IMPACT ANALYSIS OF THE CELL-CAPACITY PARAMETERS ON OPTIMAL SOLUTIONS IN A DYNAMIC CELLULAR MANUFACTURING SYSTEM (D-CMS): AN ENRICHED SENSITIVITY STUDY AND THE DETERMINATION OF PROFITABILITY THRESHOLDS

In a dynamic cellular manufacturing system (D-CMS), the production-cell capacity, described by the two parameters LP (minimum number of machines per cell) and CL (maximum number of machines per cell), exerts a decisive influence on the optimal solutions of a mixed-integer linear programming (MILP) model aimed at minimizing the cellular load variation. Starting from two experiments gathering configurations solved by the LINGO solver (50 instances per configuration), this paper proposes an enriched sensitivity analysis of the impact of the parameters LP and CL. We show that the slack margin Δ = CL − LP is strongly correlated with the optimal value, but that this correlation crucially depends on the experimental protocol: when CL is held fixed and LP varies, the relationship becomes quasi-deterministic (R² ≥ 0.98), whereas when LP and CL are randomly chosen, the coefficient of determination drops to about 0.46. We also identify the profitability thresholds S⋆ below which the company realizes profits (limited machine sales) and beyond which it incurs losses (massive machine sales). The results show that in-house production systematically prevails over subcontracting whenever capacity allows, and that keeping the cell slack below the threshold S⋆ is a necessary condition to avoid losses. These results constitute a significant deepening of the reference model previously published in Statistics, Optimization and Information Computing (see Yao K.  Adrien  et al., 2025), and provide industrial decision makers with operational pre-sizing rules for the cell capacity.