As an important economic measure, the total factor productivity indices can be employed to evaluate the performance of decision-making units over time. These indices are usually based on multiplicative or additive distance functions estimated by either parametric or non parametric approaches. Under a non parametric analytic framework, this paper introduces a multiplicative directional productivity measure: the Directional Hicks-Moorsteen (DHM) indicator. A dynamical combination of multiplicative directional distance functions is introduced and non convex production technologies are assumed to estimate the distance functions. In an empirical illustration, the proposed model is applied to display productivity changes among Chinese provincial public hospitals over the period 2014-2018. The results indicate that a consistent outcome is obtained under the multiplicative technology and the production technology of free disposal hull while more productivity gains are observed under free disposal hull technology.