We consider a multi-floor facility layout problem in which the overall length and width of the facility, the size and location of each department, the number and the location of elevators and the number of floors in the facility are all modelled as decision variables. We adapt a linear approximation scheme to represent the area of each department. We consider two objective functions in our model, namely minimising material handling and facility building costs, and propose a lexicographic ordering technique to handle multiple objectives. The numerical experiments show that the slack used in the lexicographic ordering approach has a significant impact on the optimal solution. The experiments also show that the material handling cost can be significantly reduced in a multi-floor facility compared with a single-floor facility.