Viability theory proposes concepts and tools to control a dynamical system such that it can remain inside a viability constraint set. Integrating viability models in a tool support for participatory management is a new application of the viability theory. In this context, we propose an algorithm for viability kernel approximation, which focuses on improving the computing time. This algorithm uses the classification procedure based on the method of Nearest Neighbor Search. The algorithm satisfies the conditions of convergence, and is easy to use with a graphical user interface. We compare its results for models for which the exact viability kernels have been determined. The accuracy of this algorithm is always greater than 90 percent. The computing time is very interesting for decision support tools