Berth Allocation Problem Research Articles

Algorithm Design for an Online Berth Allocation Problem

In this paper, we investigate an online berth allocation problem, where vessels arrive one by one and their information is revealed upon arrival. Our objective is to design online algorithms to minimize the maximum load of all berths (makespan). We first demonstrate that the widely used Greedy algorithm has a very poor theoretical guarantee; specifically, the competitive ratio of the Greedy algorithm for this problem is lower bounded by Ω(log⁡m/log⁡log⁡m), which increases with the number of berths m. On account of this, we borrow an idea from algorithms for the online strip packing problem and provide a comprehensive theoretical analysis of the Revised Shelf (RS) algorithm as applied to our berth allocation problem. We prove that the competitive ratio of RS for our problem is 5, improving on the original competitive ratio of 6.66 for the online strip packing problem. Through numerical studies, we examine the RS algorithm and Greedy algorithm in an average case. The numerical simulation of competitive ratios reveals distinct advantages for different algorithms depending on job size. For smaller job sizes, the Greedy algorithm emerges as the most efficient, while for medium-sized jobs, the RS algorithm proves to be the most effective.

Optimization berth allocation in container terminals: A Pyomo and Google Colab approach

Efficient berth allocation profoundly influences container terminal operations, affecting vessel waiting and turnaround times, and overall performance. This study presents a mixed-integer linear programming (MILP) model addressing the Berth Allocation Problem (BAP) in a Malaysian container port. By incorporating the Pyomo optimization library and CBC (Coin-or Branch and Cut) solver in Google Colab, optimal berth allocations are determined, minimizing vessel turnaround times. Visualized in a Space-Time diagram, the results highlight efficient allocation strategies. Despite limitations, the study optimally resolved three instances, achieving a remarkable 38.54% reduction in overall vessel turnaround time compared to FCFS (First-Come-First-Serve) allocation. By prioritizing port turnaround time, the optimization substantially reduced berthing and departure delays, aligning with UNCTAD's call for enhanced port efficiency and accelerated decarbonization efforts.

Optimizing integrated berth allocation and quay crane assignment: A distributionally robust approach

In this research, we have formulated a Two-Stage Distributionally Robust Optimization (TDRO) model within the context of a mean–variance ambiguity set, specifically designed to address the challenges in the Integrated Berth Allocation and Quay Crane Assignment Problem (BACAP). A key consideration in this study is the inherent uncertainty associated with ships’ arrival times. During the initial stage, we derive a baseline schedule governing berth allocation and quay crane assignment. Anticipating potential disruptions arising from uncertain arrival delays, the second stage is meticulously formulated to determine the worst-case expectation of adjustment costs within the mean–variance ambiguity set. Subsequently, we undertake an equivalent transformation, converting the general TDRO model into a Two-Stage Robust Second-Order Cone Programming (TRO-SOCP) model. This transformation facilitates the application of the Column and Constraint Generation (C&CG) algorithm, ensuring the derivation of an exact solution. To address the computational intricacies associated with second-order cone programming, we propose two enhancement strategies for upper and lower bounds, aimed at expediting the solution process. Additionally, to contend with large-scale instances, we introduce a refinement and approximation method, transforming the TDRO model into a Mixed-Integer Programming (MIP) model. Furthermore, extensive numerical experiments are executed on both synthetic and real-life instances to validate the superior performance of our model and algorithms. In terms of the total cost, the TDRO model demonstrates superior performance compared with Two-Stage Stochastic Programming (TSP) and Two-Stage Robust Optimization (TRO) models.

A new model for multi-port berth allocation problem based on an improved genetic algorithm

Port integration can enhance operational efficiency and service level in response to heightened competition among container ports. Nevertheless, container ports are still considered independent systems separately in formulating scheduling plans. This research explores a new multi-port berth allocation problem (MPBAP) with continuous berth layout considering the mutual influence between ports. The MPBAP is compared with the single port berth allocation, and effects of different numbers of vessels continuously berthing at all ports on a single route on the MPBAP are discussed through vessel operation rate. The problem is formulated by a mixed integer programming model by minimising the total port stay time of all vessels. The quay is highly discretised and a GA coupled with parallel computing is applied to accelerate the search for the optimal model solution. A case study is conducted on two adjacent container ports located along the Yangtze River. Results show that multi-port coordinated scheduling is efficiency and the total port stay time of all vessels reduces by an average of 2.63% under the MPBAP. With more than four vessels berthing continuously at two ports on a single route, the MPBAP shows a higher vessel operation rate and the rate gap between the two models exceeds 2%. The approach suggested in this study can enhance the port system’s efficiency and provide a new idea for coordinated scheduling in other port groups.

An accelerated Benders decomposition algorithm for the integrated storage space assignment, berth allocation, and yard crane deployment problem

In this paper, storage space assignment problem, berth allocation problem, and yard crane deployment problem are integrated with due attention to traffic congestion in the passing lines of storage yards. The paper provides a mixed-integer programming model for the integrated problem with the objective of minimizing the movement and operating costs of yard cranes, the cost of moving container flow between the storage yard and berths, and the delay cost of vessels. The planning horizon is considered to be one day and the berth layout is assumed to be discrete. Since the integrated storage space assignment and yard crane deployment problem is NP-hard and so is berth allocation problem, the integration of these three problems will be at least equally complex. Thus, an Accelerated Benders Decomposition Algorithm is also developed for solving the integrated problem. This is done by introducing a combinatorial Benders cut to the classical Benders decomposition algorithm to improve its performance and also adding 8 valid inequalities derived from the problem properties and assumptions to the algorithm formulation to accelerate the solution process. The proposed mathematical model and solution approach are evaluated by generating instances of different sizes for the problem and assessing the solution results. The results show the good performance of the proposed accelerated Benders decomposition algorithm. Taking the integrated approach to the modeling of the three problems rather than the non-integrated approach improved the cost of terminal operations by 11.15% on average.

An Improved Equilibrium Optimizer for Solving Multi-quay Berth Allocation Problem

The multi-quay berth allocation problem (MQBAP) is an important problem in the planning of seaside operations (POSO) to find the best berthing solution for all the vessels. In this paper, an efficient method based on equilibrium optimizer (EO) is proposed for MQBAP. The dynamic multi-swarm strategy (DMS) is proposed to improve rapid decline problem in population diversity during the iterative process of EO, which is subsequently applied to MQBAP. In this paper, a certain improvement is also made on the original model of MQBAP by proposing an alternate quay selection mechanism, which aims to make the MQBAP model more complete. To verify the effectiveness of the proposed algorithm on MQBAP, this paper uses six test cases and seven comparative algorithms to verify it comprehensively from total service cost, berthing time, and berthing location. The results show that DEO achieved the smallest total service costs of 7584 and 19,889 on medium-scale, and 44,998, 38,899, and 57,626 on large-scale systems.

Neural network assisted branch and bound algorithm for dynamic berth allocation problems

One of the key challenges in maritime operations at container terminals is the need to improve or optimize berth operation schedules, thus allowing terminal operators to maximize the efficiency of quay usage. Given a set of vessels and a set of berths, the goal of the dynamic berth allocation problem is to determine the allocation of each vessel to a berth and the berthing time that minimizes the total service time. This problem can be solved using exact solution methods such as branch and bound (BB) algorithms or heuristic methods, however, exact methods do not scale to large-scale terminal operations. To this end, this paper proposes a BB algorithm in which branching decisions are made with a deep neural network. The proposed exact algorithm utilizes the search order of nodes based on the output of the neural network, with the goal of speeding up the search. Three types of solution representations are compared, along with machine learning models are created for each of them. Computational results confirm the effectiveness of the proposed method, which leads to computation times that are on average around half of those without the neural network.

Integrated optimization of berth allocation problem with berth shifting strategies and ballast water management for dry bulk ports

In maritime operations, ballast water operations and cargo handling operations are carried out simultaneously to determine the operational efficiency of vessels in port. However, the ballast water pumping rate lags behind the growing efficiency of bulk cargo handling, resulting in operational interruptions and extended stay times at ports. To address this challenge, this paper introduces a novel ballast water management strategy: vessels first handle a portion of their cargo and then shift to a lay-by berth for mid-pumping. This strategy results in multiple shifting movements of vessels within the berth allocation plan. Therefore, to better implement this strategy, we develop an integrated model of berth allocation and ballast water pumping management, with the special considerations of multi-berth shifting strategies and ballast water weight. To efficiently solve this model, we present a hybrid heuristic algorithm based on adaptive genetic algorithms and the critical path method. The computer experiments reveal that the mid-pumping strategy effectively circumvents untimely pumping, shortens the vessel port stay time, and yields a 9.42% reduction in the total stay time. This research further elucidates managerial insights to inform and enhance port operations.

Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

Background: Improving the performance of marine terminals is one of the major concerns of both researchers and decision-makers in the maritime transportation sector. The problem of container storage planning and the berth allocation problem (BAP) are the two mainstays of optimizing port operations. Methods: In this work, we address these two issues, proposing two mathematical models that operate sequentially and are applicable to both static and dynamic cases. The first developed model is a mixed-integer linear problem model aimed at minimizing vessel traffic time in the port. The second model developed is a multi-objective optimization model based on goal programming (GP) to minimize both container transfer time and the number of storage areas (minimizing container dispersion). Results: The robustness of the proposed models has been proven through a benchmark with tests using data from the literature and real port data, based on the IBM ILOG CPLEX 12.5 solver. Conclusions: The two developed mathematical models allowed the both minimization of the transfer time and the number of used storage areas, whatever the number of operations handling companies (OHCs) operating in the seaport and for both static and dynamic cases. We propose, as prospects for this work, the development of a heuristic model to deal with the major instances relating to the case of large ports.

Variable Neighborhood Search for Multi-Port Berth Allocation with Vessel Speed Optimization

This paper delves into the multi-port berth allocation problem (MBAP), enriching the traditional berth allocation problem (BAP) with vessel speed optimization (VSO). In the MBAP, it is assumed that there is cooperation between the port and the shipping companies, and the operation of the vessels and the ports is planned to maximize the overall benefits. Exploring this potential collaboration between ports and shipping entities has the potential to mitigate, or even resolve, the challenges plaguing maritime transportation, e.g., port congestion and suboptimal vessel schedules, to ultimately enhance the efficiency of maritime trade. In this paper, a new mixed-integer linear programming (MILP) model for the MBAP is formulated, which attempts to minimize the total cost incurred during operations, with various constraints such as vessel sailing, the vessel space–time relationship in ports, and the planning period. Meanwhile, an innovative variable neighborhood search (VNS) algorithm is presented, in which the initial solution generation method and neighborhood structures are proposed according to the MBAP characteristics. Furthermore, two sets of MBAP instances are generated to test the proposed MILP and VNS, of which the first set is based on real-world port data and the second on existing studies. The numerical experiments verify that the VNS can efficiently and reliably solve instances of all scales, with each neighborhood structure contributing uniquely to the iterative process. In addition, by analyzing the impact of varying oil prices on the MBAP, the study offers valuable management insights. Finally, a case study based on real data from a port group in the Yangtze River Basin is presented to further demonstrate the necessity of considering vessel service time window and planning period in the MBAP as well as the important role of the VSO in scheduling.

Dynamic berth allocation under uncertainties based on deep reinforcement learning towards resilient ports

With the evolving global trade landscape and the post-pandemic effects, the resilience of ports has become paramount. The unforeseen disturbances bring substantial challenges, especially in berth allocation, a vital task ensuring seamless resilient port operations. The unpredictability of vessel arrivals and the variability in loading/unloading times intensify these issues, pushing traditional static allocation methods beyond their limits. Fortunately, the advent of smart ports has led in an era of big data availability, enabling the application of advanced deep reinforcement learning (DRL) techniques. To capitalize on this shift, this research presents a DRL-based methodology specially designed to solve the berth allocation problem with the uncertainties in vessel arrival and container handling time to enhance port resilience. A Markov Decision Process model (MDP) of the berth allocation problem is established to minimize the mean waiting time with tailored state space, rule-based action space, and reward function to address the issue. An offline training method is designed to train the agent in selecting the optimal action based on the current state of the port berth system at each decision point even in uncertain environments, deep Q-network (DQN) is implemented for this problem. Comprehensive experiments across different problem scales are conducted to validate the effectiveness and generality of the proposed method in solving berth allocation challenges under uncertain conditions. Furthermore, the trained model also performs better than other methods in different vessel congestion levels through learning.

Distributionally robust chance-constrained optimization for the integrated berth allocation and quay crane assignment problem

In this paper, we are the first to propose a distributionally robust chance-constrained (DRCC) optimization model for the integrated berth allocation and quay crane assignment problem (BACAP) in container terminals. In contrast to the classical deterministic BACAP model, we consider the arrival time to be uncertain due to the frequent arrival delays in ports. We then impose a chance constraint that the service time must start after the uncertain arrival time with a probability of at least 1−ϵ, where 1−ϵ represents the target service level in container terminals (ϵ represents the target risk tolerance of the port manager). Under the moment-based ambiguity set, we reformulate the DRCC model into a mixed integer semi-definite programming (MISDP) model. Additionally, we develop an efficient decomposition branch-and-bound algorithm to solve the MISDP model and obtain the exact solution. Fortunately, a special case of the DRCC model arises when the mean and covariance utilized in the ambiguity set are precise, allowing for the transformation of the DRCC model into a mixed integer programming (MIP) model. This conversion significantly reduces the complexity of the problem. Impressively, the solving time of the MISDP model with the decomposition branch-and-bound algorithm is comparable to that of the transformed MIP model. The numerical results show that our model can achieve a schedule with high service at low cost. Meanwhile, we have made an intriguing discovery that the correlation between the target risk tolerance and the actual service level can be depicted as a staircase function regardless of the datasets. This finding offers crucial insights for port management, enabling them to strike a balance between the cost and actual service level by determining an appropriate target service level.

A survey on computational intelligence approaches for intelligent marine terminal operations

AbstractMarine container terminals (MCTs) play a crucial role in intelligent maritime transportation (IMT) systems. Since the number of containers handled by MCTs has been increasing over the years, there is a need for developing effective and efficient approaches to enhance the productivity of IMT systems. The berth allocation problem (BAP) and the quay crane allocation problem (QCAP) are two well‐known optimization problems in seaside operations of MCTs. The primary aim is to minimize the vessel service cost and maximize the performance of MCTs by optimally allocating berths and quay cranes to arriving vessels subject to practical constraints. This study presents an in‐depth review of computational intelligence (CI) approaches developed to enhance the performance of MCTs. First, an introduction to MCTs and their key operations is presented, primarily focusing on seaside operations. A detailed overview of recent CI methods and solutions developed for the BAP is presented, considering various berthing layouts. Subsequently, a review of solutions related to the QCAP is presented. The datasets used in the current literature are also discussed, enabling future researchers to identify appropriate datasets to use in their work. Eventually, a detailed discussion is presented to highlight key opportunities along with foreseeable future challenges in the area.

An Optimization Approach to Berth Allocation Problems

The berth allocation problem determining the berthing time and position for incoming vessels in port operations has garnered increased attention within the global transportation network. This study focuses on the berth allocation problem with a continuous quay and dynamic vessel arrivals. With the overarching goal of enhancing service quality and optimizing berth utilization rates, this article proposes a mathematical programming model that minimizes the total waiting time of vessels and the overall completion time of vessel service. The formulated model is a mixed-integer linear programming problem that deterministic optimization techniques can globally solve. For large-scale problems, this study develops a genetic algorithm optimization approach to improve computational efficiency in reaching a near-optimal solution. Several numerical experiments are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

An adaptive large neighborhood search heuristic for the multi-port continuous berth allocation problem

In this paper, we study a problem that integrates the vessel scheduling problem with the berth allocation into a collaborative problem denoted as the multi-port continuous berth allocation problem (MCBAP). This problem optimizes the berth allocation of a set of ships simultaneously in multiple ports while also considering the sailing speed of ships between ports. Due to the highly combinatorial character of the problem, exact methods struggle to scale to large-size instances, which points to exploring heuristic methods. We present a mixed-integer problem formulation for the MCBAP and introduce an adaptive large neighborhood search (ALNS) algorithm enhanced with a local search procedure to solve it. The computational results highlight the method’s suitability for larger instances by providing high-quality solutions in short computational times. Practical insights indicate that the carriers’ and terminal operators’ operational costs are impacted in different ways by fuel prices, external ships at port, and the modeling of a continuous quay.

Coarse-grained vs fine-grained optimisation in highly integrated problem environments: A case study featuring port terminal operations

The problem environment port terminal operators face is characterised by a highly integrated and complex workflow. There are numerous decisions at radically different scales which must be made, all the way from the berthing of huge vessels to the storage of individual shipping containers. Yet regardless of the specific decision at hand, the core objective typically remains the same: to minimise the travel distance of containers through the yard. In this paper we bring together all major port terminal decisions and, for the first time, seek to optimise these decisions with container distance minimisation in mind. The result is a problem we term the Berth Allocation, Crane and Yard Storage Assignment Problem (BACYSAP). We investigate the added value of treating all these decisions in a simultaneous fashion and compare our results against a more naïve, yet simpler, sequential approach which first solves the berth and crane problems independently and then uses these decisions as input for the yard assignment problem. Our results are somewhat counterintuitive and should not only offer food for thought to those working in port terminals, but any problem environment where there are multiple components with a single ultimate objective. The core contribution of this paper is therefore less to do with the specifics of port terminals and is instead more methodological in nature, namely: how should operational manager decision makers proceed in highly integrated problem environments so they can be confident their approach (i) produces sufficiently good results and (ii) is not unnecessarily complex.

A Proactive-Reactive-Based Approach for Continuous Berth Allocation and Quay Crane Assignment Problems with Hybrid Uncertainty

Port operations have been suffering from hybrid uncertainty, leading to various disruptions in efficiency and tenacity. However, these essential uncertain factors are often considered separately in literature during berth and quay crane assignments, leading to defective, even infeasible schedules. This paper addressed the integrated berth allocation and quay crane assignment problem (BACAP) with stochastic vessel delays under different conditions. A novel approach that combines both proactive and reactive strategies is proposed. First, a mixed-integer programming model is formulated for BACAP with quay crane maintenance activities under the ideal state of no delay. Then, for minor delays, buffer time is added to absorb the uncertainty of the arrival time of vessels. Thus, a robust optimization model for minimizing the total service time of vessels and maximizing the buffer time is developed. Considering that the schedule is infeasible when a vessel is seriously delayed, a reactive model is built to minimize adjustment costs. According to the characteristics of the problem, this article combined local search with the genetic algorithm and proposed an improved genetic algorithm (IGA). Numerical experiments validate the efficiency of the proposed algorithm with CPLEX and Squeaky Wheel Optimization (SWO) in different delay conditions and problem scales. An in-depth analysis presents some management insights on the coefficient setting, uncertainty, and buffer time.

Multi-Port Berth Allocation and Time-Invariant Quay Crane Assignment Problem With Speed Optimization

Multi-Port Berth Allocation and Time-Invariant Quay Crane Assignment Problem With Speed Optimization

Multiple Container Terminal Berth Allocation and Joint Operation Based on Dueling Double Deep Q-Network

In response to the evolving challenges of the integration and combination of multiple container terminal operations under berth water depth constraints, the multi-terminal dynamic and continuous berth allocation problem emerges as a critical issue. Based on computational logistics, the MDC-BAP is formulated to be a unique variant of the classical resource-constrained project scheduling problem, and modeled as a mixed-integer programming model. The modeling objective is to minimize the total dwelling time of linerships in ports. To address this, a Dueling Double DQN-based reinforcement learning algorithm is designed for the multi-terminal dynamic and continuous berth allocation problem A series of computational experiments are executed to validate the algorithm’s effectiveness and its aptitude for multiple terminal joint operation. Specifically, the Dueling Double DQN algorithm boosts the average solution quality by nearly 3.7%, compared to the classical algorithm such as Proximal Policy Optimization, Deep Q Net and Dueling Deep Q Net also have better results in terms of solution quality when benchmarked against the commercial solver CPLEX. Moreover, the performance advantage escalates as the number of ships increases. In addition, the approach enhances the service level at the terminals and slashes operation costs. On the whole, the Dueling Double DQN algorithm shows marked superiority in tackling complicated and large-scale scheduling problems, and provides an efficient, practical solution to MDC-BAP for port operators.

An efficient and eco-friendly operation mode for container transshipments through optimizing the inter-terminal truck routing problem

To enhance efficiency and reduce carbon emissions of waterway-waterway transshipments for a multi-terminal port group, a crucial strategic planning issue lies in determining whether a centralized or distributed mode of feeder vessel service is more efficient and eco-friendly. This paper proposes a two-stage integer-optimized model to optimize intra- and inter-terminal operations and determine the most effective mode of operation for feeder vessel services. Our model integrates the multi-terminal berth allocation problem and inter-terminal transportation (ITT), considering different cases of transshipment flows. To address this optimization problem, we develop a heuristic approach based on genetic and adaptive large neighborhood search algorithms, which is ideal method for large-scale scenarios. In our case study, the proposed optimization model and heuristic methods were adopted to determine the best operation mode for North Operation Area in Shanghai Yangshan Deep-Water Port (namely Yangshan Phase V). The results indicate that Yangshan Phase V should operate as a feeder vessel service terminal, providing primary feeder vessel services and complementary liner vessel services. This development plan not only minimizes container transshipment delays and overall ITT costs, but also helps reduce approximately 707.46 tons of annual carbon emissions caused by ITT at Yangshan Deep-Water Port.