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October  2016, 12(4): 1215-1225. doi: 10.3934/jimo.2016.12.1215

## Simulation and optimization of ant colony optimization algorithm for the stochastic uncapacitated location-allocation problem

 1 Business Administration Department, Gulf University for Science and Technology, Kuwait 2 Department of Engineering Management and Systems Engineering, Old Dominion University, Norfolk, VA, United States 3 Department of Civil Engineering, Lebanese American University, Byblos, Lebanon

Received  March 2014 Revised  October 2015 Published  January 2016

This study proposes a novel methodology towards using ant colony optimization ($ACO$) with stochastic demand. In particular, an optimization-simulation-optimization approach is used to solve the Stochastic uncapacitated location-allocation problem with an unknown number of facilities, and an objective of minimizing the fixed and transportation costs. $ACO$ is modeled using discrete event simulation to capture the randomness of customers' demand, and its objective is to optimize the costs. On the other hand, the simulated $ACO$'s parameters are also optimized to guarantee superior solutions. This approach's performance is evaluated by comparing its solutions to the ones obtained using deterministic data. The results show that simulation was able to identify better facility allocations where the deterministic solutions would have been inadequate due to the real randomness of customers' demands.
Citation: Jean-Paul Arnaout, Georges Arnaout, John El Khoury. Simulation and optimization of ant colony optimization algorithm for the stochastic uncapacitated location-allocation problem. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1215-1225. doi: 10.3934/jimo.2016.12.1215
##### References:
 [1] I. K. Altinel, K. C. Ozkisacik and N. Aras, Variable neighborhood search heuristics for the probabilistic multi-source weber problem,, Journal of the Operational Research Society, 62 (2011), 1813. [2] N. Aras, M. Orbay and I. K. Altinel, Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem,, Journal of the Operational Research Society, 59 (2008), 64. doi: 10.1057/palgrave.jors.2602262. [3] J-P. Arnaout, Ant Colony Optimization algorithm for the Euclidean location-allocation problem with unknown number of facilities,, Journal of Intelligent Manufacturing, 24 (2013), 45. doi: 10.1007/s10845-011-0536-2. [4] M. Bischoff , T. Fleischmann and K. Klamroth, The multi-facility location-allocation problem with polyhedral barriers,, Computers and Operations Research, 36 (2009), 1376. doi: 10.1016/j.cor.2008.02.014. [5] M. Bischoff and K. Klamroth, An efficient solution method for Weber problems with barriers based on genetic algorithms,, European Journal of Operational Research, 177 (2007), 22. doi: 10.1016/j.ejor.2005.10.061. [6] J. Brimberg, P. Hansen, N. Mladenovi and E. Taillard, Improvements and comparison of heuristics for solving the uncapacitated multisource weber problem,, Operations Research, 48 (2000), 444. doi: 10.1287/opre.48.3.444.12431. [7] M. D. H. Gamal and S. Salhi, Constructive heuristics for the uncapacitated location-allocation problem,, Journal of the Operational Research Society, 52 (2001), 821. doi: 10.1057/palgrave.jors.2601176. [8] M. Jabalameli and A. Ghaderi, Hybrid algorithms for the uncapacitated continuous location-allocation problem,, International Journal of Advanced Manufacturing Technology, 37 (2008), 202. doi: 10.1007/s00170-007-0944-9. [9] S. Krau, Extensions du Problème de Weber,, Ph.D thesis, (1996). [10] R. Kuenne and R. M. Soland, Exact and approximate solutions to the multisource Weber problem,, Mathematical Programming, 3 (1972), 193. [11] W. Liu and J. Xu, A study on facility location-allocation problem in mixed environment of randomness and fuzziness,, Journal of Intelligent Manufacturing, 22 (2011), 389. doi: 10.1007/s10845-009-0297-3. [12] R. Logendran and M. P. Terrell, Uncapacitated plant location-allocation problems with price sensitive stochasticdemands,, Computers and Operations Research, 15 (1988), 189. [13] E. Mehdizadeh, M. Tavarroth and S. Nousavi, Solving the Stochastic Capacitated Location-Allocation Problem by Using a New Hybrid Algorithm,, Proceedings of the 15th WSEAS International Conference on Applied Mathematics, (2010), 27. [14] M. Ohlemuller, Tabu search for large location-allocation problems,, Journal of the Operational Research Society, 48 (1997), 745. [15] S. H. Owen and M. S. Daskin, Strategic facility location: A review,, European Journal of Operational Research, 111 (1998), 423. doi: 10.1016/S0377-2217(98)00186-6. [16] K. C. Ozkisacik, I. K. Altinel and N. Aras, Solving probabilistic multi-facility Weber problem by vector quantization,, OR Spectrum, 31 (2009), 533. doi: 10.1007/s00291-008-0157-0. [17] S. Pasandideh and S. Niaki, Genetic application in a facility location problem with random demand within queuing framework,, Journal of Intelligent Manufacturing, (2010). [18] S. Salhi and M. D. H. Gamal, A genetic algorithm based approach for the uncapacitated continuous location-allocation problem,, Annals of Operations Research, 123 (2003), 203. doi: 10.1023/A:1026131531250. [19] E. Weiszfeld, Sur le point par lequel la somme des distances de n Points donnés est Minimum,, Tohoku Mathematical Journal, 43 (1937), 355. [20] J. Zhou and B. Liu, New stochastic models for capacitated location-allocation problem,, Computers and Industrial Engineering, 45 (2003), 111. doi: 10.1016/S0360-8352(03)00021-4. [21] J. Zhou, Uncapacitated facility layout problem with stochastic demands,, in Proceedings of the Sixth National Conferenceof Operations Research Society of China, (2000), 904.

show all references

##### References:
 [1] I. K. Altinel, K. C. Ozkisacik and N. Aras, Variable neighborhood search heuristics for the probabilistic multi-source weber problem,, Journal of the Operational Research Society, 62 (2011), 1813. [2] N. Aras, M. Orbay and I. K. Altinel, Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem,, Journal of the Operational Research Society, 59 (2008), 64. doi: 10.1057/palgrave.jors.2602262. [3] J-P. Arnaout, Ant Colony Optimization algorithm for the Euclidean location-allocation problem with unknown number of facilities,, Journal of Intelligent Manufacturing, 24 (2013), 45. doi: 10.1007/s10845-011-0536-2. [4] M. Bischoff , T. Fleischmann and K. Klamroth, The multi-facility location-allocation problem with polyhedral barriers,, Computers and Operations Research, 36 (2009), 1376. doi: 10.1016/j.cor.2008.02.014. [5] M. Bischoff and K. Klamroth, An efficient solution method for Weber problems with barriers based on genetic algorithms,, European Journal of Operational Research, 177 (2007), 22. doi: 10.1016/j.ejor.2005.10.061. [6] J. Brimberg, P. Hansen, N. Mladenovi and E. Taillard, Improvements and comparison of heuristics for solving the uncapacitated multisource weber problem,, Operations Research, 48 (2000), 444. doi: 10.1287/opre.48.3.444.12431. [7] M. D. H. Gamal and S. Salhi, Constructive heuristics for the uncapacitated location-allocation problem,, Journal of the Operational Research Society, 52 (2001), 821. doi: 10.1057/palgrave.jors.2601176. [8] M. Jabalameli and A. Ghaderi, Hybrid algorithms for the uncapacitated continuous location-allocation problem,, International Journal of Advanced Manufacturing Technology, 37 (2008), 202. doi: 10.1007/s00170-007-0944-9. [9] S. Krau, Extensions du Problème de Weber,, Ph.D thesis, (1996). [10] R. Kuenne and R. M. Soland, Exact and approximate solutions to the multisource Weber problem,, Mathematical Programming, 3 (1972), 193. [11] W. Liu and J. Xu, A study on facility location-allocation problem in mixed environment of randomness and fuzziness,, Journal of Intelligent Manufacturing, 22 (2011), 389. doi: 10.1007/s10845-009-0297-3. [12] R. Logendran and M. P. Terrell, Uncapacitated plant location-allocation problems with price sensitive stochasticdemands,, Computers and Operations Research, 15 (1988), 189. [13] E. Mehdizadeh, M. Tavarroth and S. Nousavi, Solving the Stochastic Capacitated Location-Allocation Problem by Using a New Hybrid Algorithm,, Proceedings of the 15th WSEAS International Conference on Applied Mathematics, (2010), 27. [14] M. Ohlemuller, Tabu search for large location-allocation problems,, Journal of the Operational Research Society, 48 (1997), 745. [15] S. H. Owen and M. S. Daskin, Strategic facility location: A review,, European Journal of Operational Research, 111 (1998), 423. doi: 10.1016/S0377-2217(98)00186-6. [16] K. C. Ozkisacik, I. K. Altinel and N. Aras, Solving probabilistic multi-facility Weber problem by vector quantization,, OR Spectrum, 31 (2009), 533. doi: 10.1007/s00291-008-0157-0. [17] S. Pasandideh and S. Niaki, Genetic application in a facility location problem with random demand within queuing framework,, Journal of Intelligent Manufacturing, (2010). [18] S. Salhi and M. D. H. Gamal, A genetic algorithm based approach for the uncapacitated continuous location-allocation problem,, Annals of Operations Research, 123 (2003), 203. doi: 10.1023/A:1026131531250. [19] E. Weiszfeld, Sur le point par lequel la somme des distances de n Points donnés est Minimum,, Tohoku Mathematical Journal, 43 (1937), 355. [20] J. Zhou and B. Liu, New stochastic models for capacitated location-allocation problem,, Computers and Industrial Engineering, 45 (2003), 111. doi: 10.1016/S0360-8352(03)00021-4. [21] J. Zhou, Uncapacitated facility layout problem with stochastic demands,, in Proceedings of the Sixth National Conferenceof Operations Research Society of China, (2000), 904.
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