Over the last years, the textile industry, representing 26.2% of the manufacturing employed population, has been going through a process of growth after the economic crisis caused by Covid-19. The company under study in the present investigation suffers from long cycle times in the production process due to inefficiencies. This problem generates delays in deliveries to customers and negatively affects the company's image. Furthermore, it results in expensive labor and electricity costs. This article proposes a model to face the mentioned problem by applying an integrated model of Lean Manufacturing with the tools Systematic Layout Planning (SLP), 5S and Total Productive Maintenance (TPM), complemented by the DMAIC methodology to improve the production management, reducing cycle times in production and obtaining a competitive advantage among other companies belonging to the textile sector. The validation of this model was done through Arena simulator achieving notable results where the cycle time in production was reduced form 12.24 days to 7.29 days, the OEE increased by 30% and the production capacity significantly improved by 27%. These results confirm that the proposed model is effective in decreasing cycle times in a textile company.