In this paper, we present and propose the interactive push-pull lean game with a specific approach for training/testing of production processes. With our approach of combining the psychologically effective physical lean game and the simulation lean game for deeper analyses of the production process, we can successfully overcome the communication and motivation problems of production and management workers when new production strategies are being introduced into the company to raise the competitiveness. The game only takes two hours and it has been proven to be effective with leadership teams and shop floor workers alike in more than 50 real-case production environments. The game is played in two parts where each part is in sharp contrast to the other with respect to results. Once the participants of the game see the effects of both production strategies, they become extremely engaged and motivated, and it becomes much easier to manage organizational improvements. In the third chapter of the paper, we present the Virtual factory computer models of the game dynamic, showing the same results as obtained with groups. The two simulation models serve to test and verify the interactive game. The paper ends with the discussion and conclusions.