A comparative study of different formulations for the capacitated discrete ordered median problem. This paper deals with the capacitated version of discrete ordered median problems. We present different formulations considering three-index variables or covering variables to address the order requirements in this problem. Some preprocessing phases for fixing variables and some valid inequalities are developed to enhance the initial formulations. Finally, an extensive computational analysis is addressed with data taken from the OR-library and AP-library showing the efficiency of the formulations and the improvements presented in the paper.