How to cite this paper
Khosravi, S & Jokar, M. (2018). Many to many hub and spoke location routing problem based on the gravity rule.Uncertain Supply Chain Management, 6(4), 393-406.
Refrences
Ai, Y., Lu, J., & Zhang, L. (2015). The optimization model for the location of maritime emergency supplies reserve bases and the configuration of salvage vessels. Transportation Research Part E: Logistics and Transportation Review, 83(C), 170–188.
Aros-Vera, F., Marianov, V., & Mitchell, J. E. (2013). p-Hub approach for the optimal park-and-ride facility location problem. European Journal of Operational Research, 226(2), 277–285.
Azofra, M., Pérez-Labajos, C. A., Blanco, B., & Achútegui, J. J. (2007). Optimum placement of sea rescue resources. Safety Science, 45(9), 941–951.
Bruns, A., Klose, A., & Stähly, P. (2000). Restructuring of Swiss parcel delivery services. OR-Spektrum, 22(2), 285–302.
Carling, K., & Håkansson, J. (2013). A compelling argument for the gravity p-median model. European Journal of Operational Research, 226(3), 658–660.
Castillo-López, I., & López-Ospina, H. A. (2015). School Location and Capacity Modification Considering the Existence of Externalities in Students School Choice. Comput. Ind. Eng., 80(C), 284–294.
Çetiner, S., Sepil, C., & Süral, H. (2010). Hubbing and routing in postal delivery systems. Annals of Operations Research, 181(1), 109–124.
Crainic, T. G. (1999). Long-Haul Freight Transportation. In R. W. Hall (Ed.), Handbook of Transportation Science (pp. 433–491).
de Camargo, R. S., de Miranda, G., & Løkketangen, A. (2013). A new formulation and an exact approach for the many-to-many hub location-routing problem. Applied Mathematical Modelling, 37(12–13), 7465–7480.
Drezner, T., Drezner, Z., & Kalczynski, P. (2011). A cover-based competitive location model. Journal of the Operational Research Society, 62(1), 100–113.
Drezner, Tammy, & Drezner, Z. (2001). A Note on Applying the Gravity Rule to the Airline Hub Problem. Journal of Regional Science, 41(1), 67–72.
Drezner, Tammy, & Drezner, Z. (2006). Multiple Facilities Location in the Plane Using the Gravity Model. Geographical Analysis, 38(4), 391–406.
Drezner, Tammy, & Drezner, Z. (2007). The gravity p-median model. European Journal of Operational Research, 179(3), 1239–1251.
Drezner, Tammy, & Drezner, Z. (2011). The Gravity Multiple Server Location Problem. Computers and Operations Research, 38(3), 694–701.
Erdoğan, G., Cordeau, J.-F., & Laporte, G. (2010). The Attractive Traveling Salesman Problem. European Journal of Operational Research, 203(1), 59–69.
Francis, R. L., Lowe, T. J., Rayco, M. B., & Tamir, A. (2009). Aggregation error for location models: survey and analysis. Annals of Operations Research, 167(1), 171–208.
Francis, R. L., Lowe, T. J., & Tamir, A. (2000). Aggregation Error Bounds for a Class of Location Models. Operations Research, 48(2), 294–307.
Haase, K., & Müller, S. (2013). Management of school locations allowing for free school choice. Omega, 41(5), 847–855.
Hillsman, E. L., & Rhoda, R. (1978). Errors in measuring distances from populations to service centers. The Annals of Regional Science, 12(3), 74–88.
Huff, D. L. (1964). Defining and estimating a trading area. Journal of Marketing, 28(3), 34–38.
Huff, D. L. (1966). A programmed solution for approximating an optimum retail location. Land Economics, 42(3), 293–303.
Karaoglan, I., Altiparmak, F., Kara, I., & Dengiz, B. (2012). The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach. Omega, 40(4), 465–477.
khosravi, S., & Reza Akbari Jokar, M. (n.d.). Facility and hub location model based on gravity rule. Computers & Industrial Engineering.
Marianov, V., Ríos, M., & Icaza, M. J. (2008). Facility location for market capture when users rank facilities by shorter travel and waiting times. European Journal of Operational Research, 191(1), 32–44.
Nagy, G., & Salhi, S. (1998). The many-to-many location-routing problem. Top, 6(2), 261–275.
Ni, L., Wang, X. (Cara), & Zhang, D. (2016). Impacts of information technology and urbanization on less-than-truckload freight flows in China: An analysis considering spatial effects. Transportation Research Part A: Policy and Practice, 92, 12–25.
OR-LIBRARY. (n.d.). Retrieved January 30, 2017, from http://people.brunel.ac.uk/~mastjjb/jeb/info.html
Reilly, W. J. (1931). The law of retail gravitation. New York: W.J. Reilly.
Rodríguez-Martín, I., Salazar-González, J.-J., & Yaman, H. (2014). A branch-and-cut algorithm for the hub location and routing problem. Computers & Operations Research, 50, 161–174.
Serra, D., & Colomé, R. (2001). Consumer choice and optimal locations models: Formulations and heuristics. Papers in Regional Science, 80(4), 439–464.
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.
Zabihi, A., Gharakhani, M., & Afshinfar, A. (2016). A multi criteria decision-making model for selecting hub port for Iranian marine industry. Uncertain Supply Chain Management, 4(3), 195-206.
Aros-Vera, F., Marianov, V., & Mitchell, J. E. (2013). p-Hub approach for the optimal park-and-ride facility location problem. European Journal of Operational Research, 226(2), 277–285.
Azofra, M., Pérez-Labajos, C. A., Blanco, B., & Achútegui, J. J. (2007). Optimum placement of sea rescue resources. Safety Science, 45(9), 941–951.
Bruns, A., Klose, A., & Stähly, P. (2000). Restructuring of Swiss parcel delivery services. OR-Spektrum, 22(2), 285–302.
Carling, K., & Håkansson, J. (2013). A compelling argument for the gravity p-median model. European Journal of Operational Research, 226(3), 658–660.
Castillo-López, I., & López-Ospina, H. A. (2015). School Location and Capacity Modification Considering the Existence of Externalities in Students School Choice. Comput. Ind. Eng., 80(C), 284–294.
Çetiner, S., Sepil, C., & Süral, H. (2010). Hubbing and routing in postal delivery systems. Annals of Operations Research, 181(1), 109–124.
Crainic, T. G. (1999). Long-Haul Freight Transportation. In R. W. Hall (Ed.), Handbook of Transportation Science (pp. 433–491).
de Camargo, R. S., de Miranda, G., & Løkketangen, A. (2013). A new formulation and an exact approach for the many-to-many hub location-routing problem. Applied Mathematical Modelling, 37(12–13), 7465–7480.
Drezner, T., Drezner, Z., & Kalczynski, P. (2011). A cover-based competitive location model. Journal of the Operational Research Society, 62(1), 100–113.
Drezner, Tammy, & Drezner, Z. (2001). A Note on Applying the Gravity Rule to the Airline Hub Problem. Journal of Regional Science, 41(1), 67–72.
Drezner, Tammy, & Drezner, Z. (2006). Multiple Facilities Location in the Plane Using the Gravity Model. Geographical Analysis, 38(4), 391–406.
Drezner, Tammy, & Drezner, Z. (2007). The gravity p-median model. European Journal of Operational Research, 179(3), 1239–1251.
Drezner, Tammy, & Drezner, Z. (2011). The Gravity Multiple Server Location Problem. Computers and Operations Research, 38(3), 694–701.
Erdoğan, G., Cordeau, J.-F., & Laporte, G. (2010). The Attractive Traveling Salesman Problem. European Journal of Operational Research, 203(1), 59–69.
Francis, R. L., Lowe, T. J., Rayco, M. B., & Tamir, A. (2009). Aggregation error for location models: survey and analysis. Annals of Operations Research, 167(1), 171–208.
Francis, R. L., Lowe, T. J., & Tamir, A. (2000). Aggregation Error Bounds for a Class of Location Models. Operations Research, 48(2), 294–307.
Haase, K., & Müller, S. (2013). Management of school locations allowing for free school choice. Omega, 41(5), 847–855.
Hillsman, E. L., & Rhoda, R. (1978). Errors in measuring distances from populations to service centers. The Annals of Regional Science, 12(3), 74–88.
Huff, D. L. (1964). Defining and estimating a trading area. Journal of Marketing, 28(3), 34–38.
Huff, D. L. (1966). A programmed solution for approximating an optimum retail location. Land Economics, 42(3), 293–303.
Karaoglan, I., Altiparmak, F., Kara, I., & Dengiz, B. (2012). The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach. Omega, 40(4), 465–477.
khosravi, S., & Reza Akbari Jokar, M. (n.d.). Facility and hub location model based on gravity rule. Computers & Industrial Engineering.
Marianov, V., Ríos, M., & Icaza, M. J. (2008). Facility location for market capture when users rank facilities by shorter travel and waiting times. European Journal of Operational Research, 191(1), 32–44.
Nagy, G., & Salhi, S. (1998). The many-to-many location-routing problem. Top, 6(2), 261–275.
Ni, L., Wang, X. (Cara), & Zhang, D. (2016). Impacts of information technology and urbanization on less-than-truckload freight flows in China: An analysis considering spatial effects. Transportation Research Part A: Policy and Practice, 92, 12–25.
OR-LIBRARY. (n.d.). Retrieved January 30, 2017, from http://people.brunel.ac.uk/~mastjjb/jeb/info.html
Reilly, W. J. (1931). The law of retail gravitation. New York: W.J. Reilly.
Rodríguez-Martín, I., Salazar-González, J.-J., & Yaman, H. (2014). A branch-and-cut algorithm for the hub location and routing problem. Computers & Operations Research, 50, 161–174.
Serra, D., & Colomé, R. (2001). Consumer choice and optimal locations models: Formulations and heuristics. Papers in Regional Science, 80(4), 439–464.
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.
Zabihi, A., Gharakhani, M., & Afshinfar, A. (2016). A multi criteria decision-making model for selecting hub port for Iranian marine industry. Uncertain Supply Chain Management, 4(3), 195-206.