This paper examines a new multi-objective mathematical model in a Dynamic Cell Formation Problem (DCFP), where social criteria and uncertainty conditions are considered. Although corporate social responsibility is one of the important issues that are increasingly considered by researchers and practitioners, it is largely overlooked in the literature on DCFP. In this paper the first objective function minimizes costs related to a machine (machine fixed and variable costs, machine procurement and relocation costs, intra-cell and inter-cell movement costs) and wages, while social issues are maximized (e.g. potential machine hazards are minimized, while job opportunities are maximized). A robust counterpart of the proposed model is then developed by applying the recent robust optimization theory. Afterward, due to the NP-hardness of DCFP, a non-dominated sorting genetic algorithm (NSGA-II) as a meta-heuristic method is designed. Finally, two deterministic and robust mathematical formulations are compared by a number of nominal realizations under randomly generated test problems. This serves to assess the robustness of the solution achieved by the proposed robust optimization model. The obtained results demonstrate the ability of the robust model to reach appropriate solutions at all levels of uncertainty, specifically when a feasible solution cannot be found with the deterministic model.