Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer

Motivated by a real-world application, we present a multi-container loading problem with 3-open dimensions. We formulate it as a biobjective mixed-integer nonlinear program with lexicographic objectives in order to reflect the decision maker’s optimization priorities. The first objective is to minimize the number of containers, while the second objective is to minimize the volume of those containers. Besides showing the NP-hardness of this sequential optimization problem, we provide bounds for it which are used in the three proposed algorithms, as well as, on their evaluation when a certificate of optimality is not available. The first is an exact parametric-based approach to tackle the lexicographic optimization through the second objective of the problem. Nevertheless, given that the parametric programs correspond to large nonlinear mixed-integer optimizations, we present a heuristic that is entirely mathematical-programming based. The third algorithm enhances the solution quality of the heuristic. These algorithms are specifically tailored for the real-world application. The effectiveness and efficiency of the devised heuristics is demonstrated with numerical experiments

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

Volumetric Techniques for Product Routing and Loading Optimisation in Industry 4.0: A Review

Industry 4.0 has become a crucial part in the majority of processes, components, and related modelling, as well as predictive tools that allow a more efficient, automated and sustainable approach to industry. The availability of large quantities of data, and the advances in IoT, AI, and data-driven frameworks, have led to an enhanced data gathering, assessment, and extraction of actionable information, resulting in a better decision-making process. Product picking and its subsequent packing is an important area, and has drawn increasing attention for the research community. However, depending of the context, some of the related approaches tend to be either highly mathematical, or applied to a specific context. This article aims to provide a survey on the main methods, techniques, and frameworks relevant to product packing and to highlight the main properties and features that should be further investigated to ensure a more efficient and optimised approach

Embodied carbon determination in the transportation stage of prefabricated constructions: A micro-level model using the bin-packing algorithm and modal analysis model

The prefabricated construction generates considerable embodied carbon emissions during the manufacture, transportation, and construction stages. However, the contribution from the transportation stage is usually overlooked, leading to biases in life-cycle sustainability analysis of these projects. This article provides a micro-level transportation CE calculation method that estimates the project-specific emissions according to the features of prefabricated elements. The method simulates the transportation status of prefabricated elements as bin packing (BP) problems. Then, a modal analysis model is employed to calculate the CE of each vehicle based on vehicle type, road condition, and freight weight. Considering the minimum transportation CE as objective, a genetic algorithm is then used to search for the optimal solution and corresponding CE values. The comparative results among different CE calculation methods show that this BP-algorithm-based method provides reliable data across different loading rates, rendering the method suitable for calculating the transportation CE of prefabricated construction projects. Additionally, the BP-algorithm-based method differs the emission characteristics among different element types—the prefabricated floor generates the highest emissions, followed by prefabricated beam, wall, and column—suggesting the need to identify disparate emission factors for different element types and considering the sustainability aspects when selecting prefabricated approaches of projects. The results also highlight the efficiency of considering more prefabricated elements in a single transportation batch and selecting suitable vehicles for the optimisation of embodied carbon emissions. Architects, engineers, and contractors can use the method for project-specific transportation CE calculations and transportation planning. The calculation variables concerning the geometric features of prefabricated elements and vehicles can be adopted in the optimisation of project design and construction management for achieving less embodied carbon

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

An online packing heuristic for the three-dimensional container loading problem in dynamic environments and the Physical Internet

In this paper, we consider the online three-dimensional container loading problem. We develop a novel online packing algorithm to solve the three-dimensional bin packing problem in the online case where items are not know well in advance and they have to be packed in real-time when they ar-rive. This is relevant in many real-world scenarios such as automated cargo loading in warehouses. This is also relevant in the new logistics model of Physical Internet. The effectiveness of the online packing heuristic is evalu-ated on a set of generated data. The experimental results show that the algo-rithm could solve the 3D container loading problems in online fashion and is competitive against other algorithms both in the terms of running time, space utilization and number of bins

Multi-objective engineering shape optimization using differential evolution interfaced to the Nimrod/O tool

This paper presents an enhancement of the Nimrod/O optimization tool by interfacing DEMO, an external multiobjective optimization algorithm. DEMO is a variant of differential evolution – an algorithm that has attained much popularity in the research community, and this work represents the first time that true multiobjective optimizations have been performed with Nimrod/O. A modification to the DEMO code enables multiple objectives to be evaluated concurrently. With Nimrod/O’s support for parallelism, this can reduce the wall-clock time significantly for compute intensive objective function evaluations. We describe the usage and implementation of the interface and present two optimizations. The first is a two objective mathematical function in which the Pareto front is successfully found after only 30 generations. The second test case is the three-objective shape optimization of a rib-reinforced wall bracket using the Finite Element software, Code_Aster. The interfacing of the already successful packages of Nimrod/O and DEMO yields a solution that we believe can benefit a wide community, both industrial and academic