Abstract
This paper addresses a multi-compartment tank-truck loading problem for fuel distribution. The proposed problem aims to quantify and assign products to vehicle compartments and to ensure safety throughout the entire distribution using the vehicle Load Distribution Diagram (LDD) to verify vehicle compliance with safety standards and legislation applicable to the transport of dangerous goods. We propose a mixed-integer linear programming model that incorporates axle weight distribution constraints. A new problem generator was developed to test and validate the mathematical model. In the study, three objective functions were considered: minimize operational costs by minimizing the number of compartments allocated to a filling station, maximize profits by maximizing the amount of fuel delivered, and improve safety along the entire route by minimizing the distance between the front of the tank and the load center of gravity. In addition to evaluating these objectives individually, a lexicographic multi-objective approach was implemented to analyse how companies can systematically balance efficiency, profitability, and safety priorities. The computational study demonstrated that LDD constraints are crucial for ensuring the stability and safety of cargo during distribution. Without these constraints, the solutions fail to meet safety standards in 78% of tests. The multi-objective analysis showed limited conflicts among objectives and provided additional managerial insights. Regardless of problem size or objective function, computational times remained consistently low, averaging below 3 seconds.

Abstract
This study addresses the optimization of automated order-picking systems in retail warehouses through the integration of Autonomous Mobile Robots (AMRs) in a parts-to-picker system. A mixed-integer programming model with a lexicographic objective function is developed to optimize AMR planning while maintaining predefined pallet loading sequences. The model aims to minimize the makespan and the number of stock pallets used, and to maximize the continuity of AMR-pallet pairing. Computational experiments across 81 instances demonstrate that the model consistently achieves optimal makespan values in scenarios of moderate complexity. The results indicate that, while increasing the number of AMRs provides limited benefits in simple configurations, it significantly improves performance in complex scenarios. The research contributes to the literature on warehouse automation by providing a solid foundation for the optimization of AMR-assisted order-picking.

Abstract
This work studies a two-echelon distribution system, in the context of city logistics, where storage is not permitted at intermediate transfer locations. Therefore, vehicles operating at both echelons need to be synchronised in time and space, allowing loads to be directly transferred from the first to the second echelon vehicles. Moreover, the problem considers that vehicles operating at the first echelon can perform direct deliveries to customers, that load transfers may occur at some customers' locations, and that vehicles operating at the second echelon are able to perform multiple trips before returning to the depot at the end of the day. To address this problem, we propose a novel mixed integer programming (MIP) model for the two-echelon, multi-trip vehicle routing problem with satellite synchronisation and direct deliveries (2E-MTVRPSS-DD). We tighten this formulation with several sets of valid inequalities, including symmetry breaking constraints based on lexicographical ordering, vehicle rounded capacity constraints, and satellite rounded capacity constraints. We test the model using a commercial solver with newly generated instances, and present computational results, as well as an evaluation of the performance of the proposed valid inequalities. The results show that for relatively small instances, the proposed model is able to solve the problem optimally, but in general, is unable to solve large instances in acceptable computational time, even when considering the proposed valid inequalities. Nevertheless, we show that adding these valid inequalities has a positive impact in improving the model's linear relaxation, with better lower and upper bounds, and ultimately in improving the MIP gaps. Moreover, we show that adding symmetry breaking constraints based on lexicographical ordering has a negative impact, in terms of computational time, for the solver to find a first upper bound, and that this issue may be overcome by warm-starting the MIP model.