Currently, small- and medium-sized enterprises face order fulfillment issues, thus generating reduced service levels. In addition, these companies are usually not aware of the importance of continuous improvement tools or of training staff as a mitigation strategy for this situation. Within this framework, the authors performed a literature review to compile production models through which downtimes could be reduced. The production model designed therefrom comprises Lean Manufacturing and work study tools within a Change Management approach. This design focuses on model implementation by small companies without requiring large investment, cutting-edge technology, or qualified personnel. Finally, an application case study was conducted in a small textile manufacturing company located at the Gamarra Fashion Center in Lima, Peru. The results that were reported revealed that late order fulfillment instances reduced by up to 18%, which had an impact on downtimes, unnecessary movements, and in-process inventory levels, thus increasing productivity by 85%.