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
To maintain high levels of efficiency and compliance with delivery dates, automotive repair shops must have a good system for scheduling their activities. The scheduling of the activities of an automotive repair shop is a very complex task to be performed manually. Throughout this work, a Decision Support System (DSS) was developed and tested that considers two major constraints in an automotive workshop: human resources (technicians) and physical resources (work stalls). The proposed DSS has an embedded MIP model that assigns a technician and a work stall to each job, according to the input conditions. The DSS also generates schedules with the planning of technicians and jobs. The system was tested with real data from an automotive workshop and was able to create plans and schedules not only for the human and physical resources in but also to analyse the limiting resources of the workshop.

Abstract
Additive Layer Manufacturing, particularly Fused Deposition Modelling, faces significant batch loss risks during production. The traditional Concurrent Printing Mode produces all parts simultaneously (layer-by-layer, bottom-to-top), efficiently using printing space but risking complete batch failure if problems occur. In contrast, Sequential Printing Mode produces one part at a time, reducing the risk of total batch loss but utilising printing space less efficiently. In this work, we propose an algorithm that, given a set of parts, performs the nesting of the parts for Concurrent Printing Mode, and for the first time, for the Sequential Printing Mode. A no-fit polygon based approach is used to handle geometry between pairs of parts by using multiple horizontal 2D layer projections of 3D parts, to ensure non-overlapping constraints and prevent machine-part collisions. A Greedy Randomized Adaptive Search Procedure is proposed, tested and benchmarked against a commercial software, using a new set of real-world instances. The approach shows the ability to find high-quality solutions. The approach significantly reduces the number of batches, minimises waste, reduces manufacturing time, and promotes parts quality.