A computational study and survey of methods for the single-row facility layout problem

Abstract

Abstract. The single-row facility layout problem (SRFLP) is an NP-hard combinatorial optimization problem that is concerned with the arrangement of n departments of given lengths on a line so as to minimize the weighted sum of the distances between department pairs. (SRFLP) is the one-dimensional version of the facility layout problem that seeks to arrange rectangular facilities so as to minimize the overall interaction cost. This paper compares the different modelling approaches for (SRFLP) and applies a recent SDP approach for general quadratic ordering problems from Hungerländer and Rendl to (SRFLP). In particular, we report optimal solutions for several (SRFLP) instances from the literature with up to 42 departments that remained unsolved so far. Secondly we significantly reduce the best known gaps and running times for large instances with up to 100 departments.

Semidefinite relaxations of ordering problems

“…WB has applications in computational biology [13] and additionally the single-row facility layout problem (SRFLP) and the (weighted) minimum linear arrangement problem (MinLA) are special cases. Therefore in Subsections 7.2, 7.3 and 7.4 we just point out some selected improvements achieved and refer to separate papers [12,28] for an in-depth (polyhedral) analysis of the specific problem structures and extensive computational comparisons with other methods to point out their potential and limitations.…”

“…We can also solve Amaral's new instances [2] to optimality with our approach and even achieve better computation times. For the detailed polyhedral and computational comparison of the two approaches we refer to [28]. There we also successfully apply (SDP 4 ) to the even larger SRFLP instances with up to 100 departments from [4,6].…”

Fast simulated annealing for single-row equidistant facility layout

“…(14)- (18) and (9) as InitData. The difference between the two procedures is that UpdateDataInterchange recalculates only a subset of entries of each of the matrices A and B and vectors C and C − .…”

“…Unlike the SREFLP, this problem is not a special case of the QAP. The state of the art on single-row facility layout is surveyed in the papers by Kothari and Ghosh [24] and Hungerländer and Rendl [18]. A natural generalization of the SRFLP is the corridor allocation problem (CAP) considered in [2,3].…”

“…. , n − 1, compute c i by(18) and c − i by(9). Set c − n := −c n−1 .In Step 1 of InitData, the matrices A and B are built using Eqs.…”