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This paper introduces one systematic procedure for the manager of an organization to assess units under its governance using multiple performance indices. The goal of this systematic procedure is to assist the manager in obtaining a preferable and robust ranking result for units. In this procedure, for all units, one common set of weights attached to the performance indices is determined in order to maximize the group's comprehensive score. Then, using the common set of weights, each unit's comprehensive score is evaluated and compared for ranking. In order to obtain the preferable ranking, the manager's subjective preference is considered and formulated by the virtual weights restrictions while determining the common weights in the procedure. The procedure is applied in order to obtain a robust ranking by modifying the boundary of the feasible region of virtual weights restrictions in each assessment. The final statistical ranking of all assessments provides the manager with one robust ranking, which is invariant in different feasible regions of virtual weights restrictions in the numerical example.