Slicing tree's geometric potential: an indicator for layout problems based on slicing tree structure

In this paper we propose an indicator to measure the capacity of a slicing tree to generate geometrically acceptable solutions for layout problems based on the slicing tree structure. This indicator can predict if, by making the appropriate cuts, the tree structure is able to generate layouts that satisfy the geometrical restrictions imposed on the items to be arranged. It also permits the determination of the most suitable aspect ratio of the layout zone in order to minimize non-compliance with the geometric restrictions. The method of calculating the indicator and its application to the facility layout problem are described, and the results obtained in the experiments carried out are also given.