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 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

Hybrid Approach for Solving Real-World Bin Packing Problem Instances Using Quantum Annealers

Efficient packing of items into bins is a common daily task. Known as Bin Packing Problem, it has been intensively studied in the field of artificial intelligence, thanks to the wide interest from industry and logistics. Since decades, many variants have been proposed, with the three-dimensional Bin Packing Problem as the closest one to real-world use cases. We introduce a hybrid quantum-classical framework for solving real-world three-dimensional Bin Packing Problems (Q4RealBPP), considering different realistic characteristics, such as: i) package and bin dimensions, ii) overweight restrictions, iii) affinities among item categories and iv) preferences for item ordering. Q4RealBPP permits the solving of real-world oriented instances of 3dBPP, contemplating restrictions well appreciated by industrial and logistics sectors.Comment: 9 pages, 24 figure

Imagine: Deflateables

Pneumatic structures are thoroughly investigated and developed during the 1960s. However, the energy crisis and aesthetic developments impeded the use of these structures as a mainstream construction method. Nowadays, they are typically used in special areas of architecture and design. Deflateables concentrates on the very limited knowledge of vacuum constructions and develops a range of aesthetic, technical and functional design possibilities. However, very few designs that use pressurised constructions have actually been realised, even right down to the present day - despite the fact that this technology offers simple, positive aspects: the air pressure of the earth can be used as a stabilising and form-giving parameter, creating a specific and inspiring shape. In addition, the very nature of this technology provides varying degrees of thermal and acoustic insulation. Of course, there are weak points such as potential leakage and the need for high pressurisation of the construction; but new material technologies and specific structural concepts will bring solutions to such issues. Exploiting the possibilities of extremely light and energetically active constructions, deflateables are one of the promising fields of architectural and design developments. The chance to create structures that can move and react to requests such as user and climate requirements, as well as formative demands, lifts this topic onto the level of a realistic and usable technology for as-yet unknown design possibilities.&nbsp

Imagine: Deflateables

Pneumatic structures are thoroughly investigated and developed during the 1960s. However, the energy crisis and aesthetic developments impeded the use of these structures as a mainstream construction method. Nowadays, they are typically used in special areas of architecture and design. Deflateables concentrates on the very limited knowledge of vacuum constructions and develops a range of aesthetic, technical and functional design possibilities. However, very few designs that use pressurised constructions have actually been realised, even right down to the present day - despite the fact that this technology offers simple, positive aspects: the air pressure of the earth can be used as a stabilising and form-giving parameter, creating a specific and inspiring shape. In addition, the very nature of this technology provides varying degrees of thermal and acoustic insulation. Of course, there are weak points such as potential leakage and the need for high pressurisation of the construction; but new material technologies and specific structural concepts will bring solutions to such issues. Exploiting the possibilities of extremely light and energetically active constructions, deflateables are one of the promising fields of architectural and design developments. The chance to create structures that can move and react to requests such as user and climate requirements, as well as formative demands, lifts this topic onto the level of a realistic and usable technology for as-yet unknown design possibilities.&nbsp

A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach

Increasing fuel costs, post-911 security concerns, and economic globalization provide a strong incentive for container carriers to use available container space more efficiently, thereby minimizing the number of container trips and reducing socio-economic vulnerability. A heuristic algorithm based on a tertiary tree model is proposed to handle the container loading problem (CLP) with weakly heterogeneous boxes. A dynamic space decomposition method based on the tertiary tree structure is developed to partition the remaining container space after a block of homogeneous rectangular boxes is loaded into a container. This decomposition approach, together with an optimal-fitting sequencing and an inner-right-corner-occupying placement rule, permits a holistic loading strategy to pack a container. Comparative studies with existing algorithms and an illustrative example demonstrate the efficiency of this algorithm

Moldable Items Packing Optimization

This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes

Novel approaches to container loading: from heuristics to hybrid tabu search

A thesis submitted for the degree of Doctor of Philosophy of the University ofBedford shireThis work investigates new approaches to the container loading problem which address the issue of how to load three-dimensional, rectangular items (e.g. boxes) into the container in such a way that maximum utilisation is made of the container space. This problem occurs in several industry sectors where the loading approach places cargo effectively into aeroplanes, ships, trailers or trucks in order to save considerable cost. In carrying out this work, the investigation starts by developing a new heuristic approach to the two-dimensional bin packing problem, which has lower complexity than container loading in the aspects of constraints and geometry. A novel approach, including the heuristic strategies and handling method for remaining areas, is developed that can produce good results when testing with benchmark and real world data. Based on the research for two-dimensional bin packing, a novel heuristic approach is developed to deal with the container loading problem with some practical constraints. The heuristic approach to container loading also includes heuristic strategies and the handling of remaining spaces. The heuristic strategies construct effective loading arrangements where combinations of identical or different box types are loaded in blocks. The handling method for remaining spaces further improves the loading arrangements through the representation, partitioning and merging of remaining spaces. The heuristic approach obtains better volume utilisation and the highest stability compared with other published heuristic approaches. However, it does not achieve as high a volume utilisation as metaheuristic approaches, e.g. genetic algorithms and tabu search.To improve volume utilisation, a new hybrid heuristic approach to the container loading problem is further developed based on the tabu search technique which covers the encoding, evaluation criterion and configuration of neighbourhood and candidate solutions. The heuristic strategies as well as the handling method for remaining spaces developed in the heuristic approach are used in this new hybrid tabu search approach. It is shown that the hybrid approach has better volume utilisation than the published approaches under the condition that all loaded boxes with one hundred per cent support from below. In addition, the experimental results show that both the heuristic and hybrid tabu search approaches can also be applied to the multiple container loading problem

The split delivery vehicle routing problem with three-dimensional loading constraints

 The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints (3L-SDVRP) combines vehicle routing and three-dimensional loading with additional packing constraints. In the 3L-SDVRP splitting deliveries of customers is basically possible, i.e. a customer can be visited in two or more tours. We examine essential problem features and introduce two problem variants. In the first variant, called 3L-SDVRP with forced splitting, a delivery is only split if the demand of a customer cannot be transported by a single vehicle. In the second variant, termed 3L-SDVRP with optional splitting, splitting customer deliveries can be done any number of times. We propose a hybrid algorithm consisting of a local search algorithm for routing and a genetic algorithm and several construction heuristics for packing. Numerical experiments are conducted using three sets of instances with both industrial and academic origins. One of them was provided by an automotive logistics company in Shanghai; in this case some customers per instance have a total freight volume larger than the loading space of a vehicle. The results prove that splitting deliveries can be beneficial not only in the one-dimensional case but also when goods are modeled as three-dimensional items