A New Exact Approach to the Space-Free Double Row Layout Problem

Abstract

Given a set of departments, two rows with a common left origin and pairwise connectivities between the departments, the Space-Free Double-Row Facility Layout Problem (SF-DRFLP) looks for permutations of the departments in both rows such that the weighted sum of the center-to-center distances between all pairs of departments is minimized. In this paper we present a new mixed-integer linear programming formulation for the (SF-DRFLP) with given assignment of the departments to both rows that combines distance and betweenness variables. Furthermore, we analyze the combinatorial structure of optimal solutions, which allows us to prove a certain balancing condition. We then use this formulation in an enumeration scheme for solving the (SF-DRFLP). Indeed, we test all possible row assignments, where some assignments are excluded by our new combinatorial investigations. This approach allows us to solve (SF-DRFLP) instances with up to 16 departments to optimality for the first time.