Exact approaches for the combined cell layout problem

Abstract

We consider the Combined Cell Layout Problem (CCLP) as well as the Multi-Bay Facility Layout Problem (MBFLP) and Layouts with Pier-Type Patterns, which are both special cases of the CCLP. Given a number of cells of type single-row or directed circular, pairwise distances between the cells 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 positions of the cells plus the distance between the cells. The CCLP and its variations have wide applications. Nevertheless approaches for solving the CCLP exactly have not been presented in the literature before. 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 a new well-performing exact approach for the CCLP 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.