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.
Figueroa-Torrez et al. (Thu,) studied this question.