Computational Optimization and Applications

, Volume 55, Issue 1, pp 1-20

First online:

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

  • Philipp HungerländerAffiliated withInstitut für Mathematik, Alpen-Adria Universität Klagenfurt Email author 
  • , Franz RendlAffiliated withInstitut für Mathematik, Alpen-Adria Universität Klagenfurt

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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 departments 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 110 departments.


Single-row facility layout Space allocation Semidefinite optimization Combinatorial optimization