Abstract
In this paper, we consider the two-dimensional Variable-Sized Cutting Stock Problem (2D-VSCSP) with guillotine constraint, applied to the home textile industry. This is a challenging class of real-world prob-lems where, given a set of predefined widths of fabric rolls and a set of piece types, the goal is to de-cide the widths and lengths of the fabric rolls to be produced, and to generate the cutting patterns to cut all demanded pieces. Each piece type considered has a rectangular shape with a specific width and length and a fixed demand to be respected. The main objective function is to minimize the total amount of the textile materials produced/cut to satisfy the demand. According to Wascher, Hau ss ner, & Schu-mann (2007), the addressed problem is a Cutting Stock Problem (CSP), as the demand for each item is greater than one. However, in the real-world application at stake, the demand for each item type is not very high (below ten for all item types). Therefore, addressing the problem as a Bin-Packing Problem (BPP), in which all items are considered to be different and have a unitary demand, was a possibility. For this reason, two approaches to solve the problems were devised, implemented, and tested: (1) a CSP model, based on the well-known Lodi and Monaci (2003) model (3 variants), and (2) an original BPP-based model. Our research shows that, for this level of demand, the new BPP model is more competitive than CSP models. We analyzed these different models and described their characteristics, namely the size and the quality of the linear programming relaxation bound for solving the basic mono-objective variant of the problem. We also propose an epsilon-constraint approach to deal with a bi-objective extension of the problem, in which the number of cutting patterns used must also be minimized. The quality of the models was evaluated through computational experiments on randomly generated instances, yielding promising results.(c) 2022 Published by Elsevier B.V.

Abstract
Cutting and packing problems are challenging combinatorial optimization problems that have many rel-evant industrial applications and arise whenever a raw material has to be cut into smaller parts while minimizing waste, or products have to be packed, minimizing the empty space. Thus, the optimal solution to these problems has a positive economic and environmental impact. In many practical applications, both the raw material and the cut parts have a rectangular shape, and cut-ting plans are generated for one raw material rectangle (also known as plate) at a time. This is known in the literature as the (two-dimensional) rectangular cutting problem. Many variants of this problem may arise, led by cutting technology constraints, raw-material characteristics, and different planning goals, the most relevant of which are the guillotine cuts. The absence of the guillotine cuts imposition makes the problem harder to solve to optimality.Based on the Floating-Cuts paradigm, a general and flexible mixed-integer programming model for the general rectangular cutting problem is proposed. To the best of our knowledge, it is the first mixed inte-ger linear programming model in the literature for both non-guillotine and guillotine problems. The basic idea of this model is a tree search where branching occurs by successive first-order non-guillotine-type cuts. The exact position of the cuts is not fixed, but instead remains floating until a concrete small rect-angle (also known as item) is assigned to a child node. This model does not include decision variables either for the position coordinates of the items or for the coordinates of the cuts. Under this framework, it was possible to address various different variants of the problem.Extensive computational experiments were run to evaluate the model's performance considering 16 dif-ferent problem variants, and to compare it with the state-of-the-art formulations of each variant. The results confirm the power of this flexible model, as, for some variants, it outperforms the state-of-the-art approaches and, for the other variants, it presents results fairly close to the best approaches. But, even more importantly, this is a new way of looking at these problems which may trigger even better approaches, with the consequent economic and environmental benefits.

Abstract
We consider the problem of selecting bases for firefighting activities (e.g., vigilance, water refill, initial attack) and links between them in the context of wildfire promptness. Bases can be facilities, such as watchtowers and water tanks, or positions from where an initial attack is conducted. It is assumed that it is advantageous to connect bases in such a way that resources (e.g. ground crews) can quickly move between them. The general problem is modelled in a general way as integration of a set covering problem (for selecting the location of the bases) and a travelling salesman problem where the cities are the selected locations and the arcs the links that connect them. We propose a mixed integer programming model where objectives are addressed by lexicographic optimization. The first objective is related to cover potential ignition points with a high estimate of their initial spread rate of the fire at the detection time. Computational experiments are discussed for a scenario, of an actual landscape, with parameters estimated from a fire behaviour model that takes into account slope, fuels, and wind. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

Abstract
The Manufacturer's Pallet Loading Problem involves optimising the packing of a maximal number of identical rectangular boxes onto a single rectangular pallet. This problem arises in various logistic operations that involve the storage and transportation of boxed products, where efficient packing can result in substantial cost reductions and improved operational efficiency. Logistics managers anticipate that some boxes can be damaged during handling and transport, so the stability of the pallet load is essential to avoid such damage. The interlocking method is commonly used in practice to improve stability when loading pallets, minimising product damage and reducing the risk of injury to personnel handling the pallet. This study introduces a Mixed Integer Linear Programming model that addresses the Manufacturer's Pallet Loading Problem, promoting static stability through interlocking. Stability is evaluated with respect to the relationship between successive layers of the loading plan, with three types of interlocking incorporated into the mathematical model. Computational experiments with real-world instances were conducted to assess the model's performance using different objective functions and post-optimisation heuristics that target real-world requirements. Three stability metrics were used to evaluate the load plans generated by the mathematical model. The results show the interlocking method's benefits on the pallet loads' stability while maximising the pallet volume usage.

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
The authors regret that a minor inconsistency was identified in Algorithm 1 of our published paper during subsequent experiments conducted to further improve the G16 constructive heuristic. Specifically, the original implementation of G16 did not distinguish between regular and merged earliest time windows when computing [Formula presented], which could, in some cases, affect the consistency of [Formula presented], [Formula presented], [Formula presented], [Formula presented], and [Formula presented] for requests simultaneously served at the same location, leading to infeasible routes under specific configurations. The correction is as follows (Algorithm 1, Line 15): Original: [Formula presented] Corrected: [Formula presented] where [Formula presented] denotes the merged earliest time window when a merged time service is applied; otherwise, it equals [Formula presented]. As a result, the total costs obtained with the corrected version of G16 slightly deviate, either positively or negatively, from those originally published. The average percentage gaps between the published and corrected G16 results are 2.55, 0.61, -0.64, 0.42, and -2.27% for instances with 50, 100, 200, 400, and 700 requests, respectively. Complementarily, a Spearman correlation (p = 0.98) and a Wilcoxon signed-rank test (p = 0.106) revealed no statistically significant difference between both sets of results. Therefore, the overall performance patterns and comparative findings discussed in the original paper remain valid. Updated computational results are available in the same Mendeley Data repository (DOI: https:/doi.org/10.17632/7fb9jn2wcs.1). The authors would like to apologise for any inconvenience caused. © 2025 Elsevier B.V.