Optimal three-dimensional layout of industrial facilities

Facilities layout is concerned with the spatial arrangement of a set of departments or equipment items. This is an important stage at the design level, which often results in a complex problem due to the high number of decisions involved. A Mixed Integer Linear Programming (MILP) formulation, for the optimal layout of facilities within a two-dimensional (2D) continuous space has been developed. In this paper, the proposed model is extended to account for the location of equipment units within a 3D multi-floor continuous space. Different topological characteristics are considered such as equipment items orientation, distance restrictions, equipment connectivity inputs and outputs, rectangular and irregular equipment shapes, space availability and multi-floor locations. In operational terms, production or operational sections are modelled as well as safety and operability restrictions. The final model is again described as a MILP where binary variables characterize topological choices and continuous variables describe the distances and locations involved. Finally, the applicability of the proposed formulation is shown through the resolution of a set of representative examples exploring the different model characteristics.