The Median String Problem calls for finding a string that minimizes the average distance from a given set of strings. Under the Levenshtein (or edit) metric, the problem is NP-hard even for binary strings. We devised two novel integer linear programming models for this case and tested them against the only formulation we are aware of in the literature. Our numerical experiments attest to the efficacy of the proposed approach.

The human-centric approach of Industry 5.0 underscores the integration of advanced technologies and information systems to enhance worker well-being, productivity, and safety. Significant progress has been made in automation and digitalization; however, the high prevalence of work-related musculoskeletal disorders (WRMSDs) remains a critical challenge, translating into a significant socioeconomic burden. Nevertheless, industrial practice still predominantly relies on observational ergonomic assessment methods and reactive ergonomic strategies, creating an urgent need for flexible, proactive, individualized, and easy-to-implement risk mitigation approaches. This paper addresses this gap by proposing an intelligent decision-support system based on a multi-objective optimization model that integrates heterogeneous information - workers’ anthropometric measures, task requirements, and personal habits - within an expert-system architecture for industrial applications. The method relies on a convex integer program that can be embedded in machine controllers to compute the relative position between the product and the operator, minimizing ergonomic risks. Key innovations include the adoption of ergonomic principles without complex inverse kinematics, the explicit involvement of workers to account for their preferences, and the joint consideration of tasks involving both visual and physical interaction with the product. Experimental validation was conducted in a virtual environment simulating typical manufacturing scenarios, with diverse users and products. Results showed significant reductions in ergonomic risks with optimized positions, especially for smaller products, whereas larger ones posed challenges due to their size and task distribution. Statistical analyses validated these findings, highlighting the model’s potential to reduce the REBA (Rapid Entire Body Assessment) risk index and enhance operational efficiency. Overall, the proposed system provides actionable set-points for workstation configuration and practical guidance for implementation, thus supporting human-centric manufacturing in Industry 5.0.

In our partnership with a leading company specializing in automatic cutting machines for reinforcement processes, we address the management of a work center whose optimization calls for the solution of four distinct subproblems. Focusing on the third one, the subproblem asks for the effective packing of items on the identical buffers of a stocking area. The items arrive divided into subgroups (i.e., patterns), are associated with orders, and have time windows. We devise an SVC heuristic that efficiently determines feasible packing solutions while simultaneously minimizing the number of used buffers, lowering operations and fragmented orders. The SVC incorporates the idea of reachable points to restrict the location sets on the buffers. The experimental campaign highlights the SVC’s effectiveness in achieving optimality for small realistic instances, with a specific emphasis on reducing fragmented orders. Additionally, the approach showcased its ability to explore the multi-objective space and demonstrated scalability in solving practical instances.

In this paper we deal with the problem of deciding the best assortment and cut of defective bidimensional stocks. The problem, originating in a glass manufacturing process, can arise in various industrial contexts. We propose a novel bilevel programming approach describing a competition between two decision makers with contrasting objectives: one aims at fulfilling production requirements, the other at generating defects that, damaging the products, reduce yield as much as possible. By exploiting nice properties of adversarial optimal solutions, the bilevel program is rewritten as a one-level 0-1 linear program. Computational results achieved on random instances with realistic features are discussed, showing the quality and the benefits of the proposed approach in reducing the yield loss from defective material in a worst-case perspective.

Modern energy system are evolving due to the opportunities and challenges that new technologies pose in the energy sector. These changes create the requirements of decision tools able to effectively sustain the processes of design and retrofit of energy systems. In this paper a multi-energy system management problem is taken into account and a mixed integer linear programming (MILP) formulation is proposed to model both the design and the resource scheduling of energy districts. However, since the size of the formulation restricts its applicability to small cases far from the application of interest, a matheuristic based on constraint relaxations and variable fixing has been designed. Preliminary computational results show that the proposed solution strategy is able to achieve good solutions (i.e., solutions with small optimality gaps) on restricted random instances, and to solve in reasonable times instances derived from a real case study.

Cutting operations in manufacturing are characterized by practical requirements and utility criteria that usually increase the complexity of formulations or, even worse, are difficult to be modeled in terms of mathematical programming. However, disregarding or just simplifying those requirements often leads to solutions considered not attractive or even useless by the manufacturer. In this paper we consider a rich two-dimensional cutting stock problem that covers the whole specification of a family of wood cutting machines produced by a worldwide leader in industrial machinery manufacturing. A sequential value correction heuristic is implemented to minimize the employed stock area while reducing additional objective functions.