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.