Cellular manufacturing (CM) has been identified as an innovative practice for manufacturer to achieve efficiency as well as flexibility under an uncertain environment. This study addresses a new mathematical robust model for a cellular manufacturing problem integrated with tactical aspects under supply chain network characteristics in the presence of uncertain internal parameter (processing times) and external parameter (demands). The model aims to minimize total cost consisting expected value and variance of tactical cost (scheduling), strategic cost (employment of suppliers in supply chain network) to produce exceptional elements as well as the cost of resource underutilization. The model can give up a series of the solutions that are less sensitive to the changes in input data. To solve the robust model, an efficient hybrid method based on new combination of genetic algorithm (GA), simulated annealing (SA) in a parallel structure are proposed under an optimization rule. The effectiveness of the proposed model is demonstrated by numerical results and the trade-off between solution robustness and model robustness is also analyzed.