In this paper we consider the Combined Cell Layout Problem (CCLP), the Multi-Bay Facility Layout Problem (MBFLP) and several generalizations of the MBFLP, which have wide applications, e.g., in factory planning, heavy manufacturing, semiconductor fabrication and arranging rooms in hospitals. Given a set of cells of type single-row or directed-circular and a set of one-dimensional departments with pairwise transport weights between them, the CCLP asks for an assignment of the departments to the cells such that departments in the same cell do not overlap and such that the sum of the weighted center-to-center distances is minimized. Distances between departments in the same cell are measured according to the layout type of the cell and otherwise their distance equals the sum of the distances to the associated (un-) loading stations of the cells plus possible space between the cells. We solve the CCLP exactly by enumerating over all assignments of the departments to the cells and solving several CCLP with fixed-cell assignment. We show how to reduce the number of distinguishable cell assignments significantly by merging two cells of type single-row. This leads to new well-performing exact approaches for the CCLP, the MBFLP and its generalizations where arising subproblems are solved via (new) mixed-integer linear programming models. In a computational study we compare the computation times and the optimal values of various facility layout problems in order to support the decision maker to choose a layout.
Faculty of Business and Economics, TU Dortmund University, Vogelpothsweg 87, D-44227 Dortmund; October 2020