How to cite this paper
Hadian, H., Golmohammadi, A., Hemmati, A & Mashkani, O. (2019). A multi-depot location routing problem to reduce the differences between the vehicles’ traveled distances; a comparative study of heuristics.Uncertain Supply Chain Management, 7(1), 17-32.
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References
Ahn, J., de Weck, O., Geng, Y., & Klabjan, D. (2012). Column generation based heuristics for a generalized location routing problem with profits arising in space exploration. European Journal of Operational Research, 223(1), 47-59.
Atashpaz-Gargari, E., & Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. Paper presented at the Evolutionary computation, 2007. CEC 2007. IEEE Congress on.
Balakrishnan, A., Ward, J. E., & Wong, R. T. (1987). Integrated facility location and vehicle routing models: Recent work and future prospects. American Journal of Mathematical and Management Sciences, 7(1-2), 35-61.
Boventer, E. (1961). The relationship between transportation costs and location rent in transportation problems. Journal of Regional Science, 3(2), 27-40.
C Montgomery, D. (1997). Montgomery Design and Analysis of Experiments.
Caballero, R., González, M., Guerrero, F. M., Molina, J., & Paralera, C. (2007). Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia. European Journal of Operational Research, 177(3), 1751-1763.
Çetiner, S., Sepil, C., & Süral, H. (2010). Hubbing and routing in postal delivery systems. Annals of Operations Research, 181(1), 109-124.
Christofides, N., & Eilon, S. (1969). An algorithm for the vehicle-dispatching problem. Or, 309-318.
Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science, 1917, 849-858.
Deb, K., & Pratap, A. (2002). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II.
Diabat, A. (2014). Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain. European Journal of Operational Research, 238(1), 114-121.
Drexl, M., & Schneider, M. (2015). A survey of variants and extensions of the location-routing problem. European Journal of Operational Research, 241(2), 283-308. doi: 10.1016/j.ejor.2014.08.030
Fakhrzada, M., & Esfahanib, A. S. (2013). Modeling the time windows vehicle routing problem in cross-docking strategy using two meta-heuristic algorithms. International Journal of Engineering-Transactions A: Basics, 27(7), 1113.
Goścień, R., Walkowiak, K., & Klinkowski, M. (2015). Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic. Computer Networks, 79, 148-165. doi: 10.1016/j.comnet.2014.12.004
Govindan, K., Jafarian, A., Khodaverdi, R., & Devika, K. (2014). Two-echelon multiple-vehicle location–routing problem with time windows for optimization of sustainable supply chain network of perishable food. International Journal of Production Economics, 152, 9-28. doi: 10.1016/j.ijpe.2013.12.028
Gu, J., Goetschalckx, M., & McGinnis, L. F. (2007). Research on warehouse operation: A comprehensive review. European Journal of Operational Research, 177(1), 1-21. doi: 10.1016/j.ejor.2006.02.025
Jula, A., Othman, Z., & Sundararajan, E. (2015). Imperialist competitive algorithm with PROCLUS classifier for service time optimization in cloud computing service composition. Expert Systems with Applications, 42(1), 135-145. doi: 10.1016/j.eswa.2014.07.043
Karakatič, S., & Podgorelec, V. (2015). A survey of genetic algorithms for solving multi depot vehicle routing problem. Applied Soft Computing, 27, 519-532. doi: 10.1016/j.asoc.2014.11.005
Koç, Ç., Bektaş, T., Jabali, O., & Laporte, G. (2015). A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows. Computers & Operations Research, 64, 11-27. doi: 10.1016/j.cor.2015.05.004
Kopfer, H., Schwardt, M., & Dethloff, J. (2005). Solving a continuous location‐routing problem by use of a self‐organizing map. International Journal of Physical Distribution & Logistics Management, 35(6), 390-408. doi: 10.1108/09600030510611639
Maranzana, F. (1964). On the location of supply points to minimize transport costs. OR, 261-270.
Marinakis, Y., Iordanidou, G.-R., & Marinaki, M. (2013). Particle Swarm Optimization for the Vehicle Routing Problem with Stochastic Demands. Applied Soft Computing, 13(4), 1693-1704. doi: 10.1016/j.asoc.2013.01.007
Martínez-Salazar, I. A., Molina, J., Ángel-Bello, F., Gómez, T., & Caballero, R. (2014). Solving a bi-objective Transportation Location Routing Problem by metaheuristic algorithms. European Journal of Operational Research, 234(1), 25-36. doi: 10.1016/j.ejor.2013.09.008
Megiddo, N., & Supowit, K. J. (1984). On the complexity of some common geometric location problems. SIAM journal on computing, 13(1), 182-196.
Min, H., Jayaraman, V., & Srivastava, R. (1998). Combined location-routing problems: A synthesis and future research directions. European journal of operational research, 108(1), 1-15.
Mohammadi-Ivatloo, B., Rabiee, A., Soroudi, A., & Ehsan, M. (2012). Imperialist competitive algorithm for solving non-convex dynamic economic power dispatch. Energy, 44(1), 228-240.
Mohammadkhanloo, M., & Bashiri, M. (2013). A clustering based location-allocation problem considering transportation costs and statistical properties (research note). International Journal of Engineering-Transactions C: Aspects, 26(6), 597.
Moradi, H., Zandieh, M., & Mahdavi, I. (2011). Non-dominated ranked genetic algorithm for a multi-objective mixed-model assembly line sequencing problem. International Journal of Production Research, 49(12), 3479-3499.
Nagy, G., & Salhi, S. (2007). Location-routing: Issues, models and methods. European Journal of Operational Research, 177(2), 649-672. doi: 10.1016/j.ejor.2006.04.004
Nazari-Shirkouhi, S., Eivazy, H., Ghodsi, R., Rezaie, K., & Atashpaz-Gargari, E. (2010). Solving the integrated product mix-outsourcing problem using the Imperialist Competitive Algorithm. Expert Systems with Applications, 37(12), 7615-7626. doi: 10.1016/j.eswa.2010.04.081
Norouzi, N., Sadegh-Amalnick, M., & Alinaghiyan, M. (2015). Evaluating of the particle swarm optimization in a periodic vehicle routing problem. Measurement, 62, 162-169. doi: 10.1016/j.measurement.2014.10.024
Or, I., & Pierskalla, W. P. (1979). A transportation location-allocation model for regional blood banking. AIIE transactions, 11(2), 86-95.
Prodhon, C. (2011). A hybrid evolutionary algorithm for the periodic location-routing problem. European Journal of Operational Research, 210(2), 204-212. doi: 10.1016/j.ejor.2010.09.021
Prodhon, C., & Prins, C. (2014). A survey of recent research on location-routing problems. European Journal of Operational Research, 238(1), 1-17. doi: 10.1016/j.ejor.2014.01.005
Roozbeh Nia, A., Hemmati Far, M., & Niaki, S. T. A. (2015). A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage. Applied Soft Computing, 30, 353-364. doi: 10.1016/j.asoc.2015.02.004
Salhi, S., & Nagy, G. (1999). Consistency and robustness in location-routing. Studies in Locational Analysis(13), 3-19.
Salhi, S., & Rand, G. K. (1989). The effect of ignoring routes when locating depots. European journal of operational research, 39(2), 150-156.
Schwardt, M., & Fischer, K. (2008). Combined location-routing problems—a neural network approach. Annals of Operations Research, 167(1), 253-269. doi: 10.1007/s10479-008-0377-3
Setak, M., Jalili Bolhassani, S., & Karimi, H. (2014). A node-based mathematical model towards the location routing problem with intermediate replenishment facilities under capacity constraint. International Journal of Engineering, 27(6), 911-920.
Shiripour, S., Mahdavi, I., Amiri-Aref, M., Mohammadnia-Otaghsara, M., & Mahdavi-Amiri, N. (2012). Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model. International Journal of Production Research, 50(15), 3988-4008. doi: 10.1080/00207543.2011.579639
Sim, K. M., & Sun, W. H. (2003). Ant colony optimization for routing and load-balancing: survey and new directions. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 33(5), 560-572.
Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation, 2(3), 221-248.
Tavakkoli-Moghaddam, R., Makui, A., & Mazloomi, Z. (2010). A new integrated mathematical model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm. Journal of Manufacturing Systems, 29(2-3), 111-119. doi: 10.1016/j.jmsy.2010.11.005
Ting, C.-J., & Chen, C.-H. (2013). A multiple ant colony optimization algorithm for the capacitated location routing problem. International Journal of Production Economics, 141(1), 34-44.
Wang, H., Du, L., & Ma, S. (2014). Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake. Transportation Research Part E: Logistics and Transportation Review, 69, 160-179. doi: http://dx.doi.org/10.1016/j.tre.2014.06.006
Wasner, M., & Zäpfel, G. (2004). An integrated multi-depot hub-location vehicle routing model for network planning of parcel service. International Journal of Production Economics, 90(3), 403-419.
Watson-Gandy, C., & Dohrn, P. (1973). Depot location with van salesmen—a practical approach. Omega, 1(3), 321-329.
Webb, M. (1968). Cost functions in the location of depots for multiple-delivery journeys. OR, 311-320.
Yu, V. F., & Lin, S.-Y. (2015). A simulated annealing heuristic for the open location-routing problem. Computers & Operations Research, 62, 184-196. doi: 10.1016/j.cor.2014.10.009
Zandieh, M., Dorri, B., & Khamseh, A. (2009). Robust metaheuristics for group scheduling with sequence-dependent setup times in hybrid flexible flow shops. The International Journal of Advanced Manufacturing Technology, 43(7-8), 767.
Zarandi, M. H. F., Hemmati, A., & Davari, S. (2011). The multi-depot capacitated location-routing problem with fuzzy travel times. Expert Systems with Applications, 38(8), 10075-10084.
Ahn, J., de Weck, O., Geng, Y., & Klabjan, D. (2012). Column generation based heuristics for a generalized location routing problem with profits arising in space exploration. European Journal of Operational Research, 223(1), 47-59.
Atashpaz-Gargari, E., & Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. Paper presented at the Evolutionary computation, 2007. CEC 2007. IEEE Congress on.
Balakrishnan, A., Ward, J. E., & Wong, R. T. (1987). Integrated facility location and vehicle routing models: Recent work and future prospects. American Journal of Mathematical and Management Sciences, 7(1-2), 35-61.
Boventer, E. (1961). The relationship between transportation costs and location rent in transportation problems. Journal of Regional Science, 3(2), 27-40.
C Montgomery, D. (1997). Montgomery Design and Analysis of Experiments.
Caballero, R., González, M., Guerrero, F. M., Molina, J., & Paralera, C. (2007). Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia. European Journal of Operational Research, 177(3), 1751-1763.
Çetiner, S., Sepil, C., & Süral, H. (2010). Hubbing and routing in postal delivery systems. Annals of Operations Research, 181(1), 109-124.
Christofides, N., & Eilon, S. (1969). An algorithm for the vehicle-dispatching problem. Or, 309-318.
Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science, 1917, 849-858.
Deb, K., & Pratap, A. (2002). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II.
Diabat, A. (2014). Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain. European Journal of Operational Research, 238(1), 114-121.
Drexl, M., & Schneider, M. (2015). A survey of variants and extensions of the location-routing problem. European Journal of Operational Research, 241(2), 283-308. doi: 10.1016/j.ejor.2014.08.030
Fakhrzada, M., & Esfahanib, A. S. (2013). Modeling the time windows vehicle routing problem in cross-docking strategy using two meta-heuristic algorithms. International Journal of Engineering-Transactions A: Basics, 27(7), 1113.
Goścień, R., Walkowiak, K., & Klinkowski, M. (2015). Tabu search algorithm for routing, modulation and spectrum allocation in elastic optical network with anycast and unicast traffic. Computer Networks, 79, 148-165. doi: 10.1016/j.comnet.2014.12.004
Govindan, K., Jafarian, A., Khodaverdi, R., & Devika, K. (2014). Two-echelon multiple-vehicle location–routing problem with time windows for optimization of sustainable supply chain network of perishable food. International Journal of Production Economics, 152, 9-28. doi: 10.1016/j.ijpe.2013.12.028
Gu, J., Goetschalckx, M., & McGinnis, L. F. (2007). Research on warehouse operation: A comprehensive review. European Journal of Operational Research, 177(1), 1-21. doi: 10.1016/j.ejor.2006.02.025
Jula, A., Othman, Z., & Sundararajan, E. (2015). Imperialist competitive algorithm with PROCLUS classifier for service time optimization in cloud computing service composition. Expert Systems with Applications, 42(1), 135-145. doi: 10.1016/j.eswa.2014.07.043
Karakatič, S., & Podgorelec, V. (2015). A survey of genetic algorithms for solving multi depot vehicle routing problem. Applied Soft Computing, 27, 519-532. doi: 10.1016/j.asoc.2014.11.005
Koç, Ç., Bektaş, T., Jabali, O., & Laporte, G. (2015). A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows. Computers & Operations Research, 64, 11-27. doi: 10.1016/j.cor.2015.05.004
Kopfer, H., Schwardt, M., & Dethloff, J. (2005). Solving a continuous location‐routing problem by use of a self‐organizing map. International Journal of Physical Distribution & Logistics Management, 35(6), 390-408. doi: 10.1108/09600030510611639
Maranzana, F. (1964). On the location of supply points to minimize transport costs. OR, 261-270.
Marinakis, Y., Iordanidou, G.-R., & Marinaki, M. (2013). Particle Swarm Optimization for the Vehicle Routing Problem with Stochastic Demands. Applied Soft Computing, 13(4), 1693-1704. doi: 10.1016/j.asoc.2013.01.007
Martínez-Salazar, I. A., Molina, J., Ángel-Bello, F., Gómez, T., & Caballero, R. (2014). Solving a bi-objective Transportation Location Routing Problem by metaheuristic algorithms. European Journal of Operational Research, 234(1), 25-36. doi: 10.1016/j.ejor.2013.09.008
Megiddo, N., & Supowit, K. J. (1984). On the complexity of some common geometric location problems. SIAM journal on computing, 13(1), 182-196.
Min, H., Jayaraman, V., & Srivastava, R. (1998). Combined location-routing problems: A synthesis and future research directions. European journal of operational research, 108(1), 1-15.
Mohammadi-Ivatloo, B., Rabiee, A., Soroudi, A., & Ehsan, M. (2012). Imperialist competitive algorithm for solving non-convex dynamic economic power dispatch. Energy, 44(1), 228-240.
Mohammadkhanloo, M., & Bashiri, M. (2013). A clustering based location-allocation problem considering transportation costs and statistical properties (research note). International Journal of Engineering-Transactions C: Aspects, 26(6), 597.
Moradi, H., Zandieh, M., & Mahdavi, I. (2011). Non-dominated ranked genetic algorithm for a multi-objective mixed-model assembly line sequencing problem. International Journal of Production Research, 49(12), 3479-3499.
Nagy, G., & Salhi, S. (2007). Location-routing: Issues, models and methods. European Journal of Operational Research, 177(2), 649-672. doi: 10.1016/j.ejor.2006.04.004
Nazari-Shirkouhi, S., Eivazy, H., Ghodsi, R., Rezaie, K., & Atashpaz-Gargari, E. (2010). Solving the integrated product mix-outsourcing problem using the Imperialist Competitive Algorithm. Expert Systems with Applications, 37(12), 7615-7626. doi: 10.1016/j.eswa.2010.04.081
Norouzi, N., Sadegh-Amalnick, M., & Alinaghiyan, M. (2015). Evaluating of the particle swarm optimization in a periodic vehicle routing problem. Measurement, 62, 162-169. doi: 10.1016/j.measurement.2014.10.024
Or, I., & Pierskalla, W. P. (1979). A transportation location-allocation model for regional blood banking. AIIE transactions, 11(2), 86-95.
Prodhon, C. (2011). A hybrid evolutionary algorithm for the periodic location-routing problem. European Journal of Operational Research, 210(2), 204-212. doi: 10.1016/j.ejor.2010.09.021
Prodhon, C., & Prins, C. (2014). A survey of recent research on location-routing problems. European Journal of Operational Research, 238(1), 1-17. doi: 10.1016/j.ejor.2014.01.005
Roozbeh Nia, A., Hemmati Far, M., & Niaki, S. T. A. (2015). A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage. Applied Soft Computing, 30, 353-364. doi: 10.1016/j.asoc.2015.02.004
Salhi, S., & Nagy, G. (1999). Consistency and robustness in location-routing. Studies in Locational Analysis(13), 3-19.
Salhi, S., & Rand, G. K. (1989). The effect of ignoring routes when locating depots. European journal of operational research, 39(2), 150-156.
Schwardt, M., & Fischer, K. (2008). Combined location-routing problems—a neural network approach. Annals of Operations Research, 167(1), 253-269. doi: 10.1007/s10479-008-0377-3
Setak, M., Jalili Bolhassani, S., & Karimi, H. (2014). A node-based mathematical model towards the location routing problem with intermediate replenishment facilities under capacity constraint. International Journal of Engineering, 27(6), 911-920.
Shiripour, S., Mahdavi, I., Amiri-Aref, M., Mohammadnia-Otaghsara, M., & Mahdavi-Amiri, N. (2012). Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model. International Journal of Production Research, 50(15), 3988-4008. doi: 10.1080/00207543.2011.579639
Sim, K. M., & Sun, W. H. (2003). Ant colony optimization for routing and load-balancing: survey and new directions. Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 33(5), 560-572.
Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation, 2(3), 221-248.
Tavakkoli-Moghaddam, R., Makui, A., & Mazloomi, Z. (2010). A new integrated mathematical model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm. Journal of Manufacturing Systems, 29(2-3), 111-119. doi: 10.1016/j.jmsy.2010.11.005
Ting, C.-J., & Chen, C.-H. (2013). A multiple ant colony optimization algorithm for the capacitated location routing problem. International Journal of Production Economics, 141(1), 34-44.
Wang, H., Du, L., & Ma, S. (2014). Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake. Transportation Research Part E: Logistics and Transportation Review, 69, 160-179. doi: http://dx.doi.org/10.1016/j.tre.2014.06.006
Wasner, M., & Zäpfel, G. (2004). An integrated multi-depot hub-location vehicle routing model for network planning of parcel service. International Journal of Production Economics, 90(3), 403-419.
Watson-Gandy, C., & Dohrn, P. (1973). Depot location with van salesmen—a practical approach. Omega, 1(3), 321-329.
Webb, M. (1968). Cost functions in the location of depots for multiple-delivery journeys. OR, 311-320.
Yu, V. F., & Lin, S.-Y. (2015). A simulated annealing heuristic for the open location-routing problem. Computers & Operations Research, 62, 184-196. doi: 10.1016/j.cor.2014.10.009
Zandieh, M., Dorri, B., & Khamseh, A. (2009). Robust metaheuristics for group scheduling with sequence-dependent setup times in hybrid flexible flow shops. The International Journal of Advanced Manufacturing Technology, 43(7-8), 767.
Zarandi, M. H. F., Hemmati, A., & Davari, S. (2011). The multi-depot capacitated location-routing problem with fuzzy travel times. Expert Systems with Applications, 38(8), 10075-10084.