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In this paper, we consider an integrated berth and quay crane allocation and scheduling problem. Existing ILP formulations involve large number of variables and constraints making commercial solvers unsuitable for obtaining optimal solutions. We introduce a class of solutions and present compact ILP formulations to obtain them using commercial solvers on a fast track. The size of the formulations (number of variables and constraints) is very small compared to the existing formulations to find optimal solutions. Further, unlike general optimal solutions, the new class of solutions are easy to implement and thus are desirable from pragmatic angle. The quality of new solutions, evaluated through a number of numerical experiments, appears to be good. [ABSTRACT FROM AUTHOR]

Maritime transportation plays a critical role in global trade as it accounts for over 80% of all merchandise movement. Given the growing volume of maritime freight, it is vital to have an efficient system for handling ships and cargos at ports. The current first-come-first-serve method is insufficient in maintaining operational efficiency, especially under complicated conditions such as parallel scheduling with different cargo setups. In addition, in the face of rising demand, data-driven strategies are necessary. To tackle this issue, this paper proposes a mixed-integer model for allocating quay cranes, terminals, and berths. It considers not only cargo types, but also the time required for a quay crane setup. The proposed model features a greedy-insert-based offline algorithm that optimizes berth allocation when vessel information is available. In situations where vessel information is uncertain, the model utilizes an online optimization strategy based on a reinforcement-learning algorithm that is capable of learning from feedback and of adapting quickly in real time. The results of the numerical experiments demonstrate that both the offline and online algorithms can significantly enhance cargo handling efficiency and overall harbor operation. Furthermore, they have the potential to be extended to other complex settings.

This paper describes the development of a mechanism to deal with time windows constraints. To the best of our knowledge, the time windows constraints are difficult to be fulfilled even for state-of-the-art methods. Therefore, the main contribution of this paper is to propose a new computational technique to deal with such constraints. Such technique was tested combined with two metaheuristics to solve the discrete and dynamic Berth Allocation Problem. The technique ensures obtaining feasible solutions in terms of vessels time windows constraints, which are treated as hard constraints. A data set generator was created, resulting in a diversity of problems in terms of time windows constraints. A detailed computational analysis was carried out to compare the performance of both metaheuristics considering the technique. [ABSTRACT FROM AUTHOR]

Lacking information challenges the management of port operational uncertainty in estimating the situation to support a decision on reactivity planning. This paper applies Digital Twin (DT) to model a replicated virtual port operation from a real-world port of Thailand. The proposed DT model offers a tool to accelerate generating data of the port operation with configurable uncertainty. The model is validated by using generated data from the DT model compared with the real-world data. The result shows that the DT model produces the same behaviour as the real-world system. An outcome of this paper is a DT model eligible to generate port operation data for later application with machine learning to predict the port capacity under uncertainty to support reactivity planning. [ABSTRACT FROM AUTHOR]

It is of increasing importance to carry out port terminal operations in an environmentally sustainable way. We approach the yard block assignment and internal transportation problem in a way that establishes an optimum trade-off between the time of internal truck moves and environmental objectives. The framework has a dynamic structure and aims to offer different berthing alternatives according to yard block occupancy rates. Earlier limitations of deterministic modelling are addressed. Probabilistic methods are considered in an attempt to bring our outcomes closer to real terminal circumstances. Discrete Monte Carlo simulation, integer-linear programming and multi-objective optimisation methods are integrated to address container terminal modelling complexity. The uncertainty arising from situations such as irregular vehicle queuing at the yard or quay crane stations is successfully addressed. The opinions of managers involved in decisions regarding the 'time–environment dilemma' are weighted and included in the optimisation model. In five scenarios, we show that internal truck time efficiency can improve by 27.8% to 42.8%, and CO2 emissions reduction by 30.1% to 70.3%. [ABSTRACT FROM AUTHOR]

This article investigates a low carbon-oriented berth allocation and quay crane assignment problem considering vessels' uncertain arrival time and loading/unloading workload for vessels. A two-stage stochastic programming model is formulated based on a set of scenarios. The first stage designs a baseline schedule and the second stage adjusts the schedule in each scenario. A solution method is developed by using column generation techniques. Numerical experiments are conducted to validate the efficiency of our column generation-based solution method and the effectiveness of the proposed decision model. Some sensitivity analysis is also performed to draw some managerial implications. [ABSTRACT FROM AUTHOR]

Container terminal operations are a core aspect of vessel operations in ports and necessitate an intelligent rescheduling approach to manage complex uncertainty scenarios. This paper investigates the problem of berth allocation and quay crane (QC) assignment with shifting strategies. A variable-length rolling mechanism (VLRM) is designed to identify uncertainty scenarios and determine the optimal rescheduling time point. Notably, we introduce a novel cross-wharf shifting movements strategy (CWSM) and develop a rescheduling model that accounts for constraints related to tidal time windows. The proposed Adaptive Large Neighborhood Search algorithm (ALNS) is tailored to solve this problem effectively. Computational results from various instance sizes validate the efficacy of both the model and the ALNS algorithm. These results demonstrate that the ALNS algorithm exhibits distinct advantages in solution quality and computational time for large-scale instances. Furthermore, the inclusion of tidal time window constraints significantly amplifies the complexity of uncertainty scenarios, emphasizing their importance and the impossibility of neglecting them. The cross-wharf shifting movements strategy, presented herein, effectively mitigates the impact of uncertainty scenarios within a defined scope while enhancing adjustment flexibility. • Investigated intricate scenarios emerging from the interplay between tidal constraints and uncertainty factors. • Proposed a cross-wharf shifting rescheduling strategy to enhance the terminal's emergency response capabilities. • Developed the ALNS algorithm, incorporating two types of operators—single-neighborhood and multi-neighborhood destruction and repair operators—to address the rescheduling problem. • Highlighted how tidal constraints markedly escalate the intricacy of uncertainty scenarios. • Demonstrated that the cross-wharf shifting movements strategy effectively limits the repercussions of uncertainty, thereby expanding the maneuverability within the baseline plan. [ABSTRACT FROM AUTHOR]

This paper examines one of the most important operational problems in seaport terminals, namely the Berth Allocation Problem (BAP) which finds an optimal assignment of ships to the berths that minimize the total waiting time of all ships and reduce congestion in ports. Our problem is to affect and schedule n ships on m berths to minimize the processing time and the waiting time for all the ships in the port. Therefore, ships stay time in the port known by the flow time, while respecting the physical constraints existing at the port (such as the depth of the water berth and the draft of the ship’s water), knowing that each ship can only accommodate one ship at a time. It is as if it was a case of n tasks and m machines in parallel, and we wanted to schedule the passage of different tasks on different machines, knowing that each task can only pass on one machine and that the interruption of the task is not allowed. For example, if a job started on a machine, it will remain on this machine up to its completion. In our case, tasks are ships and machines are berths that are opting to minimize the total flow time and, therefore, to decrease the residence time of all the ships in the port. In a first step, a Mixed Integer Linear Program model is designed to address the BAP with the aim of minimizing the flow time of the ships in the port, our sample can be used for both static and dynamic berth allocation cases. In a second step, this model is illustrated with a real case study in the Tunisian port of Rades and solved by a commercial solver CPLEX. Calculation results are presented and compared with those obtained by port authorities in Radès.

As maritime transportation develops, the pressure of port traffic increases. To improve the management of ports and the efficiency of their operations, vessel scheduling must be optimized. The vessel scheduling problem can be divided into channel scheduling and berth allocation. We considered the complex problem of vessel scheduling in a restricted channel and the berth allocation problem, and a combined model that considers carbon emissions was developed. This model should reduce vessel waiting times, improve the quality of the berth loading and unloading service, meet the requirements of “green” shipping, and improve the overall scheduling efficiency and safety of ports. An adaptive, double-population, multi-objective genetic algorithm NSGA-II-DP is proposed to calculate the mathematical model. In the case study, the rationality verification and sensitivity analysis of the model and algorithm are conducted, and the NSGA-II-DP and NSGA-II were compared. Results demonstrate that the overall convergence of the NSGA-II-DP algorithm is better than that of NSGA-II, demonstrating that the NSGA-II-DP algorithm is a useful development of NSGA-II. In terms of port scheduling, the results of our model and algorithm, compared with the decisions provided by the traditional First Come First Service (FCFS) strategy, are more in line with the requirements for efficiency and cost in the actual port management, and more dominant in the port management can provide better decision support for the decision-makers.

Container seaport congestion is a challenging problem in improving the service level and optimizing evacuating container vessels after congestion. There is a lack of research on container vessel evacuation strategies for continuous terminals. In this article, the weight of the objective function is regarded as the index for the service priority of vessels. The effects of the service priority on the continuous terminal are analyzed by establishing a mixed integer programming model. The model minimizes the total weighted delay departure time of vessels. Two sets of weight values are adopted, including handling volume of each ship and the squared handling volume, then the optimization results are compared with the unweighted scenario. The model is solved using a genetic algorithm. Lianyungang Port is selected as a case study. The results show that the method using the square of handled container volume is more conducive to ensuring the shipping period of large vessels after congestion. Besides, the quay crane number of large vessels affecting the scheduling strategy is discussed. The method proposed in this article provides a new idea for arranging scheduling strategies in other ports under congestion situations, which can better ensure the planned shipping period of large vessels.

This paper aims to provide an applicable managerial solution to reduce the losses and impacts from an unexpected shutdown of a terminal by facilitating cooperation between two adjacent terminals that are managed by different operators. In view of the autonomy of different terminals, we focus on not only berth scheduling in the emergency situation, but also interest coordination between different terminals. We propose a novel mechanism based on price adjustment and transfer payment, which can induce the joint optimal scheduling of different terminals in an emergency situation through cooperation between terminals based on decentralized decision making. Extensive experiments show that the berth scheduling achieved under the proposed mechanism can significantly reduce the loss that results from the shutdown of a terminal and provide economic benefits to both terminals. [ABSTRACT FROM AUTHOR]

• One-way navigation channel restrictions and heterogeneous vessel sailing speeds are incorporated in berth allocation problem. • Multi-type berths and multi-harbor basins are considered to investigate the berth planning of vessels at different terminals. • A mixed-integer linear programming model determines the optimal planning of berth allocation and vessel sequencing for port operators. • A tailored adaptive large neighborhood search algorithm is developed to solve the problem efficiently. Many seaports worldwide are equipped with one-way navigation channel, in which only one direction is allowed to sail through at a time and vessels thus have to queue up to enter and leave the port alternately. This paper proposes a mixed-integer linear programming (MILP) model for integrated planning of berth allocation and vessel sequencing in such a one-way navigation channel seaport, aiming to minimize weighted dwelling time of all vessels. A tailored adaptive large neighborhood search algorithm is developed for solving the model within a reasonable time. To evaluate the solution quality, a lower bound of the solution of the problem is given by a column generation algorithm that solves a set-partitioning model adapted from the MILP model. Numerical experiments on Jingtang port of China show that (i) the integrated planning model can reduce 20.90%-29.21% of the weighted dwelling time of vessels compared to the current port scheduling schemes; and (ii) the proposed adaptive large neighborhood search algorithm outperforms the GUROBI solver and some existing methods, solving all problem instances within 3 minutes with a 4.83% average optimality gap. Some managerial insights are offered to guide the port operations in a one-way navigation channel seaport. [ABSTRACT FROM AUTHOR]

• A new problem that allocates berths to deep-sea vessels and schedules feeder arrivals is studied. • A stochastic optimization model is developed to enhance vessel service while keeping congestion under control. • A novel three-phase simulation optimization method is proposed for solving the problem. • Computational performance is evaluated on instances generated from the operational data of a container port in Shanghai. Vessels served by a container port can usually be classified into two types: deep-sea vessels and feeders. While the arrival times and service times of deep-sea vessels are known to the port operator when berth plans are being devised, the service times of feeders are usually uncertain due to lack of data interchange between the port operator and the feeder operators. The uncertainty of feeder service times can incur long waiting lines and severe port congestion if the service plans for deep-sea vessels and feeders are poorly devised. This paper studies the problem of how to allocate berths to deep-sea vessels and schedule arrivals of feeders for congestion mitigation at a container port where the number of feeders to be served is significantly larger than the number of deep-sea vessels, and where the service times of feeders are uncertain. We develop a stochastic optimization model that determines the berth plans of deep-sea vessels and arrival schedules of feeders, so as to minimize the departure delays of deep-sea vessels and schedule displacements of feeders. The model controls port congestion through restricting the expected queue length of feeders. We develop a three-phase simulation optimization method to solve this problem. Our method comprises a global phase, a local phase, and a clean-up phase, where the simulation budget is wisely allocated to the solutions explored in different phases so that a locally optimal solution can be identified with a reasonable amount of computation effort. We evaluate the performance of the simulation optimization method using test instances generated based on the operational data of a container port in Shanghai. [ABSTRACT FROM AUTHOR]

In this work, we are interested in the multi-quays berth allocation and crane assignment problem under availability restrictions. Availability restrictions may arise due weather conditions, or when, for example, cranes must undergo planned maintenance in order to stay in good performance. This problem was inspired by a real-case of a bulk port in Morocco. To solve the problem we propose at first a mixed-integer programming model. Then, in view of the limitations of the proposed model, we investigate a set of heuristics based on general variable neighborhood search with three variants of variable neighborhood descent as a local search. To validate the proposed model and the proposed heuristic approach, real-world instances are used. The computational results reveal that CPLEX MIP solver consumes a lot of CPU time to solve this model, even sometimes failing to guarantee the optimality of the provided solution. On the other hand, the proposed GVNS heuristic turns out to be very efficient in solving the considered problem. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic ship berth allocation problem for a container handling port, focusing on vessel waiting time at the anchorage due to the unavailability of the berth and quay cranes. A mixed integer linear programming model considering the fuel cost associated with waiting time and operational time of the docked vessel is developed. The hiring of the quay cranes to load/unload the containers from the ship and arrangement of the vessels in different berths is taken into account. Fuel consumed by the vessels while performing their respective port operations is incorporated in the model for addressing the sustainability aspects in berth allocation problem. A chemical reaction optimization algorithm is proposed to solve the problem in a large-scale realistic environment and compared with the results with block-based genetic algorithm, genetic algorithm and particle swarm optimization. The computational experiment illustrates and validates the proposed model on a real case scenario of the port located in India. The case shows that the developed model achieves better utilization of port resources and available berths. [ABSTRACT FROM AUTHOR]

This paper addresses scheduling a set of jobs with release dates and deadlines on a set of unrelated parallel machines to minimize some minmax objective. This family of problems has a number of applications, e.g., in discrete berth allocation and truck scheduling at cross docks. We present a novel exact algorithm based on logic-based Benders decomposition as well as a heuristic based on a set partitioning reformulation of the problem. We show how our approaches can be used to deal with additional constraints and various minmax objectives common to the above-mentioned applications, solving a broad class of parallel machine scheduling problems. In a series of computational tests both on instances from the literature and on newly generated ones, our exact method is shown to solve most problems within a few minutes to optimality, while our heuristic can solve particularly challenging instances with tight time windows well in acceptable time. [ABSTRACT FROM AUTHOR]

In container terminals, operators normally form an initial plan for berth allocation before the arrival of incoming vessels. However, during the real operations, unforeseen incidents (e.g. delays, equipment breakdowns) happen frequently, which hinder the implementation of initial plans. In response to disruptions, terminal operators usually employ an experience-based strategy for berth allocation recovery. However, this practice may not work well in challenging situations, especially when extensive transshipment operations need to be conducted, and the berthing for mother and feeder vessels should be coordinated. This paper studies the disruption recovery problem for berth allocation in transshipment terminals, and develops decision support tools for terminal operators. A mixed integer linear programming model is established to adjust original berthing plan with the objective of minimizing recovery cost caused by deviations from the original plan. Quay crane assignment decision is also taken into account during disruption recovery. Transshipment connections between correlated feeder and mother vessels are also considered specifically in order to reduce the missing of transshipment connection opportunities. Squeaky Wheel Optimization heuristic is devised to find near-optimal solutions under large problem scales. Extensive computational experiments validate the effectiveness and the efficiency of designed method, and the results show practical benefit from incorporating transshipment consideration when rescheduling berth allocation. [ABSTRACT FROM AUTHOR]

• A two-story container port is introduced and investigated. • A model is proposed for integrated planning of this new port system. • A mixed-integer programming model and an algorithm are designed. • Some managerial insights based on experiments are drawn for practitioners. This study introduces a novel two-stage stochastic programming model tailored for the unique infrastructure of two-story container ports, a design that significantly enhances land productivity and operational efficiency. Our model, addressing uncertainties in vessel arrival times and container loads, incorporates advanced features like innovative quay cranes, rooftop solar panels, and dense container storage. An efficient metaheuristic is designed for large-scale applications, demonstrating a 25.63% reduction in operational costs compared to traditional decision rules. We also distill key managerial insights, notably the advantage of adopting solar power technology with consistent energy output throughout the day, offering practical guidance for port operators contemplating vertical expansion strategies. [ABSTRACT FROM AUTHOR]

• Investigate an integrated berth allocation, yard assignment and quay crane assignment problem in multiple cooperative terminals; • Propose a mixed integer nonlinear programming model; • Present a tailored adaptive large neighborhood search embedded with column generation and CPLEX. To further enhance the service level of a transshipment container port, this work considers terminal cooperation in terms of shore-side and yard-side resource sharing. This work proposes an integrated berth allocation, quay crane assignment and yard assignment problem in multiple cooperative terminals. In the proposed problem, container flow movements are classified into three types, i.e., import, export and transshipment containers, within a terminal and between terminals. A mixed integer nonlinear programming model is proposed for the proposed problem, aiming to minimize the total operating costs at all terminals considered. To address real-size instances, a tailored adaptive large neighborhood search (ALNS) embedded with column generation and CPLEX is proposed. Numerical experiments on different problem scales are provided to assess the proposed model and the proposed ALNS. Numerical experiments show that, i) the proposed algorithm can solve the instances with 4 terminals and 100 arriving vessels in less than 3 min; ii) compared with the two models without considering port cooperation and integrated optimization, the cost reduction obtained by our model is up to 14.02% and 22.00%, respectively. [ABSTRACT FROM AUTHOR]

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In this article, a continuous berth allocation problem is studied with stochastic ship arrival and handling times. The objective is to minimize a weighted sum of the expected waiting costs, berthing deviation costs and expected overtime costs. The sequence pair representation is utilized to project the solution space of the problem into two permutations. Then, a scenario-based method is used to capture the uncertainty. To effectively solve the problem over the sequence pair solution space, a simulated annealing is combined with two algorithms. One of the algorithms is used to determine the berthing positions and the other one is used to determine the berthing times. Computational experiments are conducted to evaluate the performance of the solution method and to verify the advantages of the proposed stochastic approach. The results indicate that the proposed methodology is both efficient and effective. [ABSTRACT FROM AUTHOR]

This paper integrates, from a tactical perspective, berth allocation and quay-crane assignment, two important, closely related decisions in container terminal operations in a single model. To obtain optimal solutions, a branch-and-price algorithm is sought in this paper under the framework of Dantzig–Wolfe decomposition. The algorithm decomposes the original problem to a master problem that links all vessels competing for the shared resources of berths and quay cranes and multiple per-vessel pricing subproblems that can be solved efficiently in polynomial time. Specifically, in the stage of generating promising initial feasible columns, three heuristics are adopted; during the column-updating stage, the subgradient-based Lagrangian relaxation is introduced to tackle the possibly encountered degeneracy phenomenon; the branching strategy is implemented in the pricing subproblem rather than in the master problem as reported in the literature with the benefit of avoiding incurring new dual prices, simplifying the branching process; and both breadth- and depth-first searching policies are tested to select the next node to explore. With real-life data, extensive numerical experiments are conducted to select the best choice for each stage with the strengths and drawbacks of each choice provided. And then the superiority of the branch-and-price algorithm configured with the selected combination of strategies is verified by comparing it with both CPLEX, a general-purpose solver, and a set-partitioning model, a dedicated algorithm reported in the literature. In addition, the decomposition by vessels adopted in this paper is also verified numerically by comparing it with the decomposition by berths reported in the literature, and the performance of the algorithm for other problem settings has also been tested. In conclusion, the numerical experiments show that our method outperforms the commercial solver and state-of-the-art solution methods reported in the literature in terms of both solution quality and computational time. [ABSTRACT FROM AUTHOR]

This study proposes a berth-flow network modeling approach to deal with the dynamic berth allocation problem (DBAP) with stochastic vessel arrival times. In this approach, uncertain vessel arrival times are represented using discrete probability distributions and a flexible berth allocation scheme based on the blocking plan concept is incorporated into the model to effectively utilize wharf space. This new model is referred to as the stochastic dynamic (vessel arrival) and flexible (berth space) berth allocation problem (SDFBAP) model. The aim is to minimize the sum of the expected values of unanticipated schedule delay costs and the penalties for being unable to service all vessels within the planning horizon. The proposed model is formulated as an integer multi-commodity network flow problem which can be solved with off-the-shelf solvers. Computational experiments are conducted using a real example to demonstrate the effectiveness and efficiency of the SDFBAP model. A simulation-based approach is adopted to evaluate the SDFBAP model. A number of scenario analyses are also conducted to gain insight into important model parameters. [ABSTRACT FROM AUTHOR]

• An exact method for integrated planning problem of export dry bulk terminals is given. • Problem consists of berth allocation, reclaimer scheduling, and stockyard allocation. • Logic-based Benders decomposition, incorporating MIP and CP, is developed. • A strong Benders cut using MIP formulation is introduced to identify infeasibility. • Proposed method effectively provides solutions for reasonably long planning horizons. We consider integrated planning problem of export dry bulk terminals. This problem consists of three important operations: (i) berth allocation, (ii) reclaimer scheduling, and (iii) stockyard allocation, and includes tidal time windows, multiple stocking pads and non-crossing of reclaimers. We exploit relationships among these operations to decompose this complex problem and propose a logic-based Benders decomposition algorithm. Master and subproblems are modeled with mixed-integer programming and constraint programming, respectively, such that complementary strengths of these programming paradigms are utilized. Computational experiments show that the proposed method can effectively solve the integrated problem for up to two weeks of planning horizon. [ABSTRACT FROM AUTHOR]

Highlights • Recoverable robustness is introduced for the weekly berth and quay crane planning problem. • Uncertainty in vessel arrival times and quay crane handling rates are considered. • A mathematical model and a heuristic method are presented to solve the problem. • Balance between efficiency, robustness and recoverability is discussed. • The value of buffers and stochastic solution, and the effect of scenario solution are presented. • Strict robustness and recoverable robustness are compared for the ports. Abstract The performance of a container terminal heavily relies on how efficiently the quayside resources, which are mainly berth and quay cranes, are used. The quayside related planning problems face uncertainty in various parameters, and this makes the efficient planning of these operations even more complicated. This study aims at developing a recoverable robust optimization approach for the weekly berth and quay crane planning problem. In order to build systematic recoverable robustness, a proactive baseline schedule with reactive recovery costs has been suggested. The uncertainty of vessel arrivals and the fluctuation in the container handling rate of quay cranes are considered. The baseline schedule includes berthing positions, times and quay crane assignments for all vessels along with vessel-specific buffer times and buffer quay cranes. The problem also introduces recovery plans for each scenario. The objective is to minimize the cost of baseline schedule, the recovery costs from the baseline schedule and the cost of scenario solutions for different realizations of uncertain parameters. A mathematical model and an adaptive large neighborhood based heuristic framework are presented to solve the novel problem. Computational results point out the strength of the solution methods and practical relevance for container terminals. [ABSTRACT FROM AUTHOR]

Berths and quay cranes (QCs) are two important resources in container terminals. Although good planning can shorten ship turnaround times, berths and QCs are interdependent. In the handling process, the number of QCs assigned to a ship may vary because of other ships berthing or departing. This variation, in turn, affects the QCs' efficiency and the ship handling time, thus affecting the following ships' berth-QC planning. In this article, a new mixed-integer programming model for simultaneous continuous berth-allocation and time-varying specific QC assignment is established. Furthermore, a genetic algorithm based on spatiotemporal conflict is designed for the model. Numerical experiments show that the proposed method can provide a reasonable solution for such an NP-hard problem in a reasonable time. In addition, the important parameters affecting the results are analysed. [ABSTRACT FROM AUTHOR]

To facilitate transportation, some mines construct specialized ore terminals for outbound shipments. However, these terminals frequently encounter challenges when synchronizing their schedules with the production plans of the mines. The primary issue arises due to the inherent deviation between vessel demand and mine production schedules. The terminals must efficiently arrange storage positions for diverse cargo types and berthing orders of vessels to reduce the time vessels spend at the terminal and operation time. In this study, we propose a comprehensive two-step model framework that considers various customer priorities to optimize the operational plans for each operation. In the first step, we propose a column-generation approach to generate candidate berth plans. Subsequently, we evaluate the feasibility of berth plans and construct an infeasible CUT to modify the model. We implement the developed framework in real-world case studies to demonstrate its practicality and potential. Computational outcomes underscore the method's efficacy in resolving coordination challenges between mines and terminals. Furthermore, it exhibits a noteworthy capability to diminish the terminal's spatial requirements, enhancing its pragmatic value. • We conducted optimization for the two decision levels: (a) The scheduling of ore inbound and outbound flows at the terminal. (b) The scheduling of equipment operation. • A mixed-integer model with time arcs as decision variables has been constructed. • A two-step solving framework employing column generation is proposed for rapid problem-solving. [ABSTRACT FROM AUTHOR]

This paper puts forward an integrated optimisation model that combines three distinct problems, namely berth allocation, quay crane assignment, and quay crane scheduling that arise in container ports. Each one of these problems is difficult to solve in its own right. However, solving them individually leads almost surely to sub-optimal solutions. Hence, it is desirable to solve them in a combined form. The model is of the mixed-integer programming type with the objective being to minimize the tardiness of vessels and reduce the cost of berthing. Experimental results show that relatively small instances of the proposed model can be solved exactly using CPLEX. Large scale instances, however, can only be solved in reasonable times using heuristics. Here, an implementation of the genetic algorithm is considered. The effectiveness of this implementation is tested against CPLEX on small to medium size instances of the combined model. Larger size instances were also solved with the genetic algorithm, showing that this approach is capable of finding the optimal or near optimal solutions in realistic times. [ABSTRACT FROM AUTHOR]

Minimizing cargo handling time and waiting time of ship are some of the most critical tasks for terminal operators during berth allocation planning. An efficient and effective berth allocation planning approach is not only significant for improving a terminal's productivity but worth even more in enhancing terminal serviceability. As berths are no longer leased by specific ship lines or ship companies in the majority of terminals, ships of various sizes and various cargo handling volume at a particular terminal of call are competing for the same berth for handling. As a result, there are always concerns from both terminal operators and ship companies regarding the service priority. This research contributes to deal with the dilemma terminal operators encountered in balancing service priority and terminal productivity maximization during berth allocation. This research deals with berth allocation problem which treats calling ships at various service priorities with physical constraints. The problem encountered is to determine how to cope with various ships with various attributes in the system, and the objective is to minimize the total service time of a set of given calling ships through proper berth allocation. This research adopts a chaotic genetic algorithm-based method to deal with the problem. The new formulation and method have been proposed and results obtained have been compared with the existing one in literature. The results show the improved feasibility of the proposed formulation and improved convergence speed of the proposed method over the existing one. Also, higher terminal serviceability is indicated. [ABSTRACT FROM AUTHOR]

The remarkable increases in containerized trade over the past few years have resulted in increased congestion and operational costs of container terminals, indicating the importance of the effective management of port resources under uncertainty. In this article, a novel berth allocation model is suggested for seaports, taking into consideration the disruptive effects of tides on the berthing schedule as well as the uncertainty in the arrival time of vessels. A rigorous mathematical model is presented along with a sample average approximation method to generate an efficient berth allocation plan. In addition, statistical analysis of real data gathered from a real case is presented. Numerical analysis has been conducted to verify the practical applications of the model proposed for the berth allocation problem under uncertainty. Computational results based on a real-world data set provided by Rajaee port, Iran, demonstrate the effectiveness of the proposed solution method. [ABSTRACT FROM AUTHOR]

This study investigates an integrated optimization problem on the three main types of resources used in container terminals: berths, quay cranes, and yard storage space. It presents a mixed integer linear programming model, which takes account of the decisions of berth allocation, quay crane assignment, and yard storage space unit assignment for incoming vessels. In addition, since the majority of the liner shipping services operate according to a weekly arrival pattern, the periodicity of the plan is also considered in the model and in the proposed algorithm. To solve the model on large-scale instances, a column generation (CG) procedure is developed to provide a lower bound for the integrated problem, in which an exact pseudopolynomial algorithm is designed for the pricing problems. Using this procedure, we propose a CG-based heuristic with different solution strategies and apply dual stabilization techniques to accelerate the algorithm. Based on some realistic instances, we conduct extensive numerical experiments to validate the effectiveness of the proposed model and the efficiency of the algorithm. The results show that the CG-based heuristic can yield a good solution with an approximate 1% optimality gap within a much shorter computation time than that of CPLEX. The online appendix is available at https://doi.org/10.1287/trsc.2018.0822. [ABSTRACT FROM AUTHOR]

Effective prediction of ship arrivals should provide the estimated delay or advance of arrival ships with greater accuracy, and improve the performance of container terminal operations. Therefore, taking Gangji (Yining) Container Terminal (GYCT), China, as an example, this paper resorts to data mining approaches to predict ship arrivals and explore the value of such predicted ship arrivals on the container terminal operation. First, this study applies three data mining approaches, including Back-Propagation network (BP), Classification and Regression Tree (CART) and Random Forest (RF), to estimate the delay or advance of ship arrivals using the collected data of ship arrivals. Then the predictive performance of these three approaches is compared and discussed, it is concluded that RF performs better than BP and CART, and ETA month and ship length are the most important determinants of ship arrivals in GYCT terminal. Finally, series simulation experiments are conducted to assess the value of the ship arrivals predicted by RF model on the improvement on daily operation planning of berth allocation and quay crane assignment in the GYCT terminal. And the results show that incorporating the predicted ship arrivals by RF model is beneficial to improve the performance of operation planning of GYCT terminal. [ABSTRACT FROM AUTHOR]

This paper examines the simultaneous allocation of berths and quay cranes under discrete berth situation in container terminals. The berths of discrete type have been broadly applied in realistic production especially for the terminals whose berths are not aligned in a straight line. The typical features of such berths including wharf length constraints, water depth constraints, and berth-bound quay cranes have been considered in this paper. In contrast to the previous work which only deployed the number of quay cranes besides the assignment of berths, this paper assigns berths and quay cranes simultaneously. In addition, to better fit the realistic production, some practical features related to quay cranes including the interference between quay cranes, the berth-dependent productivity of quay cranes, and limited adjustments of the assigned quay cranes during operations have also been considered in this paper. An integer programming model is formulated for this problem, and a sub-gradient-based Lagrangian relaxation algorithm is proposed. A simple but efficient greedy insertion heuristics is developed to solve the decomposed primal problems to optimality. Based on actual data, numerical experiments are conducted to test the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Transit management agencies often pre-allocate a multi-berth stop's berths to specific bus lines so that passengers can find the right place to wait for their buses. Developing optimal berth allocation plans that minimize the total bus delay is essential for mitigating bus queues at busy multi-berth stops. However, this problem is challenging due to the huge solution space, the high degree of stochasticity in bus queues, and the resulting extremely high computational cost. In this paper, we first propose a simple heuristic method inspired by queueing theory. It is based on the idea that evenly distributing the total traffic intensity (defined as the total bus arrival rate times the mean dwell time) among all the berths would produce a lower bus delay. Numerical results demonstrate that this simple method generated very good berth allocation plans (with optimality gaps < 6 % for no-overtaking and free-overtaking stops) in seconds! It does not rely on time-consuming simulation surrogate models or numerous input data such as the stochastic bus arrival processes and dwell time distributions of each bus line. To further improve the simple heuristic's performance (especially for limited-overtaking stops), we develop a cluster-based nested partition algorithm that can find a near-optimal plan (e.g., with an optimality gap of < 3 %) in a much shorter time than a previous algorithm. The algorithm employs the simple heuristic plan as the initial solution. Our methods can be applied to stops with various berth numbers, different proximities to nearby traffic signals, and under diverse bus queueing rules. • Devised smart heuristics to optimize line-to-berth allocation, reducing bus delays. • Proposed a simple heuristic evenly distributing bus traffic intensity among berths. • The simple heuristic offers near-optimal allocation and can be derived in seconds. • A cluster-based nested partition algorithm further improves the simple heuristic. • Our methods suit stops with varied berth numbers, signal proximities and queue rules. [ABSTRACT FROM AUTHOR]