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1 INTRODUCTION

A container terminal operates as a bustling hub, where

goods transition between different modes of

transportation. It comprises two primary areas: the

quayside and the landside. The quayside hosts

berthing positions and quay cranes for efficiently

loading and unloading containers from ships. Once

offloaded, containers embark on the next leg of their

journey to the yard, facilitated by automatic guided

vehicles, straddle carriers, or internal trucks. However,

congestion in the yard can impede this flow, causing

delays and undermining operational efficiency (see

Figure).

Decision-making in container terminal operations

spans four key areas. Firstly, berth allocation and

scheduling involve the strategic assignment of ships to

berths or quay locations, carefully balancing

operational demands within a designated timeframe.

Secondly, quay crane allocation and scheduling focus

on optimizing the assignment of quay cranes to vessels,

ensuring a smooth and timely loading, and unloading

process. Thirdly, transfer operations entail the

movement of containers between the quayside, yard,

and gate, necessitating effective vehicle routing and

dispatching strategies. Lastly, storage and stacking

strategies are devised at the block level, with containers

allocated specific positions based on their attributes

and operational requirements. These operational

components collectively drive the efficiency and

effectiveness of container terminal operations.

Figure 1. Schematic representation of a container terminal

(Steenken et al., 2004).

Optimizing Container Terminal Operations:

A Comparative Analysis of Hierarchical and Integrated

Solution Approaches

K. Mili

King Faisal University, Al-Ahsa, Saudi Arabia

ABSTRACT: Container terminals serve as crucial hubs in the global supply chain, facilitating the efficient transfer

of goods between different modes of transportation. This study explores optimization strategies for container

terminal operations, focusing on the comparison between hierarchical and integrated solution approaches. A

comprehensive literature review provides insights into the challenges and advancements in container terminal

management. The comparative analysis highlights the advantages of integrated optimization models, particularly

through the lens of the Tactical Berth Allocation Problem (TBAP). By incorporating real-world data and advanced

computational methods, the study offers nuanced insights into efficiency and time estimation aspects.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 18

Number 4

December 2024

DOI: 10.12716/1001.18.04.09

826

2 LITERATURE REVIEW:

2.1 Container Terminal Operations

Container terminal operations are vital nodes in global

supply chains, facilitating the seamless transfer of

goods across various transportation modes.

Researchers have extensively explored the

complexities inherent in these operations. For instance,

Weerasinghe et al. (2023) offer a systematic review of

optimization methodologies in container terminals,

shedding light on strategies to enhance efficiency in

berth allocation, yard planning, and equipment

scheduling. Meanwhile, Raeesi et al. (2023) delve into

the synergy between operational research and big data

analytics, aiming to promote environmentally

sustainable practices within container terminal

operations. Additionally, Gao and Ge (2022) focus on

integrated scheduling strategies for yard cranes and

trucks, emphasizing holistic approaches to enhance

terminal efficiency.

2.2 Integrated Optimization Strategies:

Integrated optimization has emerged as a promising

avenue to bolster overall efficiency in container

terminal operations. Che et al. (2023) explore planning

strategies in highly electrified terminals, considering

time-of-use tariffs to promote sustainability.

Comparative studies by Al Samrout et al. (2024)

highlight the superiority of integrated optimization

over traditional methods, particularly in berth

scheduling with ship-to-ship transshipment

operations. Similarly, Cao et al. (2023) demonstrate the

advantages of integrated optimization in automated

container terminals, focusing on AGV dispatching and

routing problems. These studies underscore the

importance of integrated approaches in addressing

operational complexities.

2.3 Traffic Congestion Analysis:

Traffic congestion poses significant challenges to

container terminal operations, impacting efficiency

and sustainability. Innovative approaches, such as

multi-agent reinforcement learning for AGV path

planning (Hu et al., 2021), and deep learning for port

congestion prediction (Peng et al., 2022), offer insights

into mitigating congestion dynamics. Strategies like

dynamic scheduling, explored by Xiang et al. (2023),

aim to adapt to changing operational environments,

enhancing overall terminal performance. Wang et al.

(2024) delve into scheduling strategies for equipment

transfer modes, further contributing to congestion

alleviation efforts.

2.4 Tactical Planning:

Tactical planning plays a crucial role in optimizing

resource allocation and capacity planning within

container terminals. Studies by Cartenì and de Luca

(2012) and Yang et al. (2013) delve into the intricacies

of tactical planning, addressing issues such as

equipment maintenance scheduling and truck arrival

management. Gumuskaya et al. (2020) explore

dynamic barge planning strategies, considering

stochastic container arrivals to enhance operational

efficiency. These studies underscore the significance of

tactical planning in ensuring long-term operational

sustainability.

2.5 State-of-the-Art Optimization Approaches:

Recent advancements in optimization techniques have

revolutionized container terminal operations,

providing decision-makers with powerful tools to

address complex challenges. Ambrosino and Xie (2022)

investigate optimization approaches for defining

storage strategies, aiming to improve space utilization

and operational efficiency. Hsu et al. (2022) explore

heuristic-based simulation optimization for integrated

scheduling, offering insights into enhancing

scheduling efficiency. Drungilas et al. (2023) utilize

deep reinforcement learning to optimize AGV

operations, emphasizing improvements in time and

energy consumption. These studies highlight the

transformative potential of advanced optimization

techniques in enhancing container terminal operations.

2.6 Current Research Trends:

The landscape of container terminal operations

continues to evolve, driven by technological

innovations and emerging trends. Current research

trends, including the integration of artificial

intelligence, adoption of sustainable practices, and

exploration of blockchain technology, offer promising

avenues for future advancements. Wang et al. (2024)

and Al Samrout et al. (2024) identify key trends

shaping the future of container terminal operations,

paving the way for innovative solutions and

sustainable practices.

In summary, the literature review underscores the

multidimensional nature of container terminal

operations and emphasizes the importance of

integrated optimization strategies in addressing

operational challenges. Our study contributes to this

body of knowledge by focusing on tactical planning,

employing the Tactical Berth Allocation Problem

(TBAP) as a case study. By incorporating congestion

management and employing advanced computational

methods, our research aims to provide practical

insights for optimizing container terminal operations

in real-world scenarios.

3 HIERARCHICAL VS INTEGRATED SOLUTION

APPROACHES

When addressing complex problems like the Berth

Allocation Problem (BAP) and the Quay Crane

Assignment Problem (QCAP) in container terminal

operations, planners often resort to either hierarchical

or integrated solution approaches. Each approach

offers distinct advantages and is chosen based on the

problem's characteristics and the desired outcomes.

3.1 Hierarchical Approach: BAP + QCAP

The hierarchical approach involves solving the BAP

and QCAP sequentially, breaking down the problem

into manageable sub-problems. Initially, vessels are

assigned to berths based on estimated handling times

827

and time windows in the BAP step. This step aims to

optimize berth template creation, considering vessel

workload and scheduling robustness. Subsequently, in

the QCAP step, quay cranes are allocated to vessels

based on the berth allocation plan, considering

workload and crane capacity constraints. This

sequential optimization allows for systematic planning

and efficient coordination of terminal operations.

− Berth Allocation Problem (BAP): In this step, vessels

are assigned to berths to minimize yard

management costs while optimizing berth template

creation for efficient vessel scheduling.

− Quay Crane Assignment Problem (QCAP): Quay

cranes are then assigned to vessels, ensuring that

the total crane capacity is not exceeded. The

objective is to maximize the monetary value

associated with the assigned quay crane profiles.

In our study, we utilized models developed by

Giallombardo et al. (2010) for both BAP and QCAP,

aligning their objective functions with the overall

objectives of the integrated TBAP model for

meaningful comparison.

3.2 Integrated Approach: TBAP

In contrast, the integrated approach tackles both the

BAP and QCAP simultaneously, aiming for greater

efficiency and resource utilization. The Tactical Berth

Allocation Problem (TBAP) integrates berth allocation

and quay crane assignment optimization, considering

the interdependencies between these decisions. This

approach, introduced by Giallombardo et al. (2010),

maximizes the monetary value of assigned quay cranes

while minimizing management costs associated with

berth allocation, thereby effectively managing

congestion.

The TBAP model treats vessel handling time as a

decision variable influenced by the number of assigned

quay cranes, allowing for dynamic resource allocation.

By integrating optimization processes traditionally

solved separately, the TBAP model provides a

comprehensive solution that optimizes terminal

operations from a holistic perspective.

In summary, while the hierarchical approach breaks

down problems into manageable steps, the integrated

approach offers a more comprehensive solution by

considering interdependencies and optimizing

multiple aspects simultaneously. Our study explores

both approaches, emphasizing the advantages and

implications of each in container terminal operations

optimization.

4 COMPARATIVE ANALYSIS

In our comparative analysis, we utilized both

hierarchical and integrated solution approaches to

address the Berth Allocation Problem (BAP) and the

Quay Crane Assignment Problem (QCAP) in container

terminal operations. We conducted experiments using

a branch-and-price algorithm for the integrated TBAP

and adapted it for the hierarchical approach in solving

the BAP model. For the QCAP model, a general-

purpose Mixed Integer Programming (MIP) solver was

employed. Our analysis focused on comparing the

performance of these approaches under different

scenarios and examining their computational

efficiency and solution quality.

4.1 Handling Time Estimation

In the hierarchical approach, handling time estimation

is crucial and typically relies on input from terminal

planners. Two scenarios were considered for

estimating handling time: Scenario A, which uses the

longest feasible quay crane assignment profile for

every vessel, and Scenario B, which prioritizes mother

vessels by using the shortest feasible profile for them

and the longest for feeders. Both scenarios have their

merits, with Scenario A providing a conservative

estimate and Scenario B offering a more realistic

reflection of vessel priority.

4.2 Experimentation

Tables 1 and 2 present a comparison of the objective

function values between the integrated solution and

the hierarchical approach under scenarios A and B,

respectively. The integrated approach consistently

outperforms the hierarchical approach, with notable

improvements in objective function values across

instances.

Table 1. Objective function: integrated solution vs

hierarchical approach under scenario A

________________________________________________

Instance hierarchical Integrated Improvement

approach (A) Solution in %

________________________________________________

1 812167 815735 44%

2 812117 816011 48%

3 812151 816045 48%

4 755702 758276 34%

5 755418 760646 69%

6 755454 760682 69%

7 538661 540902 41%

8 538696 543049 80%

9 538731 543084 80%

10 584683 589831 87%

________________________________________________

Table 2. Objective function; integrated solution vs

hierarchical approach under Scenario B

________________________________________________

Instance hierarchical Integrated Improvement

approach (B) Solution in %

________________________________________________

1 814478 815735 15%

2 814754 816011 15%

3 814788 816045 15%

4 758276 758276 0%

5 757659 760646 39%

6 757695 760682 39%

7 540017 540902 16%

8 540052 543049 55%

9 540087 543084 55%

10 586705 589831 53%

________________________________________________

Tables 3 and 4 provide a comparison of the time

estimations for the hierarchical and integrated

approaches under scenarios A and B, respectively. The

integrated approach generally requires more

computational time but achieves better results,

indicating its effectiveness in handling complex

instances.

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Table 3. Time estimation; integrated solution vs hierarchical

approach under Scenario A.

________________________________________________

Hierarchical approach (A) Integrated Solution Time

________________________________________________

15 114 87%

16 995 98%

16 557 97%

3 12 75%

6 29 79%

4 25 84%

85 4054 98%

21 761 97%

21 470 96%

30 4697 99%

________________________________________________

Table 4. Time estimation; integrated solution vs hierarchical

approach under Scenario B.

________________________________________________

Hierarchical approach (B) Integrated Solution Time

________________________________________________

26 114 77%

16 995 98%

16 557 97%

2 12 83%

6 29 79%

6 25 76%

308 4054 92%

171 761 78%

173 470 63%

24 4697 99%

________________________________________________

4.3 Interpretation

Under both scenarios A and B, the integrated approach

demonstrates superior performance in terms of

objective function values compared to the hierarchical

approach. Although the integrated approach requires

more computational effort, it consistently finds optimal

solutions within a reasonable time frame, particularly

for congested instances closely resembling real-world

scenarios.

In scenarios with more congestion, the limitations

of the hierarchical approach become apparent, as it

may struggle to provide feasible solutions due to

constraints on quay crane assignments. In contrast, the

integrated approach proves robust and efficient in

utilizing terminal resources effectively.

While the improvement in objective function values

may seem modest for cases where the hierarchical

approach is feasible, every incremental gain is

significant in optimizing terminal operations. The

integrated TBAP approach emerges as the preferred

solution, especially for congested instances,

highlighting the importance of considering

interdependencies in decision-making processes.

4.4 Additional Results

Table 5 presents the results of the week, showcasing the

objective function values, berth allocations, and

computational times for both the hierarchical and

integrated approaches. These results further reinforce

the superiority of the integrated approach in

optimizing terminal operations.

Overall, our comparative analysis underscores the

effectiveness of the integrated TBAP approach in

achieving optimal solutions for the Berth Allocation

Problem and the Quay Crane Assignment Problem in

container terminal operations.

5 STUDY CONSTRAINTS AND

RECOMMENDATIONS FOR FUTURE

RESEARCH

While this study provides valuable insights into the

optimization of container terminal operations, several

limitations warrant consideration. Firstly, the

contextual specificity of the dataset and models

utilized may restrict the generalizability of findings to

different terminal settings. Additionally, the simplified

modeling assumptions and reliance on available data

may overlook certain complexities inherent in real-

world operations. Future research could explore the

incorporation of more dynamic and realistic factors

into the models. Moreover, the computational

scalability of the methods employed poses challenges

for larger and more complex instances, indicating a

need for further advancements in optimization

techniques. Addressing these limitations could

enhance the robustness and applicability of

optimization strategies in container terminal

management.

6 CONCLUSION

In conclusion, this study has delved into the intricate

domain of container terminal operations, offering a

comprehensive analysis of key decision problems and

optimization strategies. The literature review provided

valuable insights into the pivotal role of container

terminals in global supply chain management and

underscored recent advancements in operational

research and optimization methodologies.

Table 5. Results of the week

___________________________________________________________________________________________________

BPA&QCAP (scenario A) BPA&QCAP (scenario B) Integrated Solution

___________________________________________________________________________________________________

Instance objective berths time objective berths time objective berths time scenario A scenario B

function function function

___________________________________________________________________________________________________

1 _ _ _ _ _ _ 809620 3 55 +∞ +∞

2 808553 3 11 _ _ _ 811896 3 146 45% +∞

3 808587 3 12 _ _ _ 814522 3 89 78% +∞

4 _ _ _ _ _ _ 754653 3 41 +∞ +∞

5 752149 3 7 754896 3 8 756567 3 51 63% 25%

6 752220 3 5 754896 3 8 757807 3 49 80% 42%

7 539750 3 5 _ _ _ 544755 2 13 101% +∞

8 539587 3 4 540727 3 8 544755 2 103 104% 81%

9 539622 3 4 540762 3 8 545213 2 1721 112% 90%

10 586193 3 6 588401 3 11 590972 2 65 88% 48%

___________________________________________________________________________________________________

829

Through a comparative analysis of hierarchical and

integrated solution approaches, particularly focusing

on the Tactical Berth Allocation Problem (TBAP),

intriguing findings emerged. While the hierarchical

approach proved computationally efficient in less

congested scenarios, it encountered difficulties in

providing feasible solutions under heightened

congestion. Conversely, the integrated TBAP approach

consistently exhibited superior performance,

delivering optimal solutions even in complex, real-

world scenarios.

The integration of yard management costs into the

TBAP model addressed a crucial aspect of container

terminal operations, emphasizing practical

implications and supporting the industry's imperative

for efficient congestion management. Additionally, the

consideration of multiple scenarios for handling time

estimation added depth to the analysis, offering a

nuanced understanding of the model's robustness and

practical applicability.

The study's distinctive contributions lie in its

focused exploration of tactical planning, utilizing the

TBAP as a case study. By leveraging real-world data

and advanced computational methods, the research

presented a nuanced comparison that transcended

traditional objective functions, shedding light on both

efficiency and time estimation aspects.

As container terminal operations evolve in response

to technological innovations and emerging trends, the

insights from this study contribute to the ongoing

discourse in the field. Emphasizing integrated

optimization, congestion analysis, and tactical

planning, the research aligns with current industry

trends, highlighting the need for holistic approaches to

tackle the multifaceted challenges of container terminal

management.

In the ever-evolving landscape of container

terminal operations, continuous exploration and

adaptation are imperative. By remaining attuned to the

dynamic nature of the industry, researchers and

practitioners can contribute to the development of

robust strategies that ensure the seamless flow of goods

in the global supply chain.

FUNDING

The authors gratefully acknowledge financial support from

the Deanship of Scientific Research, King Faisal University

(KFU) in Saudi Arabia, under Grant No. A436."

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