The single row facility layout problem: state of the art

The single row facility layout problem (SRFLP) is a NP-hard problem concerned with the arrangement of facilities of given lengths on a line so as to minimize the weighted sum of the distances between all the pairs of facilities. The SRFLP and its special cases often arise while modeling a large variety of applications. It has been actively researched until the mid-nineties, and then again since 2005. Interestingly, research on many aspects of this problem is still in the initial stages, and hence the SRFLP is an interesting problem to work on. In this paper, we review the literature on the SRFLP and comment on its relationship with other layout problems. We then provide an overview of different formulations of the problem that appear in the literature. We provide exact and heuristic approaches that have been used to solve SRFLPs, and also present details about the benchmark instances widely used in the literature. We finally point out research gaps and promising directions for future research on this problem.

[1]  Andrew Kusiak,et al.  Machine Layout Problem in Flexible Manufacturing Systems , 1988, Oper. Res..

[2]  John M. Wilson,et al.  Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search , 1999, Journal of the Operational Research Society.

[3]  J. Y. Wong,et al.  On Solving A One-Dimensional Space Allocation Problem With Integer Programming , 1976 .

[4]  André R. S. Amaral.  A mixed 0-1 linear programming formulation for the exact solution of the minimum linear arrangement problem , 2009, Optim. Lett..

[5]  André R. S. Amaral.  A new lower bound for the single row facility layout problem , 2009, Discret. Appl. Math..

[6]  Miguel F. Anjos,et al.  Provably near-optimal solutions for very large single-row facility layout problems , 2009, Optim. Methods Softw..

[7]  Marcello Braglia.  Heuristics for single row layout problems in flexible manufacturing systems , 1997 .

[8]  André R. S. Amaral.  An Exact Approach to the One-Dimensional Facility Layout Problem , 2008, Oper. Res..

[9]  Maurice Queyranne,et al.  On the One-Dimensional Space Allocation Problem , 1981, Oper. Res..

[10]  Wen-Chyuan Chiang,et al.  A simulated annealing procedure for single row layout problems in flexible manufacturing systems , 1992 .

[11]  Ravi Shankar,et al.  An ant algorithm for the single row layout problem in flexible manufacturing systems , 2005, Comput. Oper. Res..

[12]  Rafael Martí,et al.  Intensification and diversification with elite tabu search solutions for the linear ordering problem , 1999, Comput. Oper. Res..

[13]  Franz Rendl,et al.  A computational study and survey of methods for the single-row facility layout problem , 2013, Comput. Optim. Appl..

[14]  Andrew A. Kennings,et al.  A semidefinite optimization approach for the single-row layout problem with unequal dimensions , 2005, Discret. Optim..

[15]  Hamed Samarghandi,et al.  A Particle Swarm Optimization for the Single Row Facility Layout Problem , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[16]  André R. S. Amaral.  On the exact solution of a facility layout problem , 2006, Eur. J. Oper. Res..

[17]  Thomas E. Vollmann,et al.  An Experimental Comparison of Techniques for the Assignment of Facilities to Locations , 1968, Oper. Res..

[18]  Kourosh Eshghi,et al.  An efficient tabu algorithm for the single row facility layout problem , 2010, Eur. J. Oper. Res..

[19]  P. Hansen,et al.  Deux problèmes d'affectation non linéaires , 1982 .

[20]  P. Asokan,et al.  SCATTER SEARCH ALGORITHM FOR SINGLE ROW LAYOUT PROBLEM IN FMS , 2008 .

[21]  Mário Mestria,et al.  Metaheuristic methods for a class of the facility layout problem , 2000, J. Intell. Manuf..

[22]  David Romero,et al.  Methods for the one-dimensional space allocation problem , 1990, Comput. Oper. Res..

[23]  S. Heragu,et al.  Efficient models for the facility layout problem , 1991 .

[24]  Wen-Chyuan Chiang,et al.  Optimal and Heuristic Procedures for Row Layout Problems in Automated Manufacturing Systems , 1996 .

[25]  Harvey J. Greenberg,et al.  An annotated bibliography for post-solution analysis in mixed integer programming and combinatorial optimization , 1997 .

[26]  Gerhard Reinelt,et al.  The Linear Ordering Problem , 2011 .

[27]  L. H. Harper.  Optimal Assignments of Numbers to Vertices , 1964 .

[28]  Jordi Petit,et al.  Experiments on the minimum linear arrangement problem , 2003, ACM J. Exp. Algorithmics.

[29]  A. Alfa,et al.  Experimental analysis of simulated annealing based algorithms for the layout problem , 1992 .

[30]  José Rui Figueira,et al.  Single row facility layout problem using a permutation-based genetic algorithm , 2011, Eur. J. Oper. Res..

[31]  Donald M. Simmons.  One-Dimensional Space Allocation: An Ordering Algorithm , 1969, Oper. Res..

[32]  Michel Gourgand,et al.  A new heuristic procedure for the single-row facility layout problem , 2001, Int. J. Comput. Integr. Manuf..

[33]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[34]  Marian Gheorghe,et al.  A particle swarm optimization based on P systems , 2010, 2010 Sixth International Conference on Natural Computation.

[35]  Anthony Vannelli,et al.  Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes , 2008, INFORMS J. Comput..

[36]  JOSEP DÍAZ,et al.  A survey of graph layout problems , 2002, CSUR.

[37]  Franz Rendl,et al.  Semidefinite relaxations of ordering problems , 2013, Math. Program..

[38]  Adam N. Letchford,et al.  A polyhedral approach to the single row facility layout problem , 2013, Math. Program..

[39]  Fred W. Glover,et al.  A Template for Scatter Search and Path Relinking , 1997, Artificial Evolution.

[40]  K. Ravi Kumar,et al.  A heuristic procedure for the single-row facility layout problem , 1995 .