{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T17:05:34Z","timestamp":1793379934262,"version":"4.5.0"},"reference-count":49,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T00:00:00Z","timestamp":1776902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>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)\u2014a population-based metaheuristic inspired by cannibalistic reproduction\u2014is 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.<\/jats:p>","DOI":"10.3390\/biomimetics11050294","type":"journal-article","created":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T08:11:14Z","timestamp":1776931874000},"page":"294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhancing Manufacturing Cell Formation Through Availability-Based Optimization Using the Black Widow Optimizer Metaheuristic"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-6998-6408","authenticated-orcid":false,"given":"Paulo","family":"Figueroa-Torrez","sequence":"first","affiliation":[{"name":"Departamento de Ciencias Industriales, Medio Ambiente y Energ\u00eda, Universidad Cat\u00f3lica Boliviana \u201cSan Pablo\u201d, Col\u00f3n 734, Tarija, Bolivia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9745-0512","authenticated-orcid":false,"given":"Orlando","family":"Duran","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Mec\u00e1nica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Valpara\u00edso 2362807, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5500-0188","authenticated-orcid":false,"given":"Broderick","family":"Crawford","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Avenida Brasil 2241, Valpara\u00edso 2362807, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7723-7012","authenticated-orcid":false,"given":"Felipe","family":"Cisternas-Caneo","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Inform\u00e1tica, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, Avenida Brasil 2241, Valpara\u00edso 2362807, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5154","DOI":"10.1080\/00207543.2018.1530478","article-title":"Agile manufacturing: An evolutionary review of practices","volume":"57","author":"Gunasekaran","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1080\/09537287.2021.2005173","article-title":"Supply chain risks in Industry 4.0 environment: Review and analysis framework","volume":"34","author":"Pandey","year":"2023","journal-title":"Prod. Plan. Control"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Henriques, A., and Richardson, J. (2013). Triple Bottom Line, Routledge.","DOI":"10.4324\/9781849773348"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.ejor.2023.08.050","article-title":"Flexibility in manufacturing system design: A review of recent approaches from Operations Research","volume":"315","author":"Weckenborg","year":"2024","journal-title":"Eur. J. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4565","DOI":"10.1080\/00207543.2023.2263577","article-title":"A comprehensive literature review of the flowshop group scheduling problems: Systematic and bibliometric reviews","volume":"62","year":"2024","journal-title":"Int. J. Prod. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1016\/j.eswa.2009.06.061","article-title":"Collaborative particle swarm optimization with a data mining technique for manufacturing cell design","volume":"37","author":"Rodriguez","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/00207548708919861","article-title":"The generalized group technology concept","volume":"25","author":"Kusiak","year":"1987","journal-title":"Int. J. Prod. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6159","DOI":"10.1080\/00207543.2019.1668072","article-title":"NP-completeness of cell formation problem with grouping efficacy objective","volume":"58","author":"Batsyn","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106719","DOI":"10.1016\/j.asoc.2020.106719","article-title":"Joint cell formation, cell scheduling, and group layout problem in virtual and classical cellular manufacturing systems","volume":"97","author":"Forghani","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.ijpe.2006.04.015","article-title":"Reliability consideration in the design and analysis of cellular manufacturing systems","volume":"105","author":"Das","year":"2007","journal-title":"Int. J. Prod. Econ."},{"key":"ref_11","unstructured":"Pinedo, M. (2008). Theory, Algorithms, and Systems, Springer. [3rd ed.]."},{"key":"ref_12","first-page":"233","article-title":"A series\u2014Parallel redundant reliability system for cellular manufacturing design","volume":"223","author":"Safaei","year":"2009","journal-title":"Proc. Inst. Mech. Eng. Part J. Risk Reliab."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1007\/s00170-007-1269-4","article-title":"Modelling the effects of machine breakdowns in the generalized cell formation problem","volume":"39","author":"Ameli","year":"2008","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1080\/0951192X.2016.1224388","article-title":"A multi-objective imperialist competitive algorithm for integrating intra-cell layout and processing route reliability in a cellular manufacturing system","volume":"30","author":"Shirzadi","year":"2017","journal-title":"Int. J. Comput. Integr. Manuf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5585","DOI":"10.1080\/00207543.2022.2105763","article-title":"Cellular manufacturing design 1996\u20132021: A review and introduction to applications of Industry 4.0","volume":"61","author":"YounesSinaki","year":"2023","journal-title":"Int. J. Prod. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4627","DOI":"10.1080\/00207543.2018.1484953","article-title":"A longitudinal literature network review of contributions made to the academy over the past 55 years of the IJPR","volume":"57","author":"Silva","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1080\/00207549408956995","article-title":"Cell formation: The need for an integrated solution of the subproblems","volume":"32","author":"Arvindh","year":"1994","journal-title":"Int. J. Prod. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0925-5273(96)00027-8","article-title":"The first step in planning group technology","volume":"43","author":"Burbidge","year":"1996","journal-title":"Int. J. Prod. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Figueroa-Torrez, P., Dur\u00e1n, O., Crawford, B., and Cisternas-Caneo, F. (2023). A binary black widow optimization algorithm for addressing the cell formation problem involving alternative routes and machine reliability. Mathematics, 11.","DOI":"10.3390\/math11163475"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Figueroa-Torrez, P., Dur\u00e1n, O., and Sellitto, M. (2024). Cell formation problem with alternative routes and machine reliability: Review, analysis, and future developments. Systems, 12.","DOI":"10.3390\/systems12080288"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1080\/00207548708919868","article-title":"A within-cell utilization based heuristic for designing cellular manufacturing systems","volume":"25","author":"Ballakur","year":"1987","journal-title":"Int. J. Prod. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0951-5240(97)00001-3","article-title":"A genetic algorithm based cell design considering alternative routing","volume":"10","author":"Lee","year":"1997","journal-title":"Comput. Integr. Manuf. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume":"Volume 4","author":"Kennedy","year":"1995","journal-title":"Proceedings of ICNN\u201995\u2014International Conference on Neural Networks"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3466","DOI":"10.1080\/00207543.2013.867085","article-title":"Automatic clustering for generalised cell formation using a hybrid particle swarm optimisation","volume":"52","author":"Kao","year":"2014","journal-title":"Int. J. Prod. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3743","DOI":"10.1007\/s00521-017-3302-3","article-title":"Optimization of the material handling costs and the machine reliability in cellular manufacturing system using cuckoo search algorithm","volume":"31","author":"Karoum","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1450021","DOI":"10.1142\/S0217595914500213","article-title":"Applying simulated annealing to a generalized cell formation problem considering alternative routings and machine reliability","volume":"31","author":"Jouzdani","year":"2014","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1080\/00207540500151283","article-title":"Tabu search approach based on a similarity coefficient for cell formation in generalized group technology","volume":"43","author":"Lei","year":"2005","journal-title":"Int. J. Prod. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1287\/ijoc.1.3.190","article-title":"Tabu search\u2014Part I","volume":"1","author":"Glover","year":"1989","journal-title":"Orsa J. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s11740-017-0751-6","article-title":"A clonal selection algorithm for the generalized cell formation problem considering machine reliability and alternative routings","volume":"11","author":"Karoum","year":"2017","journal-title":"Prod. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"103249","DOI":"10.1016\/j.engappai.2019.103249","article-title":"Black widow optimization algorithm: A novel meta-heuristic approach for solving engineering optimization problems","volume":"87","author":"Hayyolalam","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Djenadic, S., Ignjatovic, D., Tanasijevic, M., Bugaric, U., Jankovic, I., and Subaranovic, T. (2019). Development of the availability concept by using fuzzy theory with AHP correction, a case study: Bulldozers in the open-pit lignite mine. Energies, 12.","DOI":"10.3390\/en12214044"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.cie.2010.08.016","article-title":"An efficient tabu search algorithm to the cell formation problem with alternative routings and machine reliability considerations","volume":"60","author":"Chung","year":"2011","journal-title":"Comput. Ind. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1007\/s00170-006-0753-6","article-title":"Cell formation with alternative process routings and machine reliability consideration","volume":"35","author":"Arkat","year":"2008","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s00170-010-2842-9","article-title":"Dynamic cellular manufacturing systems design","volume":"53","author":"Saxena","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1080\/00207543.2015.1083626","article-title":"Cellular manufacturing system design considering machines reliability and parts alternative process routings","volume":"54","author":"Alhourani","year":"2016","journal-title":"Int. J. Prod. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4018\/IJAMC.292498","article-title":"An enhanced tabu search cell formation algorithm for a cellular manufacturing system","volume":"13","author":"Sharma","year":"2022","journal-title":"Int. J. Appl. Metaheuristic Comput."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Antosz, K., Machado, J., Mazurkiewicz, D., Antonelli, D., and Soares, F. (2022). Systems engineering: Availability and reliability. Appl. Sci., 12.","DOI":"10.3390\/books978-3-0365-3624-8"},{"key":"ref_39","first-page":"261","article-title":"Applying metaheuristics in the generalized cell formation problem considering machine reliability","volume":"25","author":"Jabalameli","year":"2008","journal-title":"J. Chin. Inst. Ind. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.ress.2015.11.004","article-title":"Multi-objective optimization of IT service availability and costs","volume":"147","author":"Bosse","year":"2016","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Talbi, E.-G. (2009). Metaheuristics: From Design to Implementation, John Wiley & Sons.","DOI":"10.1002\/9780470496916"},{"key":"ref_42","first-page":"3219","article-title":"Investigation into skill leveled operators in a multi-period cellular manufacturing system with the existence of multi-functional machines","volume":"27","author":"Rafiee","year":"2020","journal-title":"Sci. Iran. Trans. Ind. Eng."},{"key":"ref_43","first-page":"405","article-title":"A new mathematical model for integration of cell formation with machine layout and cell layout by considering alternative process routing reliability; A novel hybrid metaheuristic","volume":"30","author":"Golmohammadi","year":"2019","journal-title":"Int. J. Ind. Eng. Prod. Res."},{"key":"ref_44","unstructured":"Liang, J.J., Qu, B.Y., and Suganthan, P.N. (2013). Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on sinGle Objective Real-Parameter Numerical Optimization, Nanyang Technological University. Technical Report."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Awad, N.H., Ali, M.Z., Suganthan, P.N., and Reynolds, R.G. (2016). An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems. 2016 IEEE Congress on Evolutionary Computation (CEC), IEEE.","DOI":"10.1109\/CEC.2016.7744163"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Mousavirad, S.J., Moghadam, M.H., Saadatm, M., Chakrabortty, R., Schaefer, G., and Oliva, D. (2022). RWS-L-SHADE: An effective L-SHADE algorithm incorporating roulette wheel selection strategy for numerical optimisation. International Conference on the Applications of Evolutionary Computation (Part of EvoStar), Springer.","DOI":"10.1007\/978-3-031-02462-7_17"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1766","DOI":"10.1016\/j.matpr.2017.11.274","article-title":"Genetic algorithm approach for machine cell formation with alternative routings","volume":"5","author":"Hazarika","year":"2018","journal-title":"Mater. Today Proc."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Tanabe, R., and Fukunaga, A.S. (2014). Improving the search performance of SHADE using linear population size reduction. 2014 IEEE Congress on Evolutionary Computation (CEC), IEEE.","DOI":"10.1109\/CEC.2014.6900380"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.eswa.2016.10.054","article-title":"Analyzing the effects of binarization techniques when solving the set covering problem through swarm optimization","volume":"70","author":"Crawford","year":"2017","journal-title":"Expert Syst. Appl."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/5\/294\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T04:25:58Z","timestamp":1777091158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/5\/294"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,23]]},"references-count":49,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["biomimetics11050294"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11050294","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,23]]}}}