The Cell Formation Problem (CFP) involves the clustering of machines to enhance productivity and capitalize on various benefits. This study addresses a variant of the problem where alternative routes and machine reliability are included, which we call a Generalized Cell Formation Problem with Machine Reliability (GCFP-MR). This problem is known to be NP-Hard, and finding efficient solutions is of utmost importance. Metaheuristics have been recognized as effective optimization techniques due to their adaptability and ability to generate high-quality solutions in a short time. Since BWO was originally designed for continuous optimization problems, its adaptation involves binarization. Accordingly, our proposal focuses on adapting the Black Widow Optimization (BWO) metaheuristic to tackle GCFP-MR, leading to a new approach named Binary Black Widow Optimization (B-BWO). We compare our proposal in two ways. Firstly, it is benchmarked against a previous Clonal Selection Algorithm approach. Secondly, we evaluate B-BWO with various parameter configurations. The experimental results indicate that the best configuration of parameters includes a population size $\left(Pop\right)$ set to 100, and the number of iterations $\left(Ma{x}_{i}ter\right)$ defined as 75. Procreating Rate $\left(PR\right)$ is set at 0.8, Cannibalism Rate $\left(CR\right)$ is set at 0.4, and the Mutation Rate $\left(PM\right)$ is also set at 0.4. Significantly, the proposed B-BWO outperforms the state-of-the-art literature’s best result, achieving a noteworthy improvement of 1.40%. This finding reveals the efficacy of B-BWO in solving GCFP-MR and its potential to produce superior solutions compared to alternative methods.

The Cell Formation Problem (CFP) is a widely studied issue that aims to group machines effectively based on criteria such as productivity, lower costs, and greater efficiency. In recent years, more characteristics were summarized relating to this problem. This paper provides a bibliographic examination of methodologies addressing the CFP in cellular manufacturing, focusing on novel approaches such as alternative routes and machine reliability. The articles were obtained from Scopus and Web of Science and filtered using the PRISMA methodology. Classification based on objective functions, constraints, and methodologies facilitated informative visualizations for analysis. Findings indicate a focus on capital utilization optimization, with cost reduction via intercellular moves minimization as the primary objective. Common constraints include limits on the number of machines per cell, restricting machines to a single cell and singular production routes per part. The genetic algorithm predominates as a non-exact solution approach, while the “$\epsilon$-constraint” method is commonly used. This study offers insights into contemporary trends in solving the CFP with alternative routings and machine reliability, aiding researchers and professionals in the field to improve the quality of their investigations.

This study presents a multi-period Generalized Cell Formation Problem with Machine Availability (GCFP-MA) aimed at designing manufacturing cells that explicitly account for equipment reliability, maintainability, and temporal degradation. The proposed model extends classical formulations by introducing (i) availability-based constraints derived from Mean Time Between Failures (MTBF) and Mean Time to Repair (MTTR) and Markov-Chain models, (ii) downtime penalty costs reflecting non-production losses, and (iii) a multi-period horizon that captures system dynamics over time. To solve the resulting NP-hard problem, the Black Widow Optimizer (BWO)—a population-based metaheuristic inspired by cannibalistic reproduction—is implemented and validated against an exhaustive search benchmark. Computational experiments confirm that the BWO attains the global optimum with substantially reduced computational effort, achieving a balanced trade-off between exploration and exploitation. Results highlight that incorporating availability and repair dynamics prevents infeasible or over-optimistic configurations and yields cost-effective, robust cell layouts. The proposed approach provides both theoretical and practical contributions by integrating availability engineering and production system design within a unified optimization framework.

Background: Pressure injury (PI) prevention relies heavily on the application of the Braden Scale, yet its predictive performance is limited mainly due to subjective measurements and fixed cut-off points, yielding potential errors in terms of false-positive alarm rates and workforce misuse. Machine learning (ML) has emerged as a promising approach to improve discrimination, but fair comparisons with traditional tools remain scarce in clinical settings. Methods: Using data from 446 hospitalized patients in a tertiary hospital in Chile, we compared five classic ML models for classification against the Braden Scale. ML models were trained exclusively on routinely collected clinical and nursing variables, excluding Braden inputs. A matched operating-point framework was applied, aligning ML decision thresholds with Braden cutoffs based on equivalent recall or specificity. Results: The XGB model showed the highest overall discrimination performance (AUC = 0.835). When matched to Braden recall, XGB achieved about 17% gains in specificity, substantially reducing false positives. When matched on specificity, recall improvements ranged from 13% to 25%. These gains were consistent across clinically relevant thresholds considered during the comparison. Conclusions: ML models, particularly XGB, outperform the Braden Scale under equivalent clinical operating conditions. Rather than replacing Braden, ML has emerged as a promising approach that preserves patient safety while improving precision and resource allocation.

The Cell Formation Problem plays a fundamental role in cellular manufacturing due to its impact on efficiency, flexibility, and reliability. Its complexity increases under real-world conditions involving alternative process routes and machine reliability constraints, leading to the Generalized Cell Formation Problem with machine reliability. Researchers have classified the Cell Formation Problem as an NP-Hard problem. To address this computational complexity, this study presents a comparative and hybrid evaluation of the Black Widow Optimizer and the Golden Eagle Optimizer for the Generalized Cell Formation Problem with machine reliability, examining whether mechanisms derived from the Black Widow Optimizer can enhance the search behavior of the Golden Eagle Optimizer. The Black Widow Optimizer provides strong intensification through procreation, cannibalism, and mutation mechanisms, whereas the Golden Eagle Optimizer provides a balanced search process through its cruise and attack strategies. Experimental results show that the Black Widow Optimizer achieved better individual performance than the Golden Eagle Optimizer, with average RPD values of 0.855% and 1.068%, respectively. However, the hybrid strategy based on incorporating the mutation mechanism into the Golden Eagle Optimizer produced the best result, reaching an RPD of 0.592%. The study also employed the Wilcoxon–Mann–Whitney statistical test to validate the performance differences among algorithms, and the respective Big-O computational complexity was calculated. These findings highlight the potential of hybrid metaheuristics for designing robust and efficient manufacturing systems.

The present work focuses on the Cell Formation Problem (CFP), which groups machines to get several benefits, including productivity improvement, reduced tooling needs, reduced setup time, and reduced manufacturing lead time. In modern manufacturing systems, equipment availability is an important requirement, as it ensures a higher possibility of utilizing productive resources, which are usually of high value. Therefore, the incorporation of reliability aspects into cell formation algorithms becomes necessary. Various researchers currently consider reliability based on individual machine failures. However, this overlooks a crucial factor, the systemic approach of clustering, in other words, the reliability of the entire production line. Since for the system to function correctly, all participating machines must be operational. So far, an approach considering the cell as a production line and taking its reliability as a whole into account has not been found. This work proposes an optimization model that incorporates machine reliability, considering the equipment as a production line. To demonstrate the effectiveness of our model, an example is given and compared with an existing model. The results show that there is a considerable cost difference between the new model and the old model. The latter will allow us to detect uncalculated costs that can be very detrimental to the correct formation of the cells.