A Branch and Bound Algorithm for Multi-floor Facility Layout Problems

Abstract

We consider multi-floor facility layout problems where lmn machines (facility modules) are assigned to cells. These cells are arranged into a rectangular pattern with l floors, m rows, and n columns. As the objective function, we consider flow costs and adjacent factors between machines. In these facility layout problems, we aim to obtain the machine layout that has the minimum objective value namely, the optimal layout. In precedent research on single-floor facility layout problems, Yamamoto et al.[8],[17] proposed a condition which enumerates only original layouts and automatically removes the layouts that are different due to rotation and/or reverse operation but have same objective value. They call it the condition for removing symmetry. They also proposed an efficient algorithm using this condition, which is based on a branch and bound method. In this paper, we expand the condition in order to apply it to multi-floor facility layout problems. We also propose two kinds of efficient algorithms for these facility layout problems using the condition, which are based on a branch and bound method. Moreover, these algorithms adopt a characteristic proper to multi-floor facility layout problems. We executed some numerical experiments with a personal computer in order to compare our proposed algorithms with existing algorithms. The results show that our proposed algorithm is useful.