Branch and bound for the fixed-shape unequal area facility layout problem

Journal article, 2025

Models of the Facility Layout Problem (FLP) can be useful for guiding the placement of resources in a factory building or similar. In real-world situations, the placement of the resources is often subject to a set of complex geometrical constraints, consisting of safety distances and work areas that cannot be encroached. This can result in disjoint regions or irregular shapes that must be placed so that a set of overlapping rules are fulfilled. In this paper, we formulate this problem as placing a fixed set of arbitrary polygon unions in a plane such that the overlapping constraints are not violated and the sum of weighted distances between them is minimized. A grid-based approximation and a branch and bound algorithm to solve this variation of the problem are developed. We compare the performance with a linearized QAP formulation solved with state-of-the art MILP solvers. The algorithm shows favorable results, solving problem instances with up to 8 resources to optimality within 48 h.