We address the problem of designing and planning a multi-period, multi-echelon, multi-commodity logistics network with deterministic demands. This consists of making strategic and tactical decisions: opening, closing or expanding facilities, selecting suppliers and defining the product flows. We use a heuristic approach based on the linear relaxation of the original mixed integer linear problem (MILP). The main idea is to solve a sequence of linear relaxations of the original MILP, and to fix as many binary variables as possible at every iteration. This simple process is coupled with several rounding procedures for some key decision variables. The number of binary decision variables in the resulting MILP is small enough for it to be solved with a solver. The main benefit of this approach is that it provides feasible solutions of good quality within an affordable computation time.