Container Stowage Research Articles

A model for container stowage planning considering stability constraints

The growth in global trade has led to the deployment of mega-container ships to meet increasing transportation demands. However, the larger vessel sizes pose significant challenges for planners in arranging container loading. This study addresses the container stowage planning problem for near-sea routes, incorporating stability constraints, container types, and technical limitations related to stack weight and stress. We propose a mixed integer linear programming model to describe this problem and generate load plans that minimize total costs associated with re-stowing and bending moments (BM). To solve the model efficiently, we design a dynamic weight and time-varying particle swarm optimization (PSO) algorithm, which combines particle classification and time-varying acceleration constants. The effectiveness of the model and the efficiency of the algorithm are validated through extensive numerical experiments. The results demonstrate that our proposed algorithm outperforms the traditional PSO algorithm in both solution quality and computation time. Additionally, sensitivity analyses are conducted to derive potentially useful managerial insights for supporting shipping liners’ decision-making. This study highlights the benefits of particle classification and time-varying acceleration constants, and reveals the influence of container bay capacity and permitted frame BM.

Reconfiguring Shortest Paths in Graphs

Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely: (a) repaving road networks, (b) rerouting data packets in a synchronous multiprocessing setting, (c) the shipping container stowage problem, and (d) the train marshalling problem. When modelled as graph problems, (a) is the most general case while (b), (c), (d) are restrictions to different graph classes. We show that (a) does not admit polynomial-time algorithms (assuming P≠NP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\\mathrm{\ exttt {P}}\\,}}\ e {{\\,\\mathrm{\ exttt {NP}}\\,}}$$\\end{document}), even for relaxed variants of the problem (assuming P≠PSPACE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\\mathrm{\ exttt {P}}\\,}}\ e {{\\,\\mathrm{\ exttt {PSPACE}}\\,}}$$\\end{document}). For (b), (c), (d), we present polynomial-time algorithms to solve the respective problems. We also generalize the problem to when at most k (for a fixed integer k≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k\\ge 2$$\\end{document}) contiguous vertices on a shortest path can be changed at a time.

Reconfiguring Shortest Paths in Graphs

Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time, so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely: (a) revamping road networks, (b) rerouting data packets in a synchronous multiprocessing setting, (c) the shipping container stowage problem, and (d) the train marshalling problem. When modelled as graph problems, (a) is the most general case while (b), (c) and (d) are restrictions to different graph classes. We show that (a) is intractable, even for relaxed variants of the problem. For (b), (c) and (d), we present efficient algorithms to solve the respective problems. We also generalise the problem to when at most k (for some k >= 2) contiguous vertices on a shortest path can be changed at a time.

Many-Objective Container Stowage Optimization Based on Improved NSGA-III

The container ship stowage planning problem (CSPP) is a very complex and challenging issue concerning the interests of shipping companies and ports. This article has developed a many-objective CSPP solution that optimizes ship stability and reduces the number of shifts over the whole route while at the same time considering realistic constraints such as the physical structure of the ship and the layout of the container yard. Use the initial metacentric height (GM) along with the ship’s heeling angle and trim to measure its stability. Meanwhile, use the total amount of relocation in the container terminal yard, the voluntary shift in the container ship’s bay, and the necessary shift of the future unloading port to measure the number of shifts on the whole route. This article proposes a variant of the nondominated sorting genetic algorithm III (NSGA-III) combined with local search components to solve this problem. The algorithm can produce a set of non-dominated solutions, then decision-makers can choose the best practical implementation based on their experience and preferences. After carrying out a large number of experiments on 48 examples, our calculation results show that the algorithm is effective compared with NSGA-II and random weighted genetic algorithms, especially when applied to solve many-objective CSPPs.

Multi-objective optimization of the 3D container stowage planning problem in a barge convoy system

Mainly motivated by the massification of flows in inland shipping, where several barges can be assembled in convoys to transport a large number of containers to and from the hinterland, we introduce an original extension of the Container Stowage Planning Problem (CSPP) (which we denote the 3D – barge Convoy Container Stowage Planning Problem (3D –CCSPP)). The requirements for stowing all containers in a barge convoy entail additional constraints related to both the containers and the convoy. In this paper, the 3D –CCSPP is dealt with, on the basis of its relation to the 3D Bin-Packing Problem (3D-BPP), in which the filled objects represent the containers, and the bins indicate the convoy barges. We consider the multi-objective aspect of the problem with three realistic functions to be optimized: shifting movements, the convoy stability and the number of real-used barges. This is a new and effective aspect considering the state of the art of CSPP in inland shipping. We develop a multi-objective mathematical formulation of the 3D-CCSPP and propose a novel adaptation of the multi-objective evolutionary algorithm NSGA-II (Non-Dominated Sorting Genetic Algorithm-II) based on a set of heuristics introduced by the BPP resolution methods. Specific encoding method, generation of the initial population and genetic operators are designed based on the mathematical description of the problem. Extensive experiments are then carried out on a varied set of instances. The computational results demonstrate the effectiveness of the proposed approaches, they are evaluated using CPLEX solver and their performance is verified by a set of measurements which are adapted to the problem in real-world applications in relation to each objective function. Additional studies are carried out in sensitivity analysis to provide decision makers with a better knowledge of the problem. They can then choose, from the set of compromise solutions of the Pareto front, the most promising one for practical implementation based on their experience and preferences.

AUTOMATIC SHIP LOADING PLAN GENERATION

The purpose of this paper is to implement the optimization of container stowage plan problem for a container vessel for multiple ports using heuristic algorithm. The containers in the ship visit many different ports on their way to the ultimate destination. This work presents an implementation for the Stowage Planning Problem which raises in the ship industry when the planning for container vessel needs to be done. We have used the Greedy Approach to solve the problem. The approach is able to find a good solution for placement of container stowage. The problem's aim is to increase the total number of containers transported while lowering the penalty cost of re-handling operations.

Penyelesaian Container Stowage Problem untuk Kontainer Ukuran 20 Feet menggunakan Whale Optimization Algorithm

This paper has purpose to solve Container Stowage Problem (CSP) for 20 feet container using Whale Optimization Algorithm (WOA). CSP is a problem discussing about how to stowage a container on the ship where the purpose to minimize the unloading time. Moreover, 20 feet container is one of container types. WOA is a recently developed swarm-based metaheuristic algorithm that is based on the bubble net hunting maneuver technique of humpback whales for solving complex optimization problems. WOA had three procedures, first encircling prey, second bubble-net attacking method or exploitation phase, and third search for prey or exploration phase. WOA application program or resolving solve CSP for 20 feet container was made by using Borland C++ programming language which was implemented in three cases types of CSP data, first, the small data taking about nine containers with the number of bays, rows and tiers, respectively, are 4, 4, 4. The second and third data was medium data and big data with 62 containers and 95 containers each data, and had the number of bays, rows and tiers, respectively, are 14, 4, 5. After executing the program can be concluded the unloading time will be better if the number of whales is larger, while the number of iterations and the number of parameter control for shape of a logaritma spiral don’t affect the solution.

Solving the generalized multi-port container stowage planning problem by a matheuristic algorithm

We focus on a simplified container stowage planning problem where containers of different size and weight must be loaded and unloaded at multiple ports while maintaining the stability of the ship. We initially investigate how the difficulty in solving the problem changes with and without the consideration of container sizes and weight constraints. For this purpose, we provide integer programming formulations for the general problem as well as some special cases with identical container size and/or identical weights and evaluate their performance in randomly generated small- and medium-scale instances. We develop a matheuristic procedure, namely, an insert-and-fix heuristic, exploiting the special structure of the proposed formulations. The Insert-and-Fix method, in combination with a constructive algorithm that gives the solver an initial solution in each iteration, provides solutions with a low number of rehandles for instances with up to 5000 TEUs.

Joint optimization of container slot planning and truck scheduling for tandem quay cranes

This paper examines the loading operations of a new type of quay crane, the tandem quay crane (TQC), which has been designed to increase the terminal productivity by lifting more containers simultaneously. Due to the special characteristics of the TQC, more than one truck is required to serve a tandem-lift of it, and the containers handled in a tandem-lift must be loaded into two neighboring rows in the same tier of the containership. Of particular importance in schedules at the terminal is to coordinate the truck scheduling and container stowage slot plan with the TQCs, which is a key challenge in practice. This paper is an attempt to tackle this issue by developing a mixed integer linear programming (MILP) model with an objective of minimizing the completion time of the loading operation under the full utilization of the TQC. Due to the complexity of the MILP model, we then propose a model to derive lower bounds of the problem, and a greedy randomized adaptive search procedure (GRASP) to solve the problem. Computational experiments are conducted with a variety of instances. The results derived by GRASP for solving small size problems are within 0.04% of the optimal results obtained by the Gurobi. For large scale instances, GRASP outperforms the Gurobi in terms of the solution quality and computation time. Additionally, on average results derived by GRASP are within 8.2% of the lower bound. Further experiments demonstrate the advantage of the integrated optimization of container slot planning and truck scheduling for TQCs.

Nalysis of mathematical methods for solving the container stowage problem of container ships to ensure safety of transportation

Nalysis of mathematical methods for solving the container stowage problem of container ships to ensure safety of transportation

Design and application of reuse stage algorithm of case-based reasoning method on container stowage planning

Stowage planning is a container arrangement planning activity on container ships. The Case-Based Reasoning method can solve the newest stowage plan cases by taking a stowage plan case that has the highest similarity and has been resolved in the past as a reference for arranging. The Case-Based Reasoning method has four-stage, there are Retrieve, Reuse, Revise, Retain. The Reuse stage is to adapt the Container Loading List so that it is arranged to resemble the case that was taken at the Retrieve stage. Algorithms for the Reuse stage of the Case-Based Reasoning Method has been designed and obtained the Container Loading List Adaptation, Fill-Blank, Adding the Remaining Container, Trim Optimization, and GM Optimization Functions. The functions can be implemented in software design and automatically or manually arranged the containers based on Casebase. Hence, users make the new stowage plans easier and faster. Based on the results of software testing, the difference between LCB and LCG is less than 1% LBP so that the Trim was fulfilled, and GM obtained a positive value so that the ship was in a stable condition.

A Mathematical Model and Two-Stage Heuristic for the Container Stowage Planning Problem With Stability Parameters

Owing to the significant increase in the volume of world trade, mega-container vessels are being used to meet transportation demands. As the size of the vessels increases, the loading sequence of containers onto the vessels presents an important challenge for planners. In this study, we consider the container stowage planning problem with stability constraints (e.g. shear force, bending moment, trim) and develop a mixed integer linear programming (MILP) formulation which generates load plans by minimizing total cost associated with the over-stows and trimming moments. Our study adopts a holistic perspective which encompasses several real-world features such as different container specifications, a round-robin tour of multiple ports, technical limitations related to stack weight, stress, and ballast tanks. We also propose a two-stage heuristic solution methodology that employs an integer programming (IP) formulation and then a swapping heuristic (SH) algorithm. This approach first acquires a lower bound on the total over-stow cost with the IP model, thereby creating an initial bay plan. Then, it applies the SH algorithm to this initial bay plan to minimize cost resulting from trimming moments. The efficiency of the MILP formulation and heuristic algorithm is investigated through numerical examples. The results have shown that the heuristic has greatly improved the solution times as well as the size of the solvable problems compared to the MILP formulation. In particular, the two-stage heuristic can solve all size problem instances within an average optimality gap of 0-25% in less than 8 minutes, whereas the MILP can only achieve an approximate optimality gap of 55-80% in 2 hours.

Operational strategies for managing container terminals. An approach based on closed queueing networks.

The port performance can be improved by a well-defined operations plan. We present a closed Jackson network (CJN) approach to analyse port operations from vessel to yard. The tool is not only focused on the berthing line, but also on the service level at the storage yard. It aims to determine the best way to operate a containership using two crucial parameters: container stowage and truck traffic. Thus, the CJN model determines the impact of cargo stowage on port performance (μ1) and the impact of traffic on port performance (μ2). Both are crucial to set the best strategy and ensure the efficient use of handling equipments. The CJN model is flexible in the sense that managers may plan different scenarios. The study suggests that terminal operators can achieve substantial benefits by means of the best resource allocation in each scenario.

A decision-support framework for the stowage of maritime containers in inland shipping

The typical voyage of a barge transporting maritime containers inland, consists of visiting a set of terminals where loading/unloading operations occur. The required stowage plans must meet stability requirements during all transport phases and avoid costly re-handling operations. In this paper, we formalize this problem and consider a typical dry-port transport system. We propose a comprehensive mathematical model that seeks to maximize stowed containers. To solve it, we develop a hybrid metaheuristic approach, based on local search and an industrial solver. Numerical experiments, based on real-world data, provide insights into the performances of the proposed framework and current stowage practices.

Minimizing overstowage in master bay plans of large container ships

This study proposes a mathematical model that minimizes overstowage in class-based master bay plans for large container ships. With the advantage of an underlying multi-commodity network structure, solutions are obtained within reasonable computation time in the case of 14,000-TEU ships. In addition, changeable bay configuration patterns due to different container sizes—an important but rarely discussed issue—are efficiently addressed by adding specially designed arcs and side constraints. Our model can support container stowage planners by providing a flexible and efficient approach for allocating ship slots to containers of different lengths when preparing class-based master bay plans for large container ships.

Including Containers with Dangerous Goods in the Multi-Port Master Bay Planning Problem

In this paper we extend existing models for Master Bay Planning by handling containers holding dangerous goods, so-called IMO containers. Incompatible IMO containers must be separated from each other on board a vessel according to specic rules. These rules affect both Master Bay Planning and Slot Planning, which are the two planning problems normally handled in container stowage planning. Some research is doneto include IMO containers in Slot Planning, but, to the best of our knowledge, this is the rst time handling of IMO containers is included in Master Bay Planning. We present results from computational tests showing that our model can be solved to optimality, or near optimality, in reasonable time for realistically sized instances.

A Forecast Model of the Number of Containers for Containership Voyage

Container ships must pass through multiple ports of call during a voyage. Therefore, forecasting container volume information at the port of origin followed by sending such information to subsequent ports is crucial for container terminal management and container stowage personnel. Numerous factors influence container allocation to container ships for a voyage, and the degree of influence varies, engendering a complex nonlinearity. Therefore, this paper proposes a model based on gray relational analysis (GRA) and mixed kernel support vector machine (SVM) for predicting container allocation to a container ship for a voyage. First, in this model, the weights of influencing factors are determined through GRA. Then, the weighted factors serve as the input of the SVM model, and SVM model parameters are optimized through a genetic algorithm. Numerical simulations revealed that the proposed model could effectively predict the number of containers for container ship voyage and that it exhibited strong generalization ability and high accuracy. Accordingly, this model provides a new method for predicting container volume for a voyage.

An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay

Stowage operations in container terminals are an important part of a port's operational system, as the quality of stowage operations will directly affect the efficiency of port loading and discharge operations, and the scheduling of container shipping liners. The intelligent stowage of containers in container ships was studied in this work. A multi-objective integer programming model was constructed with the minimization of container rehandling, yard crane movements, and the sum of weight differences between stacked container pairs as its objective functions, to address the need for intelligent optimization of single bay export container stowage on a ship's deck. This model also satisfies the stability requirements of preliminary stowage plans drawn by shipping companies, and the operational requirements of container terminals. Linear computational methods were then constructed to transform non-linear constraints into linear ones for better AIMMS solution. Through numerous case analyses and systematic tests, it was shown that our system is able to rapidly solve for stowage planning optimization problems with complex preliminary stowage data, thus proving the applicability and effectiveness of this model. In particular, the application of this model will simultaneously address the safety of ship voyages, the transportation quality of shipping containers and other forms of cargo, and the cost efficiency of ship operations. In addition, this model will also contribute to the optimization of loading and discharge processes in container terminals. Therefore, our model has immense practical value for improving port productivity, as it will contribute to the organization of port operations in a rational, orderly and effective manner.

A Decomposition Method for Finding Optimal Container Stowage Plans

In transportation of goods in large container ships, shipping industries need to minimize the time spent at ports to load/unload containers. An optimal stowage of containers on board minimizes unnecessary unloading/reloading movements, while satisfying many operational constraints. We address the basic container stowage planning problem (CSPP). Different heuristics and formulations have been proposed for the CSPP, but finding an optimal stowage plan remains an open problem even for small-sized instances. We introduce a novel formulation that decomposes CSPPs into two sets of decision variables: the first defining how single container stacks evolve over time and the second modeling port-dependent constraints. Its linear relaxation is solved through stabilized column generation and with different heuristic and exact pricing algorithms. The lower bound achieved is then used to find an optimal stowage plan by solving a mixed-integer programming model. The proposed solution method outperforms the methods from the literature and can solve to optimality instances with up to 10 ports and 5,000 containers in a few minutes of computing time. The online appendix is available at https://doi.org/10.1287/trsc.2017.0795 .

A Near-Optimal Algorithm for Constraint Test Ordering in Automated Stowage Planning

The container stowage planning problem is known to be NP-hard and heuristic algorithms have been proposed. Conventionally, the efficiency of the stowage planning algorithms are improved by pruning or reducing the search space. We observe that constraint evaluation is the core of most algorithms. In addition, the order at which the constraints are evaluated can have significant impact on the efficiency of the constraint evaluation engine. We propose random sample model (RSM) and sequential sample model (SSM) for analysis of the problem. We present and evaluate seven strategies in optimizing the constraint evaluation engine. We show how to achieve the optimal constraint ordering with respect to RSM and SSM, respectively. However, the optimal ordering for SSM requires perfect information about the states of the constraint tests, which is impractical. We present an alternative strategy and show empirically that its efficiency is close to the optimal. Experiments show that, compared to a naive ordering, an average of 2.74 times speed up in the evaluation engine can be achieved. Note to Practitioners —Automated stowage planning has become a trend as the number of mega-scale containerships being deployed has increased drastically over the past decade. Due to the nature of the problem, it is impractical to expect the best stowage plan within a limited amount of time, and hence, many heuristics have been devised to reduce the solution space. Many heuristics algorithms share a common core-repeatedly selecting a stowage slot and a container (selection mechanism) and evaluate whether all of the constraints are satisfied. To improve the efficiency, most studies aim to reduce the number of location-container pairs being considered. We consider an alternative approach that improves the efficiency of the constraint evaluation engine. Specifically, we show how to improve the efficiency by strategically reordering the sequence in which the constraints are evaluated. With the improvements on the efficiency, the stowage algorithm is one step closer to being able to generate solutions in real time. This may enable the shipping companies to take last-minute shipment order and react to changes in demands quickly.