Facility location problems and more generally supply chain design models have been the subject of a large number of models and exact or approximate solution techniques. Yet, the Large Neighborhood Search technique (LNS) has almost never been proposed for solving such problems, although it has proven its efficiency and flexibility to solve complex combinatorial optimization problems. In this paper we propose a new solution framework for solving a four-layer single period multi-product supply chain network design problem involving multimodal transport. Location decisions for intermediate facilities (e.g. plants and distribution centers) are made using LNS while transportation modes and product flow decisions are determined by a greedy heuristic. Finally, an a posteriori flow optimization dual simplex procedure is used to finalize the solution. Extensive experiments based on randomly generated instances of different sizes and characteristics show the effectiveness of the method compared with a state-of-the-art solver. Further research aims at extending the model and solution technique to encompass other advanced supply chain design features.