Optimization problems can often be tackled with respect to several objectives. In such cases, there can be several incomparable Pareto-optimal solutions. Computing or approximating such solutions is a major challenge in algorithm design. Here, we show how to use an extended beam-search technique to solve a multi-criteria scheduling problem for heterogeneous machines. This method, called MO-Greedy (for Multi-Objective greedy), allows the design of a multi-objective algorithm when a single-objective greedy one is known. We show that we can generate, in a single execution, a Pareto front optimized with respect to the preferences specified by the decision maker. We compare our approach to other heuristics and an approximation algorithm and show that the obtained front is, on average, better with our method.