Making decision under uncertainty in dynamic situations consists on choosing, at each period of time, a decision that maximizes at the end the decision-maker[alpha]s outcomes. In several situations, these outcomes should be measured against a set of heterogeneous and conflicting criteria. Such situations could be represented using multi-criteria decision trees. The common approach considered to solve this problem consists on generating a set of non-dominated solutions. But, generating the set of non-dominated solutions becomes a very challenging endeavor for large problems. In this paper, we present a methodology to solve multi-criteria decision trees without generating the set of all non-dominated solutions. The proposed methodology is based on the decomposition principle. We present a decomposition theorem that generalizes the Bellman decomposition principle to the multi-criteria discrete decision trees. We propose then an algorithm that aggregates, for each criterion and period, the evaluations of each action over the decision horizon. Then, for each decision node, the recursive algorithm uses the multi-criteria decision aid (MCDA) method to choose among partial strategies. From one period to another, only partial strategies of best compromise are retained for the following iterations. This paper describes the proposed methodology and illustrates it with an academic example.