An efficient multiple-stage mathematical programming method for advanced single and multi-floor facility layout problems

Abstract Single floor facility layout problem (FLP) is related to finding the arrangement of a given number of departments within a facility; while in multi-floor FLP, the departments should be imbedded in some floors inside the facility. The significant influence of layout design on the effectiveness of any organization has turned FLP into an important issue. This paper presents a three- (two-) stage mathematical programming method to find competitive solutions for multi- (single-) floor problems. At the first stage, the departments are assigned to the floors through a mixed integer programming model (the single floor version does not require this stage). At the second stage, a nonlinear programming model is used to specify the relative position of the departments on each floor; and at the third stage, the final layouts within the floors are determined, through another nonlinear programming model. The multi-floor version is studied in the states in which the locations of the elevators are either formerly specified or not. Computational results show that this framework can find a wide variety of high quality layouts at competitive cost (up to 43% reduction) within a short amount of time for small and especially large size problems, compared to the existing methods in the literature. Also, the proposed method is flexible enough to accommodate the complicated and real-world problems, because of using mathematical programming model and solving it directly.

[1]  Ahmad Hemmati,et al.  Optimal Multi Floor Facility Layout , 2010 .

[2]  Kyu-Yeul Lee,et al.  An improved genetic algorithm for facility layout problems having inner structure walls and passages , 2003, Comput. Oper. Res..

[3]  M. Sir,et al.  A multi-objective mixed-integer programming model for a multi-floor facility layout , 2013 .

[4]  Abbas Afrazeh,et al.  A new model for dynamic multi floor facility layout problem , 2010 .

[5]  M. Bazaraa.  Computerized Layout Design: A Branch and Bound Approach , 1975 .

[6]  William J. Mitchell,et al.  Optimal space planning in practice , 1981 .

[7]  P. Pardalos,et al.  Network design : connectivity and facilities location : DIMACS Workshop, April 28-30, 1997 , 1998 .

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

[9]  Yavuz A. Bozer,et al.  A new simulated annealing algorithm for the facility layout problem , 1996 .

[10]  Hanif D. Sherali,et al.  Applying the sequence-pair representation to optimal facility layout designs , 2007, Oper. Res. Lett..

[11]  Surya Prakash Singh,et al.  Modified simulated annealing based approach for multi objective facility layout problem , 2013 .

[12]  Anthony Vannelli,et al.  An Attractor-Repeller approach to floorplanning , 2002, Math. Methods Oper. Res..

[13]  Yavuz A. Bozer,et al.  Alternative approaches to solve the multi-floor facility layout problem , 1997 .

[14]  Giuseppe Aiello,et al.  A multi objective genetic algorithm for the facility layout problem based upon slicing structure encoding , 2012, Expert Syst. Appl..

[15]  Rrk Sharma,et al.  A review of different approaches to the facility layout problems , 2006 .

[16]  Yavuz A. Bozer,et al.  A reexamination of the distance-based facility layout problem , 1997 .

[17]  Leon F. McGinnis,et al.  Facility Layout and Location: An Analytical Approach , 1991 .

[18]  Panos M. Pardalos,et al.  Nonlinear assignment problems : algorithms and applications , 2000 .

[19]  Chaomin Luo,et al.  Elsevier Editorial System(tm) for European Journal of Operational Research Title: a Convex Optimisation Framework for the Unequal-areas Facility Layout Problem a Convex Optimisation Framework for the Unequal-areas Facility Layout Problem , 2022 .

[20]  Daniel Scholz,et al.  STaTS: A Slicing Tree and Tabu Search based heuristic for the unequal area facility layout problem , 2009, Eur. J. Oper. Res..

[21]  Mahdi Bashiri,et al.  An analytical comparison to heuristic and meta-heuristic solution methods for Quadratic Assignment Problem , 2010, The 40th International Conference on Computers & Indutrial Engineering.

[22]  Yavuz A. Bozer,et al.  Solving the facility layout problem with simulated annealing , 1992 .

[23]  Sue Abdinnour-Helm,et al.  Tabu search based heuristics for multi-floor facility layout , 2000 .

[24]  Panos M. Pardalos,et al.  Simulated Annealing and Genetic Algorithms for the Facility Layout Problem: A Survey , 1997, Comput. Optim. Appl..

[25]  Ming-Der May,et al.  Multiple-floor facilities layout design , 2010, Proceedings of 2010 IEEE International Conference on Service Operations and Logistics, and Informatics.

[26]  Yeong-Dae Kim,et al.  A space partitioning method for facility layout problemswith shape constraints , 1998 .

[27]  Roger V. Johnson.  Spacecraft for Multi-Floor Layout Planning , 1982 .

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

[29]  G. Thompson,et al.  A heuristic method for the multi-story layout problem , 1988 .

[30]  Yavuz A. Bozer,et al.  An improvement-type layout algorithm for single and multiple-floor facilities , 1994 .

[31]  Henri Pierreval,et al.  Facility layout problems: A survey , 2007, Annu. Rev. Control..

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

[33]  Kamran Shahanaghi,et al.  Multi-floor dynamic facility layout: a simulated annealing-based solution , 2013 .

[34]  Abdullah Konak,et al.  Unequal area flexible bay facility layout using ant colony optimisation , 2011 .

[35]  Mohammad Mohammadi,et al.  A novel approach for considering layout problem in cellular manufacturing systems with alternative processing routings and subcontracting approach , 2014 .

[36]  K. Y. Tam,et al.  A simulated annealing algorithm for allocating space to manufacturing cells , 1992 .

[37]  Marc Goetschalckx,et al.  Efficient Formulations for the Multi-Floor Facility Layout Problem with Elevators , 2007 .

[38]  Chir-Ho Chang,et al.  Multiple-Floor Facility Layout Design with Aisle Construction , 2006 .

[39]  Maurício Resende.  A Branch and Bound Algorithm for the Quadratic Assignment Problem using a Lower Bound Based on Linear Programming , 1996 .

[40]  J. S. Kochhar.  MULTI-HOPE: A tool for multiple floor layout problems , 1998 .

[41]  J. A. Bland,et al.  Large-scale layout of facilities using a heuristic hybrid algorithm , 1994 .

[42]  RohMyung-Il,et al.  An improved genetic algorithm for multi-floor facility layout problems having inner structure walls and passages , 2005 .

[43]  Mario Enea,et al.  The facility layout problem approached using a fuzzy model and a genetic search , 2005, J. Intell. Manuf..

[44]  M. Bashiri,et al.  Effective heuristics and meta-heuristics for the quadratic assignment problem with tuned parameters and analytical comparisons , 2012 .

[45]  D. Camp,et al.  A nonlinear optimization approach for solving facility layout problems , 1992 .

[46]  Alice E. Smith,et al.  Unequal-area facility layout by genetic search , 1995 .

[47]  Miguel F. Anjos,et al.  A two-stage mathematical-programming method for the multi-floor facility layout problem , 2013, J. Oper. Res. Soc..

[48]  Anthony Vannelli,et al.  A New Mathematical-Programming Framework for Facility-Layout Design , 2006, INFORMS J. Comput..

[49]  Reza Tavakkoli-Moghaddam,et al.  A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines , 2016 .