Journal of Intelligent Manufacturing

, Volume 24, Issue 2, pp 331–348 | Cite as

A multi-objective facility location model with batch arrivals: two parameter-tuned meta-heuristic algorithms

  • Seyed Hamid Reza Pasandideh
  • Seyed Taghi Akhavan Niaki
  • Vahid Hajipour


Many research works in mathematical modeling of the facility location problem have been carried out in discrete and continuous optimization area to obtain the optimum number of required facilities along with the relevant allocation processes. This paper proposes a new multi-objective facility-location problem within the batch arrival queuing framework. Three objective functions are considered: (I) minimizing the weighted sum of the waiting and the traveling times, (II) minimizing the maximum idle time pertinent to each facility, and (III) minimizing the total cost associated with the opened facilities. In this way, the best combination of the facilities is determined in the sense of economical, equilibrium, and enhancing service quality viewpoints. As the model is shown strongly NP-hard, two meta-heuristic algorithms, namely genetic algorithm (GA) and simulated annealing (SA) are proposed to solve the model. Not only new coding is developed in these solution algorithms, but also a random search algorithm is proposed to justify the efficiency of both algorithms. Since the solution-quality of all meta-heuristic algorithms severely depends on their parameters, design of experiments and response surface methodologies have been utilized to calibrate the parameters of both algorithms. Finally, computational results obtained by implementing both algorithms on several problems of different sizes demonstrate the performances of the proposed methodology.


Multi objective facility location Queuing theory Batch arrival MODM techniques GA SA RSM 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Al Jadaan O., Rao C. R., Rajamani L. (2006) Parametric study to enhance genetic algorithm performance using ranked based roulette wheel selection method. In SciT, Merida, Spain V2: 274–278Google Scholar
  2. Aytug H., Saydam C. (2002) Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study. European Journal of Operational Research 141: 480–494CrossRefGoogle Scholar
  3. Balinski M. L. (1965) Integer programming: Methods, uses, computations. Management Science 12: 253–313CrossRefGoogle Scholar
  4. Berman O., Drezner Z. (2007) The multiple server location problem. Journal of the Operational Research Society 58: 91–99CrossRefGoogle Scholar
  5. Berman O., Krass D. (2001) Facility location problems with stochastic demands and congestion. In: Drezner Z., Hamacher H.W. (eds) Facility location: Applications and theory. Springer, BerlinGoogle Scholar
  6. Berman O., Krass D., Wang J. (2006) Locating service facilities to reduce lost demand. IIE Transactions 38: 933–946CrossRefGoogle Scholar
  7. Boffey B., Galvao R., Espejo L. (2007) A review of congestion models in the location of facilities with immobile servers. European Journal of Operational Research 178: 643–662CrossRefGoogle Scholar
  8. Chambari A. H., Rahmaty S. H., Hajipour V., Karimi A. (2011) A bi-objective model for location-allocation problem within queuing framework. World Academy of Science. Engineering and Technology 78: 138–145Google Scholar
  9. Chan F. T. S., Kumar V. (2009) Performance optimization of a leagility inspired supply chain model: A CFGTSA algorithm based approach. International Journal of Production Research 47: 777–799CrossRefGoogle Scholar
  10. Cooper R. B. (1980) Introduction to queuing theory (2nd ed). Elsevier North Holland, New YorkGoogle Scholar
  11. Costa M. G., Captivo M. E., Climaco J. (2008) Capacitated single allocation hub location problem—A bi-criteria approach. Computer and Operations Research 35: 3671–3695CrossRefGoogle Scholar
  12. Current J., Daskin M., Schilling D. (2002) Discrete network location models. In: Drezner Z., Hamacher H. W. (eds) Facility location: Applications and theory. Springer, BerlinGoogle Scholar
  13. Deb K. (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester, UKGoogle Scholar
  14. Dong M., Wua C., Hou F. (2009) Shortest path based simulated annealing algorithm for dynamic facility layout problem under dynamic business environment. Expert Systems with Applications 36: 11221–11232CrossRefGoogle Scholar
  15. Ehrgott M., Gandibleux X. (2000) An annotated bibliography of multi-criteria combinatorial optimization. OR Spectrum 22: 425–460CrossRefGoogle Scholar
  16. Ehrgott, M., & Gandibleux, X. (2003). Multiple criteria optimization: State of the art annotated bibliographic surveys, New York, Boston, Dordrecht, London, Moscow.Google Scholar
  17. Farahani R. Z., SteadieSeifi M., Asgari N. (2009) Multiple criteria facility location problems: A survey. Applied Mathematical Modelling 34: 1689–1709CrossRefGoogle Scholar
  18. Francis R. L., Megginis L. F., White J. A. (1992) Facility layout and location: An analytical approach (2nd ed). Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  19. Gen M., Cheng R., Lin L. (2008) Network models and optimization multiobjcetive GA approach. Springer, LondonGoogle Scholar
  20. Ghosh A., Rushton G. (1987) Spatial analysis and location-allocation models. Van Nostrand Reinhold Company, New York, NYGoogle Scholar
  21. Gross D., Harris C. M. (1998) Fundamental of queuing theory (3rd ed). Wiley Interscience, New York, NYGoogle Scholar
  22. Hakimi S. L. (1964) Optimum locations of switching centres and the absolute centres and medians of a graph. Operations Research 12: 450–459CrossRefGoogle Scholar
  23. Harewood S. I. (2002) Emergency ambulance deployment in Barbados: A multi-objective approach. Journal of Operations Research Society 53: 185–192CrossRefGoogle Scholar
  24. Haupt R. L., Haupt S. E. (2004) Practical genetic algorithms (2nd ed). Wiley, New YorkGoogle Scholar
  25. Hodgson M. J., Berman O. (1997) A billboard location model. Geographical and Environmental Modeling 1: 25–43Google Scholar
  26. Holland J. H. (1975) Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control and artificial intelligence. University of Michigan Press, MichiganGoogle Scholar
  27. Hwang C. L., Yoon K. (1981) Multiple attribute decision making—Methods and applications: A state-of-the-art survey. Springer, New YorkCrossRefGoogle Scholar
  28. Kerbache L., Smith M. G. (2000) Multi-objective routing within large scale facilities using open finite queueing networks. European Journal of Operational Research 121: 105–123CrossRefGoogle Scholar
  29. Kirkpatrick S., Gelatt C. D., Vecchi M. P. (1983) Optimization by simulated annealing. Science 220: 671–680CrossRefGoogle Scholar
  30. Love, R. L., Morris, J. G., & Wesolowsky, G. O. (1988). Facility location: Models and methods. North-Holland: New York (1988). [Edited by Francis, R. L., Megginis, L. F., White, J. A. Facility layout and location: An analytical approach (2nd ed.) Englewood Cliffs, NJ: Prentice-Hall (1992)].Google Scholar
  31. Marianov V., ReVelle C. (1995) Siting emergency services in facility Location: A survey of applications and methods. Springer Series in Operations Research, BerlinGoogle Scholar
  32. MATLAB Version (2010). The MathWorks, Inc. Protected by U.S. and international patents.Google Scholar
  33. McKendall A. R. Jr., Hakobyan A. (2010) Heuristics for the dynamic facility layout problem with unequal-area departments. European Journal of Operational Research 201: 171–182CrossRefGoogle Scholar
  34. Montgomery D.C. (2004) Response surface methodology. Wiley, New YorkGoogle Scholar
  35. Montgomery DC. (2005) Design and analysis of experiments (6th ed). Wiley, New York, USAGoogle Scholar
  36. Najafi A. A., Niaki S. T. A., Shahsavar A. (2009) A parameter-tuned genetic algorithm for the resource investment problem with discounted cash flows and generalized precedence relations. Computer and Operations Research 36: 2994–3001CrossRefGoogle Scholar
  37. Ohsawa Y. (1999) A geometrical solution for quadratic bicriteria location models. European Journal of Operational Research 114: 380–388CrossRefGoogle Scholar
  38. Pasandideh, S. H. R., & Niaki, S. T. A. (2010). Genetic application in a facility location problem with random demand within queuing framework. Journal of Intelligent Manufacturing. (in press).
  39. Porter A., Roper A., Mason T., Rossini F., Banks J. (1991) Forecasting and management of technology. Wiley, New YorkGoogle Scholar
  40. Rastrigin L. A. (1963) The convergence of the random search method in the external control of a many parameter system. Automation and Remote Control 24: 1337–1342Google Scholar
  41. Shavandi H., Mahlooji H. (2006) A fuzzy queuing location model with a genetic algorithm congested systems. Applied Mathematics and Computation 181: 440–456CrossRefGoogle Scholar
  42. Singh S. P., Singh V. K. (2010) An improved heuristic approach for multi-objective facility layout problem. International Journal of Production Research 48: 1171–1194CrossRefGoogle Scholar
  43. Stadler W. (1984) Applications of multicriteria optimization in engineering and the sciences (a survey). In: Zeleny M. (eds) Multiple criteria decision making—Past decade and future trends. JAI, Greenwich, CTGoogle Scholar
  44. Topcuoglua H., Coruta F., Ermisb M., Yilmaza G. (2005) Solving the uncapacitated hub location problem using genetic algorithms. Computers & Operations Research 32: 967–984CrossRefGoogle Scholar
  45. Vose M. D. (1991) Generalizing the notion of schema in genetic algorithms. Artificial Intelligence 50: 385–396CrossRefGoogle Scholar
  46. Wang Q., Batta R., Rump C. (2002) Algorithms for a facility location problem with stochastic customer demand and immobile servers. Annals of Operations Research 111: 17–34CrossRefGoogle Scholar
  47. Weber, A. (1909). Alfred Weber’s theory of the location of industries (English Translation by C. J. Friedrich). University of Chicago: Chicago University Press, 1929Google Scholar
  48. Yeniay O., Ankare B. (2005) Penalty function methods for constrained optimization with genetic algorithms. Mathematical and Computational Application 10: 45–56Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Seyed Hamid Reza Pasandideh
    • 1
  • Seyed Taghi Akhavan Niaki
    • 2
  • Vahid Hajipour
    • 1
  1. 1.Faculty of Industrial and Mechanical EngineeringIslamic Azad UniversityQazvinIran
  2. 2.Department of Industrial EngineeringSharif University of TechnologyTehranIran

Personalised recommendations