New complexity measures for the facility layout problem: an empirical study using traditional and neural network analysis

Abstract The most frequent application of the quadratic assignment problem has been in facility layout, which is concerned with locating the activities or departments of an organization in a fixed set of locations such that those activities with the strongest interrelationships are closest to each other. Early attempts to explain the varying performance of optimal and heuristic solution procedures on different layout problems focused on a univariate complexity measure such as the coefficient of variation. Recently, a multivariate measure for assessing the complexity of the quadratic assignment problem (QAP) formulation of the facility layout problem has been proposed. This paper introduces a new thresholding procedure for capturing critical relationship information, expands the eight components of the multivariate complexity measure by adding two new components, demonstrates a new solution value bound and experimentally determines the effect on solution quality of using either one of two heuristic solution procedures versus an optimal procedure. This result is important because it enables layout planners to determine in advance the likelihood of obtaining an optimal solution. It also tells them which problem characteristics are important and their relative weights in determining the solution outcome.

[1]  Bernard Widrow,et al.  Neural networks: applications in industry, business and science , 1994, CACM.

[2]  A. S. Carrie,et al.  Flow complexity—a data suitability index for flowline systems , 1983 .

[3]  H. Lee Hales.  Computer-Aided Facilities Planning , 1984 .

[4]  Denis R. Coleman.  Note--Plant Layout: Computers Versus Humans , 1977 .

[5]  R. Bharath,et al.  Neural Network Computing , 1994 .

[6]  Chee-Kit Looi,et al.  Neural network methods in combinatorial optimization , 1992, Comput. Oper. Res..

[7]  G. Thompson,et al.  An exact algorithm for the general quadratic assignment problem , 1986 .

[8]  Roger C. Vergin,et al.  Comparison of Computer Algorithms and Visual Based Methods for Plant Layout , 1975 .

[9]  Anil K. Jain,et al.  Artificial Neural Networks: A Tutorial , 1996, Computer.

[10]  C. J. Huberty,et al.  Issues in the use and interpretation of discriminant analysis , 1984 .

[11]  Willy Herroelen,et al.  On the use of flow dominance in complexity measures for facility layout problems , 1985 .

[12]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[13]  Elwood S. Buffa,et al.  The Facilities Layout Problem in Perspective , 1966 .

[14]  Allan S. Carrie.  Computer-aided layout planning—the way ahead , 1980 .

[15]  R. Burkard,et al.  Assignment and Matching Problems: Solution Methods with FORTRAN-Programs , 1980 .

[16]  Elwood S. Buffa,et al.  A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities , 1963 .

[17]  Chi Hau Chen,et al.  Fuzzy logic and neural network handbook , 1996 .

[18]  Melody Y. Kiang,et al.  Managerial Applications of Neural Networks: The Case of Bank Failure Predictions , 1992 .

[19]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[20]  D.R. Hush,et al.  Progress in supervised neural networks , 1993, IEEE Signal Processing Magazine.

[21]  Robin Liggett,et al.  The Quadratic Assignment Problem: An Experimental Evaluation of Solution Strategies , 1981 .

[22]  F. Hillier,et al.  Quadratic Assignment Problem Algorithms and the Location of Indivisible Facilities , 1966 .

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

[24]  Larry P. Ritzman.  The Efficiency of Computer Algorithms for Plant Layout , 1972 .

[25]  B. Gillett,et al.  Modular Allocation Technique (MAT) , 1970 .

[26]  T. E. Block.  Note---On the Complexity of Facilities Layout Problems , 1979 .

[27]  Theodosios Pavlidis,et al.  Structural pattern recognition , 1977 .

[28]  James P. Ignizio,et al.  Neural networks and operations research: An overview , 1992, Comput. Oper. Res..

[29]  Donald F. Specht,et al.  Probabilistic neural networks and general regression neural networks , 1996 .

[30]  Michael H. Kutner.  Applied Linear Statistical Models , 1974 .

[31]  Hanif D. Sherali,et al.  On the Use of Exact and Heuristic Cutting Plane Methods for the Quadratic Assignment Problem , 1982 .

[32]  Mark C. Springer,et al.  A Multivariate Approach for Assessing Facility Layout Complexity , 1990 .

[33]  Andrew Kusiak,et al.  The facility layout problem , 1987 .

[34]  Ramesh Sharda,et al.  Neural Networks for the MS/OR Analyst: An Application Bibliography , 1994 .

[35]  W. P. Lewis,et al.  On the application of computer aids to plant layout , 1980 .

[36]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[37]  J. W. Gavett,et al.  The Optimal Assignment of Facilities to Locations by Branch and Bound , 1966, Oper. Res..

[38]  Benjamin W. Wah,et al.  Global Optimization for Neural Network Training , 1996, Computer.

[39]  E. Lawler.  The Quadratic Assignment Problem , 1963 .

[40]  Donald F. Specht,et al.  Probabilistic neural networks , 1990, Neural Networks.

[41]  Richard Muther,et al.  Systematic Layout Planning , 1985 .

[42]  G. G. Hitchings,et al.  An efficient heuristic procedure for solving the layout design problem , 1976 .

[43]  P. Gilmore.  Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem , 1962 .

[44]  Bill C. Hardgrave,et al.  Predicting graduate student success: A comparison of neural networks and traditional techniques , 1994, Comput. Oper. Res..

[45]  L. D. Hopkins,et al.  Humans vs. Computer Algorithms for the Plant Layout Problem , 1980 .