Healthcare systems are recognized for their disarticulated logistics models due to their interconnected services' complex structure. There is evidence in the literature that these systems require the implementation of supply chain management practices to strengthen their integration with customers and suppliers and improve their competitiveness. Then, this research aimed to analyze competitiveness in a supply chain integration and logistics for a Colombian public hospital applying a competence and capability assessment. The results show that the supply chain integration competitiveness of the studied hospital is 72.24%, and the logistics competitiveness is 77.79%. Based on the Bowersox model, most performance results are above the defined threshold set by the performance of established world-class companies, showing an acceptable level. To reduce the identified GAPs, we provided strategies for the improvement of competitiveness in supply chain integration and logistics for the selected Colombian public hospital.