Arabian Journal for Science and Engineering

, Volume 44, Issue 8, pp 7261–7276 | Cite as

Mixed Integer Programming Formulations for Single Row Facility Layout Problems with Asymmetric Material Flow and Corridor Width

  • Xuhong Yang
  • Wenming Cheng
  • Peng GuoEmail author
  • Qiaoting He
Research Article - Systems Engineering


In both the research and industry studies, mixed integer programming (MIP) is often the default method for solving facility layout problems. While MIP models for the single row layout problem have existed since the 1970s, comprehensive computational research has not been performed since then. In this paper, four different MIP models for the single row facility layout problem with simultaneous asymmetric material flow and corridor width (dubbed SRFLP_AC) are developed based on the decision variable paradigm. We present the computational results and discuss the model efficacy in terms of solution quality and computational budget. Moreover, the performance of two disjunctive models, MIP1 and MIP2, with indicator constraints is also analyzed. Finally, we analyze the effect of the symmetry-breaking constraint and different non-overlapping constraints on the most promising model.


Single row facility layout problem Mixed integer programming (MIP) Disjunctive constraints Symmetry-breaking constraint 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was partially supported by the Sichuan Province Miaozi Innovation Project of China (Grant No. 2017119), the National Natural Science Foundation of China (Grant Nos. 51405403, and 51705436), and the Fundamental Research Funds for the Central Universities (Grant No. 2682018CX09).


  1. 1.
    Tompkins, J.A.; White, J.A.; Bozer, Y.A.; Tanchoco, J.M.A.: Facilities Planning. Wiley, New York (2010)Google Scholar
  2. 2.
    Drira, A.; Pierreval, H.; Hajri-Gabouj, S.: Facility layout problems: a survey. Annu. Rev. Control 31(2), 255–267 (2007)Google Scholar
  3. 3.
    Keller, B.; Buscher, U.: Single row layout models. Eur. J. Oper. Res. 245(3), 629–644 (2015)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Simmons, D.M.: One-dimensional space allocation: an ordering algorithm. Oper. Res. 17(5), 812–826 (1969)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chung, J.; Tanchoco, J.M.A.: The double row layout problem. Int. J. Prod. Res. 48(3), 709–727 (2010)zbMATHGoogle Scholar
  6. 6.
    Amaral, A.R.S.: The corridor allocation problem. Comput. Oper. Res. 39(12), 3325–3330 (2012)zbMATHGoogle Scholar
  7. 7.
    Gen, M.; Ida, K.; Cheng, C.: Multirow machine layout problem in fuzzy environment using genetic algorithms. Comput. Ind. Eng. 29(1–4), 519–523 (1995)Google Scholar
  8. 8.
    Hungerländer, P.: The checkpoint ordering problem. Optimization 66(10), 1699–1712 (2017)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Amaral, A.R.S.: A parallel ordering problem in facilities layout. Comput. Oper. Res. 40(12), 2930–2939 (2013a)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Amaral, A.R.S.: A new lower bound for the single row facility layout problem. Discrete Appl. Math. 157(1), 183–190 (2009)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Garey, M.R.; Johnson, D.S.: Computers and intractability: a guide to the theory of np-completeness. W. H. Freeman, New York (1979)zbMATHGoogle Scholar
  12. 12.
    Wang, H.-F.; Chang, C.-M.: Facility layout for an automated guided vehicle system. Procedia Comput. Sci. 55, 52–61 (2015)Google Scholar
  13. 13.
    Amaral, A.R.S.: On the exact solution of a facility layout problem. Eur. J. Oper. Res. 173(2), 508–518 (2006)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Amaral, A.R.S.: An exact approach to the one-dimensional facility layout problem. Oper. Res. 56(4), 1026–1033 (2008)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Gurobi Optimization Inc.: Gurobi optimizer reference manual (2015). Accessed 1 Feb 2018
  16. 16.
    Anjos, M.F.; Vieira, M.V.C.: Mathematical optimization approaches for facility layout problems: the state-of-the-art and future research directions. Eur. J. Oper. Res. 261(1), 1–16 (2017)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Hosseini-Nasab, H.; Fereidouni, S.; Ghomi, S.M.T.F.; Fakhrzad, M.B.: Classification of facility layout problems: a review study. Int. J. Adv. Manuf. Technol. 94(1–4), 957–977 (2018)Google Scholar
  18. 18.
    Heragu, S.S.; Kusiak, A.: Machine layout problem in flexible manufacturing systems. Oper. Res. 36(2), 258–268 (1988)Google Scholar
  19. 19.
    Picard, J.-C.; Queyranne, M.: On the one-dimensional space allocation problem. Oper. Res. 29(2), 371–391 (1981)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Suryanarayanan, J.K.; Golden, B.L.; Wang, Q.: A new heuristic for the linear placement problem. Comput. Oper. Res. 18(3), 255–262 (1991)zbMATHGoogle Scholar
  21. 21.
    Atkinson, J.; Chartier, Y.; Silvia, C.L.P.; Jensen, P.; Li, Y.; Seto, W.H.: Natural Ventilation for Infection Control in Health-Care Settings. World Health Organization, Geneva (2009)Google Scholar
  22. 22.
    Anjos, M.F.; Vannelli, A.: Computing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes. INFORMS J. Comput. 20(4), 611–617 (2008)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Amaral, A.R.S.; Letchford, A.N.: A polyhedral approach to the single row facility layout problem. Math. Program. 141(1–2), 453–477 (2013)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Love, R.; Wong, J.: On solving a one-dimensional space allocation problem with integer programming. INFOR Inf. Syst. Oper. Res. 14(2), 139–143 (1976)zbMATHGoogle Scholar
  25. 25.
    Heragu, S.S.; Kusiak, A.: Efficient models for the facility layout problem. Eur. J. Oper. Res. 53(1), 1–13 (1991)zbMATHGoogle Scholar
  26. 26.
    Solimanpur, M.; Vrat, P.; Shankar, R.: An ant algorithm for the single row layout problem in flexible manufacturing systems. Comput. Oper. Res. 32(3), 583–598 (2005)zbMATHGoogle Scholar
  27. 27.
    Anjos, M.F.; Kennings, A.; Vannelli, A.: A semidefinite optimization approach for the single-row layout problem with unequal dimensions. Discrete Optim. 2(2), 113–122 (2005)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Hungerländer, P.; Rendl, F.: A computational study and survey of methods for the single-row facility layout problem. Comput. Optim. Appl. 55(1), 1–20 (2013a)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Hungerländer, P.; Rendl, F.: Semidefinite relaxations of ordering problems. Math. Program. 140(1), 77–97 (2013b)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Andrade, R.C.; da Ferreira, M.S.: Single row facility layout problem. In: Brazilian Symposium on Operational Research, pp. 2874–2879 (2017)Google Scholar
  31. 31.
    Guan, J.; Lin, G.: Hybridizing variable neighborhood search with ant colony optimization for solving the single row facility layout problem. Eur. J. Oper. Res. 248(3), 899–909 (2016)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Ning, X.; Li, P.: A cross-entropy approach to the single row facility layout problem. Int. J. Prod. Res. 56, 1–14 (2017)Google Scholar
  33. 33.
    Keller, B.: Construction heuristics for the single row layout problem with machine-spanning clearances. INFOR Inf. Syst. Oper. Res. 1, 1–24 (2017)Google Scholar
  34. 34.
    Kalita, Z.; Datta, D.: A constrained single-row facility layout problem. Int. J. Adv. Manuf. Technol. 98(5–8), 2173–2184 (2018)Google Scholar
  35. 35.
    Unlu, Y.; Mason, S.J.: Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Comput. Ind. Eng. 58(4), 785–800 (2010)Google Scholar
  36. 36.
    Fortet, R.: Lalgebre de boole et ses applications en recherche opérationnelle. Trabajos de Estadistica y de Investigación Operativa 11(2), 111–118 (1960)zbMATHGoogle Scholar
  37. 37.
    Fan, L.; Wang, J.; Jiang, R.; Guan, Y.: Min–max regret bidding strategy for thermal generator considering price uncertainty. IEEE Trans. Power Syst. 29(5), 2169–2179 (2014)Google Scholar
  38. 38.
    Ahonen, H.; de Alvarenga, A.G.; Amaral, A.R.S.: Simulated annealing and tabu search approaches for the corridor allocation problem. Eur. J. Oper. Res. 232(1), 221–233 (2014)MathSciNetzbMATHGoogle Scholar
  39. 39.
    Lofberg, J.: Yalmip: A toolbox for modeling and optimization in matlab. In: 2004 IEEE International Symposium on Computer Aided Control Systems Design, pp. 284–289. IEEE (2004)Google Scholar
  40. 40.
    Ku, W.-Y.; Beck, J.C.: Mixed integer programming models for job shop scheduling: a computational analysis. Comput. Oper. Res. 73, 165–173 (2016)MathSciNetzbMATHGoogle Scholar
  41. 41.
    Sherali, H.D.; Fraticelli, B.M.P.; Meller, R.D.: Enhanced model formulations for optimal facility layout. Oper. Res. 51(4), 629–644 (2003)MathSciNetzbMATHGoogle Scholar
  42. 42.
    Amaral, A.R.S.: Optimal solutions for the double row layout problem. Optim. Lett. 7(2), 407–413 (2013b)MathSciNetzbMATHGoogle Scholar
  43. 43.
    Djellab, H.; Gourgand, M.: A new heuristic procedure for the single-row facility layout problem. Int. J. Comput. Integr. Manuf. 14(3), 270–280 (2001)Google Scholar
  44. 44.
    Samarghandi, H.; Eshghi, K.: An efficient tabu algorithm for the single row facility layout problem. Eur. J. Oper. Res. 205(1), 98–105 (2010)MathSciNetzbMATHGoogle Scholar
  45. 45.
    Keha, A.B.; Khowala, K.; Fowler, J.W.: Mixed integer programming formulations for single machine scheduling problems. Comput. Ind. Eng. 56(1), 357–367 (2009)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan ProvinceChengduChina
  3. 3.School of Chemical EngineeringSichuan UniversityChengduChina

Personalised recommendations