Cellular manufacturing systems (CMS) are essential for achieving efficient production ocesses, and their success relies on effective cell formation and layout design. This research paper presents a novel nonlinear mathematical programming model that employs the rectilinear distance notion to define the layout within a continuous space. The proposed model incorporates the stochastic nature of machine failures, considering the unreliability with the inclusion of a stochastic time between failures. With a bi-objective approach, the model aims to minimize inter and intra-cell movements of parts, as well as the associated costs related to exceptional elements (EEs), cell reconfigurations, and machine failures. To optimize the proposed model, several multiobjective meta-heuristic algorithms, including the multi-objective particle swarm optimization (MOPSO), multi-objective taboo search (MOTS), and non-dominated sorting genetic algorithm (NSGA-II), are introduced. The effectiveness of these algorithms is validated through numerical instances and a real case study. The results indicate that the MOPSO algorithm exhibits superior performance in optimizing various multi-objective criteria. The presented mathematical model and algorithms provide valuable tools for manufacturers to optimize their CMS, resulting in reduced costs, enhanced production efficiency, and increased competitiveness. By considering the simultaneous effects of time and cost associated with machine failures, this research offers practical insights and solutions for improving the performance of cellular manufacturing systems.
