Purpose – The purpose of this paper is to overcome the deficiency of the current GM(1,N) such as low‐prediction precision, extend the scope of GM(1,N) and provide an effective grey dynamic model GM(1,N) for the relationship of cost and variability.Design/methodology/approach – The relationship between two factors of variety and the cost of manufacturing system is studied on the basis of the variety reduction program theory. Based on the Grey system and the gradient algorithm, a Grey dynamic model GM(1,N) is proposed between cost and variety by optimizing the coefficient and background value of the model which is used to check validity for the relation of plasm‐yarn machine product and variety.Findings – The proposed Grey dynamic prediction model GM(1,N) for the relationship of cost and variability has high precision and easy‐to‐use.Research limitations/implications – A Grey model GM(1,N) for prediction is proposed.Practical implications – The proposed model should also have potential for multifactor syste...