A branch-and-bound algorithm for the single-row equidistant facility layout problem

In this paper, we deal with the single-row equidistant facility layout problem (SREFLP), which asks to find a one-to-one assignment of n facilities to n locations equally spaced along a straight line so as to minimize the sum of the products of the flows and distances between facilities. We develop a branch-and-bound algorithm for solving this problem. The lower bound is computed first by performing transformation of the flow matrix and then applying the well-known Gilmore–Lawler bounding technique. The algorithm also incorporates a dominance test which allows to drastically reduce redundancy in the search process. The test is based on the use of a tabu search procedure designed to solve the SREFLP. We provide computational results for problem instances of size up to 35 facilities. For a number of instances, the optimal value of the objective function appeared to be smaller than the best value reported in the literature.