Optimal berth allocation, time-variant quay crane assignment and scheduling with crane setups in container terminals (original) (raw)
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Optimal berth allocation and time-invariant quay crane assignment in container terminals
European Journal of Operational Research, 2014
Due to the dramatic increase in the world's container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BA-CAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.
Operations Research Proceedings, 2013
In this work, we focus on the integrated planning of the following problems faced within the context of seaside operations at container terminals: berth allocation, quay crane assignment, and quay crane scheduling. First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment problems called BACAP. Then we extend it by incorporating the crane scheduling problem as well, which is named BACASP. Although the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality, only small instances for BACASP can be solved optimally. To be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BA-CAP using a postprocessing algorithm. We also develop a cutting plane algorithm for the case where this condition is not satisfied. This algorithm solves BACAP repeatedly by adding cuts generated from the optimal solutions at each trial until the aforementioned condition holds.
Computers & Industrial Engineering, 2009
This paper presents a novel, mixed-integer programming (MIP) model for the quay crane (QC) scheduling and assignment problem, namely QCSAP, in a container port (terminal). Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper, thus, proposes a genetic algorithm (GA) to solve the above-mentioned QCSAP for the real-world situations. Further, the efficiency of the proposed GA is compared against the LINGO software package in terms of computational times for smallsized problems. Our computational results suggest that the proposed GA is able to solve the QCSAP, especially for large sizes.
Mathematical model for Quay Crane Scheduling Problem with spatial constraints
In the last decades, competition between port container terminals, especially between geographically close one, is rapidly increasing. To improve this competitiveness, terminal managers try to achieve rapid container vessel loading and unloading, that corresponds to a reduction of the time in port for vessels. In this paper, we focus our attention on the operational decision problem related to the seaside area of maritime container terminals. In particular, we study The Quay Crane Scheduling Problem (QCSP) which is considered as a core task of managing maritime container terminals and the optimization of these operations affects significantly the time spent by vessels at berth. The main goal behind this planning problem is to find the optimized sequence of loading and unloading tasks on a set of deployed quay cranes in order to exploit the full performances of port's resources while reducing the berth's total time occupation by vessels. In this paper, we provide a rich model for quay crane scheduling problem that covers important parameters such as ready time and due dates of Quay cranes (QCs), safety margin in order to avoid congestion between QCs and precedence relations among tasks. The proposed model seeks for a more compact mathematical formulation that can be easily solved by a standard optimization solver. Thus, we formulated the Quay Crane Scheduling Problem as a mixed-integer linear model that minimizes the sum of the QCs holding cost and tardiness penalty cost.
Naval Research Logistics (NRL), 2006
In this paper, we study the problem of scheduling quay cranes (QCs) at container terminals where incoming vessels have different ready times. The objective is to minimize the maximum relative tardiness of vessel departures. The problem can be formulated as a mixed integer linear programming (MILP) model of large size that is difficult to solve directly. We propose a heuristic decomposition approach to breakdown the problem into two smaller, linked models, the vessel-level and the berth-level models. With the same berth-level model, two heuristic methods are developed using different vessel-level models. Computational experiments show that the proposed approach is effective and efficient.
A heuristics-based solution to the continuous berth allocation and crane assignment problem
Effective utilization plans for various resources at a container terminal are essential to reducing the turnaround time of cargo vessels. Among the scarcest resources are the berth and its associated cranes. Thus, two important optimization problems arise, which are the berth allocation and quay crane assignment problems. The berth allocation problem deals with the generation of a berth plan, which determines where and when a ship has to berth alongside the quay. The quay crane assignment problem addresses the problem of determining how many and which quay crane(s) will serve each vessel. In this paper, an integrated heuristics-based solution methodology is proposed that tackles both problems simultaneously. The preliminary experimental results show that the proposed approach yields high quality solutions to such an NP-hard problem in a reasonable computational time suggesting its suitability for practical use. ยช 2013 Production and hosting by Elsevier B.V. on behalf Please cite this article in press as: M.H. Elwany et al., A heuristics-based solution to the continuous berth allocation and crane assignment problem, Alexandria Eng. J. (2013), http://dx.
Berth and quay crane allocation: a moldable task scheduling model
Journal of the Operational Research Society, 2011
We study the problem of allocating berths to incoming ships and assigning the necessary quay cranes to the ships at a port container terminal. We formulate the problem as the moldable task scheduling problem by considering the tasks as ships and processors as quay cranes assigned to the ships based on the observation that the berthing duration of a ship depends on the number of quay cranes allocated to it. In the model, the processing speed of a task is considered to be a non-linear function of the number of processors allocated to it. We present a suboptimal algorithm that obtains a feasible solution to the discrete version of the problem from the continuous version, that is, where the tasks may require fractional quantities of the resources. We conducted computational experiments to evaluate the performance of the algorithm. The computational results show that the average behaviour of the algorithm is very good.
Operations Research Proceedings
This paper deals with the combination of two decision problems, which occur consecutively while planning the charge and discharge operations of container ships in container terminals. The Berth Allocation Problem (BAP) considers the allocation of ships to berths in the course of time. The Crane Assignment Problem (CAP) addresses the assignment of quay cranes to ships. We provide a heuristic approach for the integrated solution of these problems and present computational results based on real world data.
MIP approaches for the integrated berth allocation and quay crane assignment and scheduling problem
European Journal of Operational Research, 2018
In this paper we consider an integrated berth allocation and quay crane assignment and scheduling problem motivated by a real case where a heterogeneous set of cranes is considered. A first mathematical model based on the relative position formulation (RPF) for the berth allocation aspects is presented. Then, a new model is introduced to avoid the big-M constraints included in the RPF. This model results from a discretization of the time and space variables. For the new discretized model several enhancements, such as valid inequalities, are introduced. In order to derive good feasible solutions, a rolling horizon heuristic (RHH) is presented. A branch and cut approach that uses the enhanced discretized model and incorporates the upper bounds provided by the RHH solution is proposed. Computational tests are reported to show (i) the quality of the linear relaxation of the enhanced models; (ii) the effectiveness of the exact approach to solve to optimality a set of real instances; and (iii) the scalability of the RHH based on the enhanced mathematical model which is able to provide good feasible solutions for large size instances.
2014
In this research, an integrated approach is presented to simultaneously solve quay crane scheduling and yard truck scheduling problems. A mathematical model was proposed considering the main real-world assumptions such as quay crane non-crossing, precedence constraints and variable berthing times for vessels with the aim of minimizing vessels completion time. Based on the numerical results, this proposed mathematical model has suitable efficiency for solving small instances. Two versions of imperialist competitive algorithm (ICA) are presented to heuristically solve the problem. The grouping version of algorithm (G-ICA) is used to solve the large-sized instances based on considering the allocation of trucks as a grouping problem. Effectiveness of the proposed metaheuristics on small-sized problems is compared with the optimal results of the mathematical model. In order to compare the efficiency of the proposed algorithms for large-sized instances, several instances were generated and solved, and the performance of algorithms has been compared with each other. Moreover, a simulated annealing (SA) algorithm is developed to solve the problem and evaluate the performance of the proposed ICA algorithms. Based on the experimental results, the G-ICA has a better performance compared to the ICA and SA. Also an instance of a container terminal in Iran has been investigated which shows that the proposed model and solution methods are applicable in real-world problems.