Abstract
In online three-dimensional packing problems where items are received one by one and require immediate packing decisions without prior knowledge of upcoming items, considering the static stability constraint is crucial for safely packing each arriving item in real time. Unstable loading patterns can result in risks of potential damage to items, containers, and operators during loading/unloading operations. Nevertheless, static stability constraints have often been neglected or oversimplified in existing online heuristic methods in the literature, undermining the practical implementation of these methods in real-world scenarios. In this study, we analyze how different static stability constraints affect solutions' efficiency and cargo stability, aiming to provide valuable insights and develop heuristic algorithms for real-world online problems, thus increasing the applicability of this research field. To this end, we embedded four distinct static stability constraints in online heuristics, including full-base support, partial-base support, center-of-gravity polygon support, and novel partial-base polygon support. Evaluating the impact of these constraints on the efficiency of a wide range of heuristic methods on real instances showed that regarding the number of used bins, heuristics with polygon- based stabilities have superior performance against those under full-base and partial-base support stabilities. The static mechanical equilibriumapproach offers a necessary and sufficient condition for the cargo static stability, and we employed it as a benchmark in our study to assess the quality of the four studied stability constraints. Knowing the number of stable items under each of these constraints provides valuable managerial insight for decision-making in real-world online packing scenarios.

Abstract
The main goal of this paper was to develop, implement, and test a practical framework for large-scale last-mile delivery problems that employ a combination of optimisation and machine learning while focussing on different routing methods. Delivery companies in big cities choose delivery orders based on the tacit knowledge of experienced drivers, since solving a large optimisation model with several variables is not a practical solution to meet their daily needs. This framework includes three phases of districting, sequencing, and routing, and in total 30 different variants were tested in different capacities. Using the power of machine learning, a model is trained and tuned to predict driving road distances, allowing the implementation of the whole framework and improving performance from analysing 2983 stops in several hours to 58,192 stops in less than 15 minutes. The results demonstrated that Inter 1 - Centroids is the best inter-district connection method, and one of the best variants in this framework is variant 26 which managed to decrease up to 34,77% total distances with 79 fewer drivers in a full month analysis compared to the original routes of the delivery company. © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2025.

Abstract
At the practical level, the static stability constraint is one of the most important constraints in practical pallet loading problems, such as air cargo palletizing. Approaches to modeling static stability, which range from base support and mechanical equilibrium calculations to physical simulation, differ in workflow, focus, and assumptions, so choosing the right static stability approach has a substantial impact on the quality of the solution and, ultimately, on loading security. To date, little research has investigated the structural differences between approaches. The aim of this paper is to integrate knowledge and shed light on the applicability of the different approaches for the practical scenario of air cargo palletizing. We tackle this problem through (1) a reformulation and extension of static stability toward loading stability, (2) a conceptual analysis of current approaches, and (3) benchmarking that employs an independent multibody simulation on multiple heterogeneous datasets. Our results show that all approaches are prone to structure errors and vary significantly in their premises and information usage. Further, full base support is revealed to be the most restrictive approach by far, while physical simulation achieves the greatest accuracy. Given the trade-off between accuracy and runtime, the mechanical equilibrium approach is a good choice, while partial base support performs best for lower support values.

Abstract
The implementation of novel regulatory and technical requirements for the distribution of vehicle axle weights in road freight transport introduces a new set of constraints on vehicle routing. Until now, axle weight distribution in determining the load plan for freight transport units has been overlooked in the vehicle routing process. Compliance with these axle weight constraints has become paramount for road freight transport companies, since noncompliance with the axle weight distribution legislation translates into heavy fines. This work aims to provide a tool capable of generating cargo loading plans and routing sequences for a palletised cargo distribution problem. The problem addressed integrates the capacitated vehicle routing problem with time window and the two-dimensional loading problem with load balance constraints. Two integrative solution approaches are proposed, one giving greater importance to the routing and the other prioritising the loading. In addition, a novel MILP model is proposed for the 2D pallet loading problem with load-balance constraints that take advantage of the standard dimension of the pallets. Extensive computational experiments were performed with a set of well-known literature benchmark instances, extended to incorporate additional features. The computational results show the effectiveness of the proposed approaches.

Abstract
In online three-dimensional packing problems (3D-PPs), unlike offline problems, items arrive sequentially and require immediate packing decisions without any information about the quantities and sizes of the items to come. Heuristic methods are of great importance in solving online problems to find good solutions in a reasonable amount of time. However, the literature on heuristics for online problems is sparse. As our first contribution, we developed a pool of heuristics applicable to online 3D-PPs with complementary performance on different sets of instances. Computational results showed that in terms of the number of used bins, in all problem instances, at least one of our heuristics had a better or equal performance compared to existing heuristics in the literature. The developed heuristics are also fully applicable to an intermediate class between offline and online problems, referred to in this paper as a specific type of semi-online with full look-ahead, which has several practical applications. In this class, as in offline problems, complete information about all items is known in advance (i.e., full look-ahead); however, due to time or space constraints, as in online problems, items should be packed immediately in the order of their arrival. As our second contribution, we presented an algorithm selection framework, building on developed heuristics and utilizing prior information about items in this specific class of problems. We used supervised machine learning techniques to find the relationship between the features of problem instances and the performance of heuristics and to build a prediction model. The results indicate an 88% accuracy in predicting (identifying) the most promising heuristic(s) for solving any new instance from this class of problems.