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

CONTAINER LOADING ALLOCATION TO IMPROVE SPACE AND LOADING UTILIZATION OF FLEET COMPARTMENT CAPACITY BY USING GENETIC ALGORITHM

PT. XYZ is the current leading automotive company, the supplier that is part of its subsidiary company provides services in form of supply and distribution of raw material. Based on data collected from January till March, the problem appears is the compartment fleet utilization that is far from the maximum capacity. According to the plan production control department, the desired average loading utilization is 16 ton per delivery, while the average loading utilization is 42% or 6,8 ton per delivery. In addition, there are also some deliveries exceeding maximum capacity allowed. Therefore in this research, the most suitable loading pattern is needed to improve utilization of fleet compartment with heterogeneous fleet and heterogeneous material dimension. Loading pattern is also needed as supporting tools for the department by considering weight limit, physical dimension of material and compartment fleet dimension, so that overloaded and unburdened deliveries can be avoided. The research is conducted in plan production control department to gain more information about the fleet, production demand, and raw material properties. Genetic algorithm is used as method for solving the problem and visualize the loading pattern by using Matlab. The calculation is conducted toward loading and space utilization of compartment fleet. From the research, the utilization of space can be optimized to 6% and loading utilization can be optimized up to 50%

A two-stage packing procedure for a Portuguese trading company

This case study deals with a two-stage packing problem that has to be solved in the daily distribution process of a Portuguese trading company. At the first stage boxes including goods are to be packed on pallets while at the second stage these pallets are loaded into one or more trucks. The boxes have to be transported to different customers and the actual goal is to guarantee a sufficient utilization of the truck loading spaces. A two-stage packing procedure is proposed to cover both problem stages. First boxes are loaded onto pallets using a well-known container loading algorithm. Then trucks are filled with loaded pallets by means of a new tree search algorithm. The applicability and performance of the two-stage approach was evaluated with a set of instances that are based on actual company data

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

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

Multi-objective vehicle routing and loading with time window constraints:a real-life application

Motivated by a real-life application, this research considers the multi-objective vehicle routing and loading problem with time window constraints which is a variant of the Capacitated Vehicle Routing Problem with Time Windows with one/two-dimensional loading constraints. The problem consists of routing a number of vehicles to serve a set of customers and determining the best way of loading the goods ordered by the customers onto the vehicles used for transportation. The three objectives pertaining to minimisation of total travel distance, number of routes to use and total number of mixed orders in the same pallet are, more often than not, conflicting. To achieve a solution with no preferential information known in advance from the decision maker, the problem is formulated as a Mixed Integer Linear Programming (MILP) model with one objective—minimising the total cost, where the three original objectives are incorporated as parts of the total cost function. A Generalised Variable Neighbourhood Search (GVNS) algorithm is designed as the search engine to relieve the computational burden inherent to the application of the MILP model. To evaluate the effectiveness of the GVNS algorithm, a real instance case study is generated and solved by both the GVNS algorithm and the software provided by our industrial partner. The results show that the suggested approach provides solutions with better overall values than those found by the software provided by our industrial partner

Scheduling cross-docking operations under uncertainty: A stochastic genetic algorithm based on scenarios tree

A cross-docking terminal enables consolidating and sorting fast-moving products along supply chain networks and reduces warehousing costs and transportation efforts. The target efficiency of such logistic systems results from synchronizing the physical and information flows while scheduling receiving, shipping and handling operations. Within the tight time-windows imposed by fast-moving products (e.g., perishables), a deterministic schedule hardly adheres to real-world environments because of the uncertainty in trucks arrivals. In this paper, a stochastic MILP model formulates the minimization of penalty costs from exceeding the time-windows under uncertain truck arrivals. Penalty costs are affected by products' perishability or the expected customer’ service level. A validating numerical example shows how to solve (1) dock-assignment, (2) while prioritizing the unloading tasks, and (3) loaded trucks departures with a small instance. A tailored stochastic genetic algorithm able to explore the uncertain scenarios tree and optimize cross-docking operations is then introduced to solve scaled up instaces. The proposed genetic algorithm is tested on a real-world problem provided by a national delivery service network managing the truck-to-door assignment, the loading, unloading, and door-to-door handling operations of a fleet of 271 trucks within two working shifts. The obtained solution improves the deterministic schedule reducing the penalty costs of 60%. Such results underline the impact of unpredicted trucks’ delay and enable assessing the savings from increasing the number of doors at the cross-dock

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

Mathematical models for multicontainer loading problems

This paper deals with the problem of a distribution company that has to serve its customers by putting first the products on pallets and then loading the pallets onto trucks. We approach the problem by developing and solving integer linear models. We start with basic models, that include the essential features of the problem, such as respecting the dimensions of the truck, and not exceeding the total weight capacity and the maximum weigh capacity on each axle. Then, we add progressively new conditions to consider the weight and volume of pallet bases and to include other desirable features for the solutions to be useful in practice, such as the position of the center of gravity and the minimization of the number of pallets.The models have been tested on a large set of real instances involving up to 46 trucks and kindly provided to us by a distribution company. The results show that in most cases the optimal solution can be obtained in small running times. Moreover, when optimality cannot be proven, the gap is very small, so we obtain high quality solutions for all the instances that we tested