Cutting and packing problems are fundamental in manufacturing and logistics, as they aim to minimize waste and improve efficiency. The Cutting Stock Problem (CSP) concerns material cutting, whereas the Bin Packing Problem (BPP) concerns packing items into bins. Since the 1960s, these problems have been widely studied because of their industrial relevance and computational complexity. Over time, exact algorithms, often based on mixed-integer programming (MIP), have become able to solve increasingly large instances, often with hundreds of items, within minutes. In 2016, Delorme et al. showed that the algorithm BELOV, combined with a modern version of CPLEX, could solve all benchmark instances available at that time within ten minutes. Motivated by this progress, they introduced two new classes of instances, AI and ANI, which proved extremely challenging for all exact solvers and have guided research on CSP and BPP over the past decade. Despite significant subsequent advances, 13 out of 500 of these instances remain unsolved by state-of-the-art algorithms within a one-hour time limit. In this paper, we show that although AI and ANI instances are particularly hard for MIP-based methods, the BPP restricted to these classes is not strongly NP-hard. We present polynomial-time algorithms for the AI class and pseudopolynomial-time algorithms for the ANI class. Our best algorithms solve all benchmark instances from these classes orders of magnitude faster than previous approaches. They are also straightforward to adapt to the Skiving Stock Problem (SSP), which can be seen as a counterpart of the CSP. Additionally, they can be used as preprocessing routines in exact methods, as their runtime is independent of the instance class, although they are guaranteed to return an optimality status only for instances belonging to the class for which they were designed.

Motivated by a real-world case study in ceramic tile production, this paper addresses the problem of determining the minimum number of pallets required to load a given set of boxes. The problem must be solved quickly to give customers an expectation of the transportation cost of their orders. In addition, not all constraints and instance data can be easily determined in advance, and the items are loaded onto the pallets by operators who mostly rely on their personal experience. Therefore, traditional model-based solution methods do not apply well, and data-driven approaches are preferable. To solve the problem, we propose a hybrid algorithm in which a machine learning technique is trained over a company dataset comprising two years of customer orders, with the aim of predicting the number of pallets required by an order. The accuracy of the machine learning technique is largely improved by including additional features, such as lower and upper bounds, in the dataset, obtained using quick optimization algorithms. The resulting hybrid algorithm has been compared with the model-based software currently used at the company, consistently providing better-quality results in shorter computing times.

Industry X.0 robotic manufacturing demands higher accuracy and flexibility, enabling continuously adaptive processes designed and optimized through simulations and Digital Twins. To achieve this level of flexibility and productivity in high value-added processes, where limited robot position accuracy becomes a critical constraint, advanced engineering methods and digital tools are required. These solutions must predictively compensate for inevitable robot positional accuracy errors, eliminating the need for manual pose refinement and enabling the generation of “first-time-right” robot code. This work aims to address these challenges by introducing an engineering tool capable of predictively correcting robot positioning inaccuracies across the workspace, enabling accurate point-to-point motion generation. It is intended for tasks with limited process interaction forces, where positioning errors are dominated by geometric, compliance, and joint-related effects. The tool leverages a multi-parameter Machine Learning (ML) error predictor trained on a reduced experimental dataset, minimizing data acquisition time and production downtime. Realized as a Python-based framework, it can be seamlessly integrated into commercial offline programming environments to automatically generate validated robot programs. The paper details the framework structure, focusing on the definition of the ML-based position error predictor, and its implementation on a robotic cell equipped with a high-payload KUKA robot and a FARO laser tracker. A preliminary experimental analysis identified payload, approach direction, and point location as the key operational parameters, accessible at the code level, that influence positioning accuracy. These insights guided feature selection and the design of reduced training datasets. In particular, a uniform spatial grid of only 64 points, corresponding to about one hour of measurement time, was sufficient to achieve near-optimal model accuracy. Several ML algorithms were compared, with the Tabular Prior-data Fitted Network achieving superior generalization on small datasets. Experimental validation on the KUKA robot showed up to a 98.4 % reduction in positioning error and consistent performance across all tested points, confirming the tool robustness and suitability for deployment across different industrial environments. All datasets, source code, and implementation scripts are openly released to enable reproducibility and facilitate industrial deployment.

We study a personnel scheduling problem faced by a healthcare and pharmaceutical logistics company, whose goal is to schedule a set of identical employees to transport patients within different healthcare facilities of a hospital. In addition to minimizing the total number of working hours in the schedule, we also aim to maximize shift homogeneity, where two shifts are considered homogeneous if they start and end at the same time, possibly on different days. We introduce three solution methods: two based on integer linear programming (ILP) and one using a decomposition approach in which shifts are determined in the master problem and assigned to employees in the subproblem. We show that the decomposition approach can solve all real-world instances provided by the company in a short amount of time, unlike the ILP models. We also provide managerial insights regarding the effect on the optimal solution of modifying certain instance parameters, such as varying the number of employees, allowing for shorter shifts, and imposing a mandatory lunch break in each shift. Finally, we investigate instance features that make our scheduling problem more difficult to solve for the proposed approaches.

In this article, we introduce and study the Quadratic Bin Packing Problem (QBPP), which generalizes the classical bin packing problem by introducing a fixed cost for each used bin and a pairwise cost (or profit) incurred whenever two items are packed together. Beyond its theoretical relevance, the QBPP is of practical interest due to its numerous real-world applications, mainly related to cluster analysis. To address the QBPP, we propose three compact mixed-integer linear programming (MILP) formulations, along with a set-partitioning formulation. For each compact model, we present an enhanced version with a strengthened continuous relaxation, while, for the set-partitioning formulation, we develop a tailored Branch-and-Price algorithm. Computational experiments on benchmark instances demonstrated that, while the enhanced compact formulations can be effectively solved by a standard MILP solver for small-sized instances, the Branch-and-Price approach delivered superior performance overall, especially on larger and more challenging instances.

We introduce the integrated block relocation and fleet allocation problem with soft precedence constraints, which jointly determines the unloading sequence of items and their assignment to a heterogeneous fleet of capacity-limited vehicles. The new problem aims at maximizing the number of delivered items while minimizing violations of a given item precedence order. Items with different destinations cannot be allocated to the same vehicle. The problem finds applications in logistic operations in steel plants and container terminals, as well as in humanitarian supply operations in the context of natural or industrial disasters. We formalize the problem as a lexicographic bi-objective model, providing two compact integer linear programming formulations reflecting different modeling perspectives, two reformulations and a family of valid inequalities. The models incurring the best dual bounds are used as backbone for a Kernel Search heuristic exploiting problem-specific structural properties. Computational experiments on a benchmark derived from the block relocation literature show that the exact models solve most instances to optimality within one hour, while the heuristic provides high-quality solutions with short runtimes and near-optimal gaps, making it an effective and reproducible approach for larger instances.

We address the problem of scheduling non-preemptive jobs on identical parallel machines under a single renewable resource constraint, with the objective of minimizing the makespan. This setting captures relevant applications in energy-aware production planning, where energy usage must not exceed a fixed limit at any time. We introduce two mathematical formulations and propose an exact algorithm that integrates a branch-and-bound, advanced bounding techniques, and a constraint programming model. Extensive computational experiments on two benchmark sets from the literature show that the proposed approach outperforms existing exact methods, solving more instances to optimality and achieving consistently smaller optimality gaps within limited computation time.

Urban waste generation is increasing worldwide at a dramatic pace, making it crucial to develop efficient, cost-effective, and environmentally responsible waste management systems for fast-growing urban areas. This paper addresses a bi-objective facility location problem arising from the real-world waste industry, in which different classes of recyclable urban waste must be collected from sources and delivered to treatment or disposal facilities. The decisions are the number and location of the new intermediate transfer facilities to be opened and the optimal waste flow across the network. The goals are the minimization of the total costs and the CO2 emissions. We present a single-period mixed integer linear programming model and then extend it to a multi-period setting, which better reflects the dynamics of waste production with seasonal fluctuations and generalize to further applications. We apply an & varepsilon;-constraint algorithm to solve our models on two real-world case studies, obtaining approximated-but-well-structured Pareto sets of non-dominated solutions with 25% reduction of emissions with respect to the current state. The efficacy of the models is confirmed by further computational experiments on randomly created instances, showing that the models can be employed for analogous applications.

In this study, we explore Quantum Annealing (QA) as a new method for determining the optimal observation schedule for the radar MARSIS onboard the Mars Express mission, with the aim of obtaining a high-quality coverage of the South Pole of Mars. The MARSIS observation plan is greatly influenced by space weather and it is constrained by the limited hardware of the Mars Express spacecraft. In this work, we build upon previous research on classical optimization algorithms and present a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation, tailored for execution on the D-Wave quantum annealer. We test the solution of the QUBO formulation through QA on small-scale instances of the problem, derived from real data provided by the MARSIS operation center. We also study the effects of the penalties introduced in the QUBO and compare QA with classical algorithms, drawing some conclusion on the current applicability of this new technology.

Planetary remote sensing missions are critical for advancing our understanding of extraterrestrial systems. They operate in highly uncertain environments where reliability and resolution are not always guaranteed, often compromising data analysis and scientific outcomes. In this paper, we consider the challenging task of estimating the quality of the signal acquired by MARSIS, the subsurface sounder aboard ESA’s Mars Express mission, which aims to map the presence of liquid water beneath the Martian surface. Quality estimation has a strategic impact on the scheduling of MARSIS observations, since the radar operates with strict constraints that greatly limit the number and size of observation opportunities available per day. Thus, maximizing the quality of scheduled observations becomes a crucial factor in reducing resource utilization and increasing the coverage of the target areas in search of liquid water. To this end, in a previous research we proposed a predict-then-optimize approach, which included a neural network regressor to predict signal quality achievable by future observation opportunities, based on contextual features. In this work, we advance the methodology by applying explainable artificial intelligence techniques that allow domain experts to interpret the results, by enhancing the comprehension of the physical phenomena that have an impact on signal acquisition. Specifically, we applied a SHAP analysis to the neural network predictions and trained an Explainable Boosting Machine (EBM) to provide interpretable models. We then analyzed and compared the results with existing domain knowledge, uncovering promising new avenues for investigation and highlighting limitations in the current dataset construction.

This study investigates the effectiveness of quantum methods in tackling the cubic knapsack problem (CKP). The CKP is not only NP-hard but also extremely difficult to solve in practice. Benchmark instances of small size (including some with only 60 items) remain unsolved to proven optimality. We solve the CKP using the latest Digital Annealer (DA) prototype, an extended Ising machine available through the Quantum-Inspired Integrated Optimization (QIIO) service on Fujitsu's Kozuchi platform. Specifically, we propose two formulations: a higher-order unconstrained binary optimization (HUBO) and a quadratic unconstrained binary optimization. The latter is derived by reformulating the HUBO model into an equivalent quadratic form. These models are solved using the QIIO solver and compared with three state-of-the-art algorithms, a greedy heuristic, and two mixed integer programs. Additionally, we introduce a postprocessing heuristic to ensure the feasibility of solutions generated by the DA solver, as within short time limits, it does not always produce feasible solutions. Computational experiments are conducted on instances with up to 200 items and varying densities of nonzero objective coefficients. The results indicate that the HUBO formulation is highly competitive with state-of-the-art algorithms, achieving the best new solutions for six large instances.

The microservices architecture has transformed application development by providing scalability, flexibility, and resilience. However, as organizations scale their infrastructure, deploying microservices across multiple clusters - whether for fault tolerance, geographic distribution, or workload optimization — presents several challenges. Efficient orchestration in these multi-cluster environments is essential to ensure seamless service provisioning, workload distribution, and inter-cluster communication. In this paper, we propose an extension of the OASIS TOSCA standard to support the need of application owners to define deployment schemes that enable them to distribute application components across multiple clusterized environments. To test the viability of the proposed extension, we set up a small-scaled, multi-cluster environment powered with Kubernetes and employed an orchestrator of microservice-based applications that implements the mentioned capability. For the test purpose, a real application from the logistics domain was employed.

Bilevel optimization, a well-established field for modeling hierarchical decision-making problems, has recently intersected with sustainability studies and practices, resulting in a series of works focusing on bilevel optimization problems involving multiple decision makers with diverse economic, environmental, and social objectives. This survey offers a comprehensive overview of sustainable bilevel optimization applications. First, we introduce the main concepts related to the nature of bilevel optimization problems and present some typical mathematical formulations for bilevel pricing problems that cover many of the collected applications. Then, we review the most relevant works published in sustainable bilevel optimization, giving a classification based on the application domains and their association with well-known operations research problems, while briefly discussing the proposed solution methodologies. We survey applications on transportation and logistics, production planning and manufacturing, water, waste, and agriculture management, supply chains, and disaster prevention and response. Finally, we outline a list of open questions and opportunities for future research in this domain.

The timely post-impact care and the related transportation to healthcare facilities are key objectives for mitigating injuries and deaths resulting from motor vehicle crashes. Several advanced and efficient emergency operations centers (EOC) exploit the potential of a helicopter emergency medical service (HEMS) to supplement the ground fleet for life-threatening or urgent and emergency situations. Although daytime HEMS missions operating under visual flight rules (VFR) in the visual meteorological conditions (VMC) along the shortest flight path and landing as close as possible to the scene are a well-established practice, one of the priorities is the rational use of the helicopter in marginal weather conditions, at night, or whenever natural or artificial obstructions represent potential flight hazards. This involves exploiting the potential of HEMS rendez-vous missions. In this perspective, the authors proposed two mathematical models to optimize the location of certified helipads, having a transfer point function, by maximizing the coverage (MaxCoverage) of a geographic area and minimizing the total delay (MinSumD) of the interventions considering the reasonable total pre-hospital time thresholds of 45 and 60 min. The models were applied to an Italian real-world case study using an anonymized emergency medical database: electronic pre-hospital care records (4,155 events), attributable to road traffic accidents that took place in the province of Parma (Emilia Romagna, Italy) in 7 years, were considered as input data. The simulations, defining the optimal number and location of helipads for rendez-vous missions, offer analytical supports to operators and public agencies for providing on the one hand a broad spectrum of intervention strategies and facilitate the decision-making, and giving on the other hand planning and design tools for the HEMS implementation and strengthening.

This paper addresses the crucial aspect of position error modeling and compensation in industrial servomechanisms with the aim to achieve accurate control and high-performance operation in industrial robots and automated production systems. The inherent complexity and nonlinear behavior of these modules, usually consisting of a servomotor and a speed reducer, often challenge traditional analytical modeling approaches. In response, the study extensively explores the design and implementation of Machine Learning (ML) algorithms to obtain a comprehensive model of the Transmission Error (TE) in rotating vector reducers, which is a main source of robot motion accuracy errors. The ML models are trained with experimental data obtained from a special purpose test rig, where the reducer is tested under different combinations of input speed, applied load and oil temperature. In the second part of the work, the resulting predictive model, tailored to capture the intricate dynamics of the analyzed reducer, is imported into a programmable logic controller to enable online compensation strategies during the execution of custom motion profiles. Experimental tests are conducted using two distinct motion profiles: one generated with a cycloidal law, typical of industrial machinery, and the other extrapolated from the joints of an industrial robot during a pick-and-place task. The results demonstrate the effectiveness of the proposed approach, enabling accurate prediction and substantial reductions (over 90%) in the overall reducer TE through the implemented predictive model.