In this paper, we deal with the preemptive asymmetric stacker crane problem in an heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation a simple, efficient local search heuristic, as well as an original LIP model. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and at evaluating the impact of the preemption hypothesis.