The vertex splitting algorithm for facilities layout

The graph theoretic facility layout problem (GTFLP) seeks the best spatial arrangement of a set of facilities, which minimizes the total transportation cost of material flow between facilities, or maximizes total facility adjacency benefits. The GTFLP has applications in arranging rooms within a building floorplan, placing machines on a factory floor, controls on an instrument panel, or components on a circuit board. For this reason, the GTFLP is an important problem within industrial design. The GTFLP comprises two phases: the generation of a highly weighted maximal planar graph (MPG), whose edges specify adjacencies required in the layout, and the drawing of an orthogonal geometric dual to this MPG, called the block plan, under given area requirements for each facility. The first phase is NP-complete, and has been researched extensively; in the absence of a polynomial time algorithm, it appears there is little future for further research in this area. The second phase however has received far less attention due to the difficulties in not only determining algorithms for generating layouts, but also the hurdles encountered in automating these methods. This paper presents a new approach to finding a block plan from an arbitrary MPG, with facility area requirements.