for departments’ overlaps. On the other hand, in facility layout
problems, facilities have dimensions. In most of layout problems
in the literature, each facility can be placed on any point of the
floor. However, what we here mean is a facility layout problem
where each rectangular department can only be assigned to predefined
places (points) on each floor. We call it multi-floor discrete
layout problem (MFDLP). Accordingly, we have ‘‘I’’ different
departments that will be located in different locations of a building
with ‘‘F + 1’’ floors. In this building, each of ‘‘S’’ storages (each storage
may stock one of ‘‘M’’ materials and some storages may not be
used, meaning that M S) will be located in the cellar and all ‘‘I’’
departments can be arranged in the upper ‘‘F’’ floors. Moreover, an
elevator set is embedded in the building to ease the flow of materials
among departments and storages on different floors. A front
view of the building in which the elevator and departments are
located is shown in Fig. 1. In this figure, ‘‘lf’’ indicates lth location
on the fth floor and Storage ‘‘s’’ is sth location in the cellar.