Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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: 274–278
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: 480–494
Balinski M. L. (1965) Integer programming: Methods, uses, computations. Management Science 12: 253–313
Berman O., Drezner Z. (2007) The multiple server location problem. Journal of the Operational Research Society 58: 91–99
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, Berlin
Berman O., Krass D., Wang J. (2006) Locating service facilities to reduce lost demand. IIE Transactions 38: 933–946
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: 643–662
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: 138–145
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: 777–799
Cooper R. B. (1980) Introduction to queuing theory (2nd ed). Elsevier North Holland, New York
Costa M. G., Captivo M. E., Climaco J. (2008) Capacitated single allocation hub location problem—A bi-criteria approach. Computer and Operations Research 35: 3671–3695
Current J., Daskin M., Schilling D. (2002) Discrete network location models. In: Drezner Z., Hamacher H. W. (eds) Facility location: Applications and theory. Springer, Berlin
Deb K. (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester, UK
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: 11221–11232
Ehrgott M., Gandibleux X. (2000) An annotated bibliography of multi-criteria combinatorial optimization. OR Spectrum 22: 425–460
Ehrgott, M., & Gandibleux, X. (2003). Multiple criteria optimization: State of the art annotated bibliographic surveys, New York, Boston, Dordrecht, London, Moscow.
Farahani R. Z., SteadieSeifi M., Asgari N. (2009) Multiple criteria facility location problems: A survey. Applied Mathematical Modelling 34: 1689–1709
Francis R. L., Megginis L. F., White J. A. (1992) Facility layout and location: An analytical approach (2nd ed). Prentice-Hall, Englewood Cliffs, NJ
Gen M., Cheng R., Lin L. (2008) Network models and optimization multiobjcetive GA approach. Springer, London
Ghosh A., Rushton G. (1987) Spatial analysis and location-allocation models. Van Nostrand Reinhold Company, New York, NY
Gross D., Harris C. M. (1998) Fundamental of queuing theory (3rd ed). Wiley Interscience, New York, NY
Hakimi S. L. (1964) Optimum locations of switching centres and the absolute centres and medians of a graph. Operations Research 12: 450–459
Harewood S. I. (2002) Emergency ambulance deployment in Barbados: A multi-objective approach. Journal of Operations Research Society 53: 185–192
Haupt R. L., Haupt S. E. (2004) Practical genetic algorithms (2nd ed). Wiley, New York
Hodgson M. J., Berman O. (1997) A billboard location model. Geographical and Environmental Modeling 1: 25–43
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, Michigan
Hwang C. L., Yoon K. (1981) Multiple attribute decision making—Methods and applications: A state-of-the-art survey. Springer, New York
Kerbache L., Smith M. G. (2000) Multi-objective routing within large scale facilities using open finite queueing networks. European Journal of Operational Research 121: 105–123
Kirkpatrick S., Gelatt C. D., Vecchi M. P. (1983) Optimization by simulated annealing. Science 220: 671–680
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)].
Marianov V., ReVelle C. (1995) Siting emergency services in facility Location: A survey of applications and methods. Springer Series in Operations Research, Berlin
MATLAB Version 7.10.0.499 (2010). The MathWorks, Inc. Protected by U.S. and international patents.
McKendall A. R. Jr., Hakobyan A. (2010) Heuristics for the dynamic facility layout problem with unequal-area departments. European Journal of Operational Research 201: 171–182
Montgomery D.C. (2004) Response surface methodology. Wiley, New York
Montgomery DC. (2005) Design and analysis of experiments (6th ed). Wiley, New York, USA
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: 2994–3001
Ohsawa Y. (1999) A geometrical solution for quadratic bicriteria location models. European Journal of Operational Research 114: 380–388
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. http://www.springerlink.com/content/8g37q61m75g25706/ (in press).
Porter A., Roper A., Mason T., Rossini F., Banks J. (1991) Forecasting and management of technology. Wiley, New York
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: 1337–1342
Shavandi H., Mahlooji H. (2006) A fuzzy queuing location model with a genetic algorithm congested systems. Applied Mathematics and Computation 181: 440–456
Singh S. P., Singh V. K. (2010) An improved heuristic approach for multi-objective facility layout problem. International Journal of Production Research 48: 1171–1194
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, CT
Topcuoglua H., Coruta F., Ermisb M., Yilmaza G. (2005) Solving the uncapacitated hub location problem using genetic algorithms. Computers & Operations Research 32: 967–984
Vose M. D. (1991) Generalizing the notion of schema in genetic algorithms. Artificial Intelligence 50: 385–396
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: 17–34
Weber, A. (1909). Alfred Weber’s theory of the location of industries (English Translation by C. J. Friedrich). University of Chicago: Chicago University Press, 1929
Yeniay O., Ankare B. (2005) Penalty function methods for constrained optimization with genetic algorithms. Mathematical and Computational Application 10: 45–56
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pasandideh, S.H.R., Niaki, S.T.A. & Hajipour, V. A multi-objective facility location model with batch arrivals: two parameter-tuned meta-heuristic algorithms. J Intell Manuf 24, 331–348 (2013). https://doi.org/10.1007/s10845-011-0592-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-011-0592-7