Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

The Economic Impact of Container-loading Problem

Thousands of containers with different types of cargo are loaded every day in multiple manufacturing and logistics centres in the world. The main problem arising from these handlings is how to make the maximum use of all the available container capacities, while keeping the overall costs of transport per cargo unit as low as possible. The previous research mostly focuses on studying different algorithms for optimising container loading with cargo that has already been assigned based on its dimensions and weight. However, this paper will emphasise the importance of using algorithms in the planning and preparation of the cargo itself during the manufacturing processes before it is dispatched for loading into containers. Besides the length, width, height, and weight of the cargo itself, a fifth component influencing the overall transport costs will be considered, i.e. the manner of loading a container. The research will be carried out on an example of a container shipment of wooden sawn timber materials

The Air Cargo Load Planning Problem

A major operational planning problem in the air cargo industry is how to arrange cargo in an aircraft to fly safely and profitably. Therefore, a challenging planning puzzle has to be solved for each flight. Besides its complexity, the planning is mostly done manually today, which is a time consuming process with uncertain solution quality. The literature on loading problems in an air cargo context is scarce and the term is used ambiguously for different subproblems like selecting containers, packing items into containers, or loading containers into aircraft. All of the presented models only focus on certain aspects of what is in practice a larger planning problem. Additionally, some practical aspects have not been covered in the literature. In this work, we provide a comprehensive overview of the air cargo load planning problem as seen in the operational practice of our industrial partner. We formalize its requirements and the objectives of the respective stakeholders. Furthermore, we develop and evaluate suitable solution approaches. Therefore, we decompose the problem into four steps: aircraft configuration, build-up scheduling, air cargo palletization, and weight and balance. We solve these steps by employing mainly mixed-integer linear programming. Two subproblems are further decomposed by adding a rolling horizon planning approach and a Logic-based Benders Decomposition (LBBD). The actual three-dimensional packing problem is solved as a constraint program in the subproblem of the LBBD. We evaluated our approaches on instances containing 513 real and synthetic flights. The numerical results show that the developed approaches are suitable to automatically generate load plans for cargo flights. Compared to load plans from practice, we could achieve a 20 percent higher packing density and significantly reduce the handling effort in the air cargo terminal. The achieved costs of additional fuel burn due to aircraft imbalances and reloading operations at stop-over airports are almost negligible. The required runtimes range between 13 and 38 minutes per flight on standard hardware, which is acceptable for non-interactive planning. Cargo airlines can significantly profit from employing the developed approaches in their operational practice. More and especially the profitable last-minute cargo can be transported. Furthermore, the costs of load planning, handling effort, and aircraft operations can be significantly reduced

Three-Dimensional Container Loading: A Simulated Annealing Approach

High utilization of cargo volume is an essential factor in the success of modern enterprises in the market. Although mathematical models have been presented for container loading problems in the literature, there is still a lack of studies that consider practical constraints. In this paper, a Mixed Integer Linear Programming is developed for the problem of packing a subset of rectangular boxes inside a container such that the total value of the packed boxes is maximized while some realistic constraints, such as vertical stability, are considered. The packing is orthogonal, and the boxes can be freely rotated into any of the six orientations. Moreover, a sequence triple-based solution methodology is proposed, simulated annealing is used as modeling technique, and the situation where some boxes are preplaced in the container is investigated. These preplaced boxes represent potential obstacles. Numerical experiments are conducted for containers with and without obstacles. The results show that the simulated annealing approach is successful and can handle large number of packing instances

Concept design of a fast sail assisted feeder container ship

A fast sail assisted feeder container ship concept has been developed for the 2020 container market in the South East Asian and Caribbean regions.The design presented has met the requirements of an initial economic study, with a cargo capacity of 1270 twenty-foot equivalent unit containers, meeting the predictions of container throughput derived from historical data. In determining suitable vessel dimensions, account has also been taken for port and berthing restrictions, and considering hydrodynamic performance. The vessel has been designed for a maximum speed of 25 knots, allowing it to meet the demand for trade whilst reducing the number of ships operating on the routes considered.The design development of the fast feeder concept has involved rigorous analyses in a number of areas to improve the robustness of the final design. Model testing has been key to the development of the concept, by increasing confidence in the final result. This is due to the fact that other analysis techniques are not always appropriate or accurate. Two hull forms have been developed to meet requirements whilst utilising different propulsor combinations. This has enabled evaluation of efficiency gains resulting from different hydrodynamic phenomena for each design. This includes an evaluation of the hydrodynamic performance when utilising the sail system. This has been done using a combination of model test results and data from regression analysis. The final propulsor chosen is a contra-rotating podded drive arrangement. Wind tunnel testing has been used to maximise the performance of a Multi-wing sail system by investigating the effects of wing spacing, stagger and sail-container interactions. This has led to an increase in lift coefficient of 32% from initial predictions. The savings in power requirement due to the sail system are lower than initially predicted. However, another benefit of their installation, motion damping, has been identified. Whilst this has not been fully investigated, additional fuel savings are possible as well as improved seakeeping performance.The design is shown to be environmentally sustainable when compared to existing vessels operating on the proposed routes. This is largely due to the use of low-carbon and zero-sulphur fuel (liquefied natural gas) and improvements in efficiency regarding operation. This especially relates to cargo handling and scheduling. Green house gas emissions have been predicted to fall by 42% and 40% in the two regions should the design be adopted. These savings are also due to the use of the Multi-wing sail system, which contributes to reductions in power requirement of up to 6% when the vessel operates at its lower speed of 15 knots. It is demonstrated that the fast feeder is also economically feasible, with predicted daily cost savings of 27% and 33% in the South East Asian and Caribbean regions respectively. Thus the fast feeder container ship concept is a viable solution for the future of container transhipment. <br/

Constraint programming methods in three-dimensional container packing

Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and packing problems are a class of combinatorial problems in which there are specified two classes of objects: big and small items and the task is to place the small items within big items. Even in the 1-dimensional case, bin-packing is strongly NP-hard (Garey 1978), which suggests, that exact solutions may not be found in a reasonable time for bigger instances. In the literature, there are presented many various approaches to packing problems, e.g. mixed-integer programming, approximation algorithms, heuristic solutions, and local search algorithms, including metaheuristic approaches like Tabu Search or Simulated Annealing. The main goal of this work is to review existing solutions, survey the variants arising from the industry applications, present a solution based on constraint programming and compare its performance with the results in the literature. Optimization with constraint programming is a method searching for the global optima, hence it may require a higher workload compared to the heuristic and local search approaches, which may finish in a local optimum. The performance of the presented model will be measured on test data used in the literature, which were used in many articles presenting a variety of approaches to three-dimensional container packing, which will allow us to compare the efficiency of the constraint programming model with other methods used in the operational research

Predicting Static Stability with Data-Driven Physics in Air Cargo Palletizing

Proposing air cargo palletizing solutions requires an assessment by a physics engine of whether a solution is physically stable, which can take up a disproportionate amount of computation and, thus, produce a bottleneck in the optimization pipeline. This problem can be tackled by replacing the physics engine with a data-driven model that learns to map proposed packing pattern solutions directly to its stability value. We develop a prototype of such a datadriven model and find that this approach yields practicable results and does so multiple orders of magnitudes faster than a commonly used physics engine