issue, we employ a
customized ACO framework, modeled after the
foraging habits of ants, where artificial agents (ants)
construct solutions progressively using pheromone
trails and heuristic data. The amount of pheromone
deposited corresponds to the quality of the solutions:
superior schedules result in increased pheromone
concentrations. During every iteration, ants make
probabilistic choices for the next task, weighing the use
of acquired pheromone insights against the discovery
of new routes. To avoid premature convergence,
pheromone evaporation diminishes the intensity of
once-attractive routes, enabling the colony to adjust
fluidly to shifting circumstances.
In our adjustment to port operations, every ant
creates a complete timetable by allocating tasks to yard
cranes and trucks while adhering to limitations like
interference, block assignments, and priority handling
sequences. The heuristic element prefers tasks that
have reduced travel and handling durations, with
penalties added for routes that incur high rehandling
expenses or possible crane conflicts. The phase of
solution construction is directed by a transition
probability function that combines pheromone
intensity with heuristic attractiveness, which is
updated dynamically throughout the iterations.
A significant advantage of the suggested ACO
framework is its adaptability in integrating dynamic
disturbances. In actual terminal operations, unforeseen
events like crane failures or unexpected ship arrivals
can interrupt the scheduled plan. Our model
incorporates dynamic event management by adjusting
the solution space in real time. Upon detecting a
disruption, pheromone concentrations on the impacted
transitions are lowered or reset, urging the ants to
reassess paths and create alternative viable solutions.
This enables the system to stay agile and robust in
fluctuating circumstances.
The suggested methodology provides a robust and
adaptable tool for enhancing container handling
operations in maritime terminals by combining
modeling and metaheuristic optimization approaches.
The ACO-based scheduler excels in settings with high
complexity and variability, exceeding standard static
or greedy algorithms through continual learning and
adaptation to operational reality.
4 MATHEMATICAL MODEL AND SOLUTION
4.1 Mathematical Formulation
The mathematical formulation of the export container
handling problem integrates container positions, crane
interferences, and rehandling operations into a
comprehensive mixed-integer linear programming
(MILP) model. This formulation aims to minimize the
makespan while satisfying operational constraints
related to equipment coordination and terminal layout.
Decision Variables and Objective Function
Let:
−
m
ij
x
: binary variable equal to 1 if yard crane m
handles container j immediately after i.
−
n
ij
y
: binary variable equal to 1 if truck n carries
container j immediately after i.
−
'
m
bb
z
: binary variable equal to 1 if crane m moves
from block b to b’.
−
i
s
: starting time for handling container i.
−
i
d
: departure time of truck carrying container i.
−
i
H
: total handling time of container i (including
rehandling).
The objective is:
( )
minmax
i
i
d
(1)
This objective minimizes the makespan, i.e., the
total completion time, which is a critical performance
metric in port operations.
Constraints
The MILP model is subject to the following
constraints:
− Assignment constraints: Ensure each container is
processed by exactly one yard crane and
transported by one truck.
− Flow conservation constraints: Maintain
consistency in crane and truck assignments by
balancing incoming and outgoing operations.
− Handling time constraints: Integrate rehandling
delays based on container stack configuration.
− Interference constraints: Prevent two cranes from
operating in adjacent bays of the same block
simultaneously.
− Safety and operational limits: Yard cranes are
restricted to a maximum number per block, and
travel times are capped.
− Priority constraints: Enforce sequencing based on
predefined priority groups; if container i has higher
priority than j, then si < sj.
This formulation guarantees the feasibility of crane
schedules, respects terminal structure, and accounts
for real-world logistical challenges.
4.2 Implementation of the ACO Algorithm
To tackle the NP-hard nature of this optimization
problem, we implement an Ant Colony Optimization
(ACO) metaheuristic, adapted to the specificities of
maritime terminal operations. The algorithm uses the
collective behavior of ants to discover near-optimal
sequences of equipment operations.
ACO Components
− Pheromone trails (τ): Quantify the historical quality
of paths taken by ants.
− Heuristic information (η): Represents real-time
desirability, incorporating factors like crane travel
distance and container urgency.
− Transition probability:(Dorigo and Gambardella
1997)
( ) ( )
( ) ( )
mm
ij ij
m
ij
mm
ik ik
k
p
=
(2)
− Evaporation rate (ρ): Controls the decay of
pheromone levels to avoid premature convergence.
− Pheromone update rule:
87
( )
1
m m m
ij ij ij
− +
(3)
where:
−
m
ij
is the pheromone value on edge (i, j) at iteration
m
−
(
0,1
−
m
ij
is the amount of pheromone deposited by the
ants on edge (i, j) during iteration m.
ACO Process
− Initialization: Define the problem graph, set
m
ij
to
a small constant, and initialize ACO parameters (α,
β, ρ).
− Solution Construction: Each ant constructs a valid
sequence of container handling and transportation
decisions, using
m
ij
p
.
− Evaluation: The fitness of each ant’s solution is
computed based on makespan and constraint
penalties.
− Pheromone Update: The best ants deposit
additional pheromones on high-quality paths to
reinforce efficient sequences.
− Termination: The algorithm halts upon
convergence or after reaching a predefined number
of iterations.
This algorithm achieves a trade-off between
exploration of new solutions and exploitation of
promising ones, adapting well to dynamic changes
such as crane breakdowns or unexpected container
arrivals.
4.3 Illustrative Case Study
To demonstrate the efficacy of our MILP model and
ACO implementation, we analyze a realistic use case
involving a medium-sized maritime terminal
managing 50 export containers.
Scenario Assumptions
The case study assumes the following parameters:
− Terminal layout: 2 yard blocks, each with 5 bays, 3
rows, and 3 tiers.
− Resources: 3 yard cranes (YC1, YC2, YC3), 5 trucks
(T1 to T5), and 2 quay cranes (QC1, QC2).
− Container classification: Grouped by export
priority, with known destination quay cranes.
− Equipment constraints: No more than 2 yard cranes
per block; fixed crane speed and truck travel times.
Execution and Results
A Python-based simulation integrating the ACO
algorithm was executed for 100 iterations. Simplified
parameters included:
− Handling time per container: 20 seconds.
− Rehandling time: 40 seconds per obstructing
container.
− Travel time matrix generated using Euclidean
distance approximation.
Performance Metrics:
− Best makespan achieved: 1075 seconds.
− Average makespan across 10 runs: 1120 seconds.
− Standard deviation: 22.3 seconds.
Observed Benefits:
− Effective load balancing between yard cranes.
− Minimized crane interference through intelligent
task sequencing.
− Consistent prioritization of urgent containers.
Visualization and Dynamic Adjustments
Simulation outputs generated visual timelines and
a Gantt chart representing:
− Crane activity over time (color-coded per resource).
− Truck dispatch loops and idle times.
− Rehandling impacts visualized via stacked bar
segments.
Additionally, robustness was tested under dynamic
disruptions:
− Crane unavailability: One crane taken offline mid-
schedule.
− Late container arrival: 5 containers added during
runtime.
The ACO algorithm responded by reallocating
tasks dynamically, maintaining solution quality with a
marginal increase in makespan (approximately +6.5%).
This illustrates the adaptability and practical value of
the proposed method in real-time port operations.
5 MATHEMATICAL FORMULATION
This section presents the mathematical framework
adopted for optimizing container handling operations
within a terminal yard. It begins by outlining the
modeling assumptions and proceeds to a rigorous
description of the model, including the parameters,
decision variables, constraints, and the objective
function. A simplified example using fictitious data is
also provided to demonstrate the model’s
functionality. The model is solved using AMPL Studio,
and the resulting operational paths of the equipment
are visualized.
5.1 Model Assumptions
The following assumptions are adopted for the
proposed model:
− Only loading operations for export containers are
considered.
− Container positions in the yard are known and
fixed.
− The yard comprises multiple adjacent blocks.
− A block can accommodate up to two yard cranes.
− Yard cranes can switch blocks, but only once per
crane.
− Each container is assigned to a specific quay crane.
− Yard cranes and trucks can operate simultaneously.
− All containers in a single bay are destined for the
same vessel.
− Interference between yard cranes within the same
block is considered.
− Containers are grouped by handling priority.
− Non-productive movements (rehandles) are
accounted for.
− Truck unloading is assumed to be instantaneous.
− Yard crane speed is fixed at 36 km/h.
− Only 40-foot containers are modeled.
5.2 Mathematical Model
5.2.1 Indices and Parameters
Indices:.
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− i, j ∈ C: Container indices, i = 0 denotes a dummy
container
− m ∈ M: Yard cranes
− n ∈ N: Trucks
− q ∈ Q: Quay cranes
− b ∈ B: Yard blocks
Sets and Parameters:.
−
0
b
M
: Initial number of cranes in block b
− L: Storage locations defined by block, bay, row, tier
− li: Location of container i
− ai, bi, ei, ri: Bay, block, tier, and row of container i
− h1: Time to handle one container
− h2 = 2h1: Time to rehandle a container
− P: Priority pair set
− U: Set of pairs with potential interference
− T: Large constant
− kij: Travel time between containers i and j
− ti: Truck travel time for container i
− tvqa: Return time of truck from quay q to bay a
5.2.2 Decision Variables
−
YC
i
d
: Start time for crane handling container i
−
YT
i
d
: Truck departure time with container i
−
0,1
ijm
X
: Crane m handles j after i
−
0,1
ijm
Y
: Truck n loads j after i
−
'
0,1
bb m
Z
: Crane m moves from b to b’
−
0,1
ij
V
: Container j starts after i
−
''
0,1
iji j
u
: Interference indicator
−
12
i i i
p p p=+
: Total handling time
1
11
ij
ij
ij
i ij
jC
aa
rr
ee
p h h V
=
=
= +
(3)
2
1
ij
ij
ij
i ij
jC
aa
rr
ee
p h V
=
=
=
(4)
5.2.3 Objective Function
minmax
YT
i
i
d
(5)
5.2.4 Constraints
1
11
ij
ij
ij
i ij
jC
aa
rr
ee
p h h V i C
=
=
= +
(6)
2
1
ij
ij
ij
i ij
jC
aa
rr
ee
p h V i C
=
=
=
(7)
All variables satisfy:
12
' ' '
, , , 0
, , , , 0,1
YC YT
i i i i
ijm ijn bb ij iji j
d d p p
X Y Z V u
6 NUMERICAL RESULTS AND DISCUSSION
We consider a simplified yard consisting of:
− 2 blocks, each with 4 bays, 3 rows, 3 tiers
− 2 yard cranes: YC1, YC2
− 3 trucks: YT1, YT2, YT3
− 10 containers located as follows:
Table 1.
Container
Block
Bay
Row
Tier
C1
1
1
1
1
C2
1
2
2
1
C3
1
3
3
1
C4
1
4
2
2
C5
1
4
2
1
C6
2
5
3
1
C7
2
7
2
1
C8
2
7
1
1
C9
2
8
3
1
C10
2
8
2
1
This instance is modeled and solved using AMPL
Studio. The solution minimizes the makespan and
provides an optimized schedule for container
handling. A graphical illustration of equipment
movements is derived from the solution and supports
operational planning within the yard.
Container Placement and Handling in the Yard
Table 2 below visualizes the placement of
containers in the yard’s storage area using a grid
system.
Table 2. Locations of containers in the storage area (using
grid system)
We assume that containers are grouped, and each
group follows a specific priority sequence. The groups
are defined as follows:
− Group A: C1, C4, C5, C8
− Group B: C2, C7
− Group C: C9, C10
− Group D: C3, C6
Groups A and B will be serviced by quay crane 2
and are bound for containership 2. Groups C and D
will be handled by quay crane 1, destined for
containership 1 (see Table 3).
When quay cranes load containers, a particular
order must be respected for reasons such as
simplifying unloading or aligning with cargo
characteristics:
− Group B must be processed before Group A
− Group C must be processed before Group D
Group-level priorities can also transfer to
individual containers. In this model, the destination
quay crane for each container is known in advance.
Table 3. Container Quay Destinations
Ci
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
QC
2
2
1
2
2
1
2
2
1
1
89
Table 4.: General Parameters
Parameter
Value
Total containers
10
Total yard cranes
2
Total quay cranes
2
Total trucks
3
Bays per block
4
Rows per block
3
Maximum tiers
3
Table 5. Yard Crane Handling Times
Parameter
Value (in sec)
Container handling time (h1)
20
Time to move and re-place a container (h2)
40
Table 6. Transport Times (ti) for Containers to the Quay (by
Truck)
Container
Quay Crane
ti (min)
ti (sec)
C1
QC 2
3
180
C2
QC 2
3
180
C3
QC 1
2
120
C4
QC 2
3
180
C5
QC 2
3
180
C6
QC 1
2
120
C7
QC 2
2
120
C8
QC 2
2
120
C9
QC 1
3
180
C10
QC 1
3
180
Table 7. Truck Empty Return Times (tvqa) from a Quay
Crane to a Yard Bay
Quay Crane
Bay
tvqa (sec)
QC1
a1
60
QC1
a2
60
QC1
a3
60
QC1
a4
60
QC1
a5
90
QC1
a6
90
QC1
a7
90
QC1
a8
90
QC2
a1
90
QC2
a2
90
QC2
a3
90
QC2
a4
90
QC2
a5
60
QC2
a6
60
QC2
a7
60
QC2
a8
60
6.1 Solution
Following the detailed presentation of each data
category, we turned to AMPL Studio to encode the
mathematical model and generate a solution. First, we
entered the model itself into a .mod file. Afterward, we
compiled the data described earlier into a .dat file.
Finally, we utilized CPLEX to solve this model.
From the solution produced by the AMPL software
(depicted in Figure 6), we gathered substantial
information about the problem, including the
makespan and the operating sequence of each yard
crane and truck. The cumulative time required to
process 10 containers was found to be 560 seconds.
The resulting sequence for each resource is as
follows:
− YC1: C7 – C8
− YC2: C10 – C9 – C6 – C2 – C1 – C3 – C5 – C4
− YT1: C7 – C6 – C3 – C4
− YT2: C10 – C2 – C5
− YT3: C9 – C1 – C8
Figure 6. Presentation of the solution with AMPL
The AMPL solution indicates how each piece of
equipment operates. The work sequences of yard
cranes and trucks are shown graphically (Figures 7
and 8)
Figure 7. Yard Cranes’ Operating Sequences
Figure 7 illustrates the operating sequences of two
yard cranes (YC1 and YC2) assigned to handle
container tasks within the yard. Each node represents
a container task (C1 to C10), with directional arrows
indicating the execution order.
YC1 is shown in red, handling a short and direct
sequence: from the initial node (I) to container C7, and
then moving directly to C8, before completing at the
final node (F). This path suggests a minimal set of
assignments for YC1, focusing on distant but isolated
tasks that likely require minimal interference with the
route of the other crane. YC2 is depicted in black,
covering a significantly larger portion of the container
set: C10 → C9 → C6 → C2 → C1 → C3 → C5
→ C4. The sequencing of YC2 forms a continuous flow
along the upper and right-hand side of the layout,
reflecting a more intensive workload for this crane,
optimized to follow a path with minimal backtracking.
Figure 8. Trucks’ Operating Sequences
Figure 8 displays the operating sequences of three
yard trucks (YT1, YT2, and YT3) assigned to transport
containers across the terminal. Each node in the
diagram represents a container, with directional
dashed arrows indicating the task execution order and
color-coded paths for each truck.
90
YT1, illustrated in orange, follows the path: C7 →
C6 → C3 → C4, starting from the initial node and
proceeding along the upper left arc. This sequence
indicates a relatively linear and upper-path operation
with minimal detours.
YT2, represented in red, performs the sequence: C10
→ C2 → C5, forming the central path between the
initial and final nodes. This truck manages container
tasks that are central in the yard layout, providing a
balanced route between the upper and lower regions.
YT3, shown in green, moves through: C9 → C1 →
C8. Its sequence runs along the lower path of the
terminal layout, offering complementary coverage to
the other two trucks.
The structure of the figure clearly separates the
workload among the three trucks and illustrates how
their routes are strategically defined to minimize
overlap and ensure efficient transport of containers.
Figure 9. Overall Operating Sequences for Handling
Equipment
Figure 9 illustrates the coordinated operations of
two yard cranes (YC1 and YC2) and three yard trucks
(YT1, YT2, and YT3) within the terminal. Each node
corresponds to a container handling task, while the
directed edges—color-coded by resource—represent
the order of task execution for each piece of equipment.
YC1, depicted in red, handles a sequence starting
from the initial node I, proceeding through C7 and C8,
and concluding at the final node F. This route outlines
a clear lower-path handling pattern with minimal
interference.
YC2, shown in black, performs the upper-tier
sequence: I → C10 → C9 → C6 → C2 → C1 →
C3 → C5 → C4 → F. This sequence covers a more
complex chain of tasks involving multiple yard blocks.
YT1, using dashed dark red arrows, operates
through C10, C7, and C5, bridging tasks across both the
upper and lower regions. Its trajectory helps facilitate
crane coordination, especially at inter-block
transitions.
YT2, indicated in orange, services the path: C9 →
C3 → C4, assisting YC2 in upper yard deliveries while
reducing idle crane times.
YT3, highlighted in green, ensures smooth
container transfers along the route: C6 → C2 → C8,
thereby covering inter-block transport along the
central arc of the graph.
Overall, this figure visually encapsulates the
effective division of labor among cranes and trucks,
illustrating a synchronized scheduling solution aimed
at minimizing interference and enhancing yard
operational efficiency.
7 CONCLUSION
This research addressed the problem of optimizing
container handling operations in maritime terminals,
with a particular focus on the dynamic scheduling of
yard cranes and transport vehicles. The main objective
was to minimize the total processing time of export-
bound containers, while accounting for real-world
constraints such as yard-crane interference and
container rehandling. A mixed-integer linear
programming model was proposed and tested using
fictitious data in the AMPL environment, producing
operating sequences for 10 containers with a global
completion time of 560 seconds. These sequences were
visualized to analyze the cooperation between cranes
and trucks, and to highlight the sources of efficiency or
delay in the system.
One of the most significant contributions of this
work lies in the validation of the Ant Colony
Optimization (ACO) algorithm as a promising method
for dynamic port logistics. Inspired by the behavior of
natural ants, ACO allowed for adaptive decision-
making in a complex and evolving environment,
where static planning strategies may fail to respond
efficiently to unforeseen events such as congestion,
equipment breakdowns, or variations in container
demand. Compared to conventional static approaches,
ACO demonstrated greater flexibility, especially in
minimizing non-productive moves and reducing
interference between equipment. This adaptability
positions ACO as a relevant and scalable solution for
next-generation container terminals.
From a practical standpoint, the findings presented
here have important implications for port managers
and logistics operators. The dynamic scheduling
framework proposed can serve as a foundation for
real-time decision support systems. It is recommended
that terminal operators consider a progressive
integration of such intelligent algorithms into their
operational workflows. A stepwise implementation—
beginning with selected yards or during off-peak
periods—can help mitigate deployment risks and build
operator confidence. Additionally, the incorporation of
Internet of Things (IoT) technologies can significantly
enhance the model’s effectiveness. Real-time data from
connected cranes, trucks, and yard sensors would
allow the system to react more accurately to the actual
conditions on the ground, thereby improving the
efficiency and robustness of container movement
planning.
This work also opens several promising avenues for
future research. First, the combination of ACO with
machine learning techniques offers an exciting
opportunity to enhance predictive capabilities.
Machine learning models could anticipate demand
fluctuations, identify recurring congestion patterns,
and feed this information into the ACO algorithm to
improve planning foresight. This hybrid approach
would enable a more proactive and intelligent
91
scheduling process. Second, the optimization
methodology developed in this study could be
extended beyond container handling to address other
critical logistics challenges—such as energy
management, maintenance scheduling, or berth
allocation—thereby broadening the scope of its
applicability. Finally, future investigations could
explore multi-objective optimization strategies, which
take into account not only completion time but also
energy efficiency, emissions reduction, and equipment
lifespan. This would align optimization efforts with the
principles of sustainability and green port
development.
In conclusion, the integration of bio-inspired
algorithms such as ACO into port logistics systems
represents a major step forward in addressing the
increasing complexity and dynamism of terminal
operations. When combined with real-time data and
predictive analytics, these algorithms have the
potential to significantly enhance decision-making,
streamline resource allocation, and contribute to the
development of smarter, more resilient, and more
sustainable ports.
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