825

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.

827

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

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%

________________________________________________

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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.

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.

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%

___________________________________________________________________________________________________

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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.

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.

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