Currently, there is a large percentage of small and medium-sized enterprises (SMEs) in the Peruvian textile market that show economic loss because of the payment of penalties to customers, which are incurred owing to the delay in the delivery of order batches. This is due to poor production management and a lack of focus. The manufacturing sector is essential because of its high contribution to the country's gross domestic product. Currently, SMEs do not employ methodologies that help improve production and process management as they do not realize how important and necessary the methodologies are, in addition to how complex these may be. Therefore, this paper will propose a production management model designed for SMEs in this sector, based on Lean methodology where the objective is time reductions and production increases as well as exerting changes to the organizational culture. Thus, this model will help organizations to avoid incurring economic losses because of the payment of penalties for orders not delivered on time. To validate the present model, a time simulation was performed in the manufacturing area of a textile company. The result of this project was positive, since there was a 25% increase in productivity and a 20% reduction of takt time with respect to the initial data.