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The ever increasing demand for container transportation has led to the congestion of maritime container terminals in the world. In this work, the two interrelated problems of berth and quay crane scheduling are considered in an integrated multiobjective mathematical model. A special character of this model is that the arrival times of vessels and the failure (working) times of quay cranes are not deterministic and can vary based on some scenarios. Hence, a robust model is devised for the problem having three objectives of minimising the deviations from target berthing locations and times as well as departure delays of all vessels. This robust optimisation seeks to minimise the value of the objectives regarding all the scenarios. An exact solution approach based on the 𝜖 -constraint method by the Gurobi software is applied. Moreover, regarding the complexity of the problem, two Simulated Annealing (SA) based metaheuristics, namely a Multi-Objective Simulated Annealing (MOSA) and a Pareto Simulated Annealing (PSA) approach are adapted with a novel solution encoding scheme. The three methods are compared based on some multiobjective metrics and a statistical test. The advantage of the integration of berth and quay crane scheduling is examined as well.

The Container Relocation Problem (CRP) is one of the most important optimization problems in maritime container terminals. The objective is to minimize the number of relocation operations for retrieving containers in a sequence. If the container to be retrieved next is not at the top of a stack, unproductive relocations have to be carried out. Due to the large number of containers handled by busy terminals, a slight reduction in relocation rates can result in significant savings in operating costs. Most of the existing heuristics make relocation decisions for the blocking containers one by one, based on simple indicators. In this article, we propose a Three-Stage Heuristic (3SH) that extends the decision horizon to multiple containers to achieve a higher-quality solution. Computational experiments are conducted on 3 sets of benchmark instances, and the results show that the proposed heuristic outperforms the state-of-the-art heuristics documented in the research literature.

Maritime terminals need more efficiency in their handling operations due to the phenomenal evolution of world container traffic, and to the increase of the container ship capacity. In this work, we propose a new integrated modeling considering the optimization of maritime container terminals using straddle carriers. The problem is considered at import. We study a combination between two known problems, the first is the storage location assignment problem, and the second is the straddle carrier scheduling problem. This approach, which combines between two chronologically successive problems, leads to the use of multi-objective optimization. In fact, we study the multi-objective integrated problem of location assignment and Straddle carrier Scheduling (IPLASS) in maritime container terminal at import. We prove that the problem is NP-Complete. The objective is to minimize the operating cost which we evaluate according to eight components: the date of last task called makespan, the total vehicle operating time, the total storage bay occupation time, the number of vehicles used, the number of storage bays used, the number of storage locations used, and two different costs of storage location assignment. The location assignment costs are evaluated in order to facilitate the containers transfer for deliveries. We assume that the operating cost is a function of these components and that the influence of each component is variable and dependent on different parameters. These parameters are essentially: the number of quays in the terminal, the straddle carrier traffic layout, the number of container ships to serve in the terminal, the influence of concurrent operations in the terminal, the storage space configuration, the number of free storage bays, the number of free straddle carriers, the number of free quay cranes, the mobility of quay cranes, etc. To solve IPLASS efficiently, we propose an adapted multi-objective Tabu Search algorithm. Lower-bound evaluations are introduced to perform approximation of Pareto Front. To explore efficiently the non-convex Pareto Front Region, we evaluate also a maximized distance adapted to the set of objectives. Indicators of efficiency are developed to propose distinguished solutions to operator. 2D-projections of approximated Pareto Frontier are given to more understand the efficiency of proposed solutions.

(1) Background: The reliability of port equipment is of significant interest to industry stakeholders due to the economic and logistical factors governing the operation of maritime container terminals. Failures of key equipment like quay cranes can halt operations or cause economically significant delays. (2) Methods: The impact assessment of these disruptive events is conducted through terminal activity modeling and discrete-event simulation of internal processes. The system’s steady-state or transient condition, induced by disruptive events, is statistically assessed within a set of scenarios proposed by the authors. (3) Results: The Heidelberg–Welch and Geweke tests enabled the evaluation of steady-state and transient conditions within the modeled system, which was affected by the reduced reliability of container-handling equipment. (4) Conclusions: The research findings confirmed the usefulness of modeling and simulation in assessing the impact of equipment reliability on maritime container terminal operations. If the magnitude of the disruptive event exceeds the terminal’s absorption capacity, the system may become blocked or remain in a transient state without the ability to recover. This underscores the necessity of analyzing the reliability of critical handling equipment and implementing corrective maintenance actions when required.

Abstract Marine container terminals play a significant role for international trade networks and global market. To cope with the rapid and steady growth of the seaborne trade market, marine container terminal operators must address the operational challenges with appropriate analytical methods to meet the needs of the market. The berth allocation and scheduling problem is one of the important decisions faced by operators during operations planning. The optimization of a berth schedule is strongly associated with the allocation of spatial and temporal resources. An optimal and robust berth schedule remarkably improves the productivity and competitiveness of a seaport. A significant number of berth allocation and scheduling studies have been conducted over the last years. Thus, there is an existing need for a comprehensive and critical literature survey to analyze the state-of-the-art research progress, developing tendencies, current shortcomings, and potential future research directions. Therefore, this study thoroughly selected scientific manuscripts dedicated to the berth allocation and scheduling problem. The identified studies were categorized based on spatial attributes, including discrete, continuous, and hybrid berth allocation and scheduling problems. A detailed review was performed for the identified study categories. A representative mathematical formulation for each category was presented along with a detailed summary of various considerations and characteristics of every study. A specific emphasis was given to the solution methods adopted. The current research shortcomings and important research needs were outlined based on the review of the state-of-the-art. This study was conducted with the expectation of assisting the scientific community and relevant stakeholders with berth allocation and scheduling. Graphical Abstract Graphical Abstract

In the berth-allocation problem (BAP) the aim is to optimally schedule and assign ships to berthing areas along a quay. The objective is the minimization of the total (weighted) service time for all ships, defined as the time elapsed between the arrival in the harbor and the completion of handling. Two versions of the BAP are considered: the discrete case and the continuous case. The discrete case works with a finite set of berthing points. In the continuous case ships can berth anywhere along the quay. Two formulations and a tabu search heuristic are presented for the discrete case. Only small instances can be solved optimally. For these sizes the heuristic always yields an optimal solution. For larger sizes it is always better than a truncated branch-and-bound applied to an exact formulation. A heuristic is also developed for the continuous case. Computational comparisons are performed with the first heuristic and with a simple constructive procedure.

Following the advent of megaships, the performance requirements of container terminals have increased significantly, highlighting necessary changes in their layout, infrastructure, and equipment. We focus on the impact of megaships on a terminal within the port network of the Italian Region of Liguria, in terms of its ability to manage the flow of imports from arrival to inland destinations. We use discrete event simulation techniques to analyze the operations of a terminal and evaluate the relevant performance indices in different scenarios, which vary as a function of the “call size” of the larger containerships. The possibility of guaranteeing a more balanced modal split (favoring rail transport) for the inland distribution of containers is also evaluated. Dwell times at the yard and turnaround times at the berth are considered, with the objective of achieving a modal split of inland transport consisting of no less than 40% rail. Our results show that this objective can be achieved if a higher dwell time for outgoing containers is allowed.

This paper proposes an integrated approach to define the best consignment strategy for storing containers in an export yard of a maritime terminal. The storage strategy identifies the rules for grouping homogeneous containers, which are defined simultaneously with the assignment of each group of containers to the available blocks (bay-locations) in the yard. Unlike recent literature, this study focuses specifically on weight classes and their respective limits when establishing the consignment strategy. Another novel aspect of this work is the integration of a data-driven algorithm and operations research. The integrated approach is based on unsupervised learning and optimization models and allows us to solve large instances within a few seconds. Results obtained by spectral clustering are treated as input datasets for the optimization models. Two different formulations are described and compared: the main difference lies in how containers are assigned to bay-locations, shifting from a time-consuming individual container assignment to the assignment of groups of containers, which offers significant advantages in computational efficiency. Experimental tests are organized into three campaigns to evaluate the following: (i) The computational time and solution quality (i.e., space utilization) of the proposed models; (ii) The performance of these models against a benchmark model; (iii) The practical effectiveness of the proposed solution approach.

Background: Random truck arrivals at maritime container terminals are one of the primary reasons for gate congestion. Gate congestion negatively affects the terminal's and drayage firms' productivity and the surrounding communities in terms of air pollution and noise. To alleviate gate congestion, more and more terminals in the USA are utilizing a truck appointment system (TAS). Methods: This paper proposes a novel approach to modeling the truck appointment system problem. Unlike previous studies which largely treated this problem as a single-player game, this study explicitly models the interplay between the terminal and drayage firms with regard to appointments. A multi-player bi-level programming model is proposed, where the terminal functions as the leader at the upper-level and the drayage firms function as followers at the lower-level. The objective of the leader (the terminal) is to minimize the gate waiting cost of trucks by spreading out the truck arrivals, and the objective of the followers (drayage firms) is to minimize their own drayage cost. To make the model tractable, the bi-level model is transformed to a single-level problem by replacing the lower-level problem with its equivalent Karush-Kuhn-Tucker (KKT) conditions and the model is solved by finding the Stackelberg equilibrium in one-shot simultaneous-moves among players. For comparison purposes, a single-player version of the TAS model is also developed. Results: Experimental results indicate that the proposed multi-player model yields a lower gate-waiting cost compared to the single-player model, and that it yields higher cost savings for the drayage firms as the number of appointments per truck increases. Moreover, the solution of the multi-player model is not dependent on the objective function coefficients, unlike the single player model. Conclusions: This study demonstrates that a TAS is more effective if it considers how the assigned appointment slot affects a truck's drayage cost. It is recommended that terminal operators and port authorities initiate conversations with their TAS providers about incorporating this element into their TAS.

Container terminal capacity is often limited by (in)efficiency bottlenecks. This paper provides the design and proof of concept for the bottleneck mitigation cycle (BMC), consisting of three steps: bottleneck classification, detection and alleviation. While, often, the literature only focuses on alleviation of a single bottleneck and ignores bottleneck detection and interdependencies, this research uses the shifting bottleneck method and thereby considers a variety of possible infrastructural and operational bottlenecks. An empirical approach is adopted to find the cause of the detected bottleneck and to suggest suitable alleviation measures. Application of the BMC to a simulation model of the Fergusson Container Terminal in the Port of Auckland resulted in productivity improvements of 2–6%. To further improve the BMC, future research directions are to improve the empirical approach used for bottleneck alleviation and to apply the BMC in real-time.