This study develops a novel mathematical formulation for cellular manufacturing systems under parameter uncertainty, where processing times and product demands are modeled as stochastic variables characterized by their expected values and standard deviations derived from sampling data. The optimization framework simultaneously addresses three critical manufacturing objectives: (1) minimizing inter-cell and intra-cell material movements through strategic machine-cell assignment, (2) eliminating production bottlenecks via balanced workload distribution, and (3) maximizing overall profitability through systematic production cost reduction. The model’s effectiveness is demonstrated through numerical case studies, with computational analysis revealing significant solution quality improvements. To address the combinatorial complexity of large-scale implementations, we propose an innovative heuristic solution approach featuring a proprietary neighborhood search algorithm for efficient solution space exploration, and an adaptive resource allocation methodology for dynamic cell configuration.