Abstract
In physical distribution the location of depots and vehicle routes are interdependent problems, but they are usually treated independently. Location-routing is the study of solving locational problems such that routing considerations are taken into account. We present an iterative heuristic for the location-routing problem on the plane. For each depot the Weber problem is solved using the end-points of the routes found previously as input nodes to the Weiszfeld procedure. Although the improvements found are usually small they show that it pays not to ignore the routing aspects when solving continuous location problems. Possible research avenues in continuous location-routing will also be suggested.
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References
Brimberg, J., & Salhi, S. (2005). A continuous location-allocation problem with zone-dependent fixed costs. Annals of Operations Research, 136, 99–115.
Burness, R. C., & White, J. A. (1976). The traveling salesman location problem. Transportation Science, 10, 348–360.
Christofides, N., Mingozzi, A., & Toth, P. (1979). The vehicle routing problem. In N. Christofides, A. Mingozzi, P. Toth & C. Sandi (Eds.), Combinatorial optimization. Chichester: Wiley.
Drezner, Z., Klamroth, K., Schöbel, A., & Wesolowsky, G. (2001). The Weber problem. In Z. Drezner & H. W. Hamacher (Eds.), Facility location: applications and theory. Berlin: Springer.
Eilon, S., Watson-Gandy, C. D. T., & Christofides, N. (1971). Distribution management: mathematical modelling and practical analysis. London: Griffin.
Laporte, G. (1988). Location-routing problems. In B. L. Golden & A. A. Assad (Eds.), Vehicle routing: methods and studies. Amsterdam: Elsevier.
Laporte, G., Gendreau, M., Potvin, J.-Y., & Semet, F. (2000). Classical and modern heuristics for the vehicle routing problem. International Transactions in Operational Research, 7, 285–300.
Mladenović, N., Brimberg, J., Hansen, P., & Perez, M. (2007). The p-median problem: a survey of metaheuristic approaches. European Journal of Operational Research, 179, 927–939.
Nagy, G., & Salhi, S. (1996). A nested location-routing heuristic using route length estimation. Studies in Locational Analysis, 10, 109–127.
Nagy, G., & Salhi, S. (2007). Location-routing: issues, models and methods. European Journal of Operational Research, 177, 649–672.
Perl, J., & Daskin, M. S. (1985). A warehouse location-routing problem. Transportation Research, 19B, 381–396.
Pfeiffer, B., & Klamroth, K. (2006, to appear). A unified model for Weber problems with continuous and network distances. Computers and Operations Research.
Plastria, F. (1995). Continuous location problems. In Z. Drezner (Ed.), Facility location: a survey of applications and methods. New York: Springer.
Rand, G. K. (1976). Methodological choices in depot location studies. Operational Research Quarterly, 27, 241–249.
Salhi, S. (1987). The integration of routing into the location-allocation and vehicle fleet composition problems (PhD dissertation). Lancaster: Lancaster University.
Salhi, S. (1997). A perturbation heuristic for a class of location problems. Journal of the Operational Research Society, 48, 1233–1240.
Salhi, S., & Fraser, M. (1996). An integrated heuristic approach for the combined location vehicle fleet mix problem. Studies in Locational Analysis, 8, 3–21.
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, 150–156.
Salhi, S., & Sari, M. (1997). Models for the multi-depot vehicle fleet mix problem. European Journal of Operational Research, 103, 95–112.
Schwardt, M., & Dethloff, J. (2005). Solving a continuous location-routing problem by use of a self-organising map. International Journal of Physical Distribution & Logistics Management, 35, 390–408.
Toth, P., & Vigo, D. (2002). Models, relaxations and exact approaches for the capacitated vehicle routing problem. Discrete Applied Mathematics, 123, 487–512.
Wassan, N. A. (2006). A reactive tabu search for the vehicle routing problem. Journal of the Operational Research Society, 57, 111–116.
Weiszfeld (Vázsonyi), E. (1937). Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Mathematical Journal, 43, 355–386.
Zainuddin, Z. M., & Salhi, S. (2007). A perturbation-based heuristic for the capacitated multisource Weber problem. European Journal of Operational Research, 179, 1194–1207.
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Salhi, S., Nagy, G. Local improvement in planar facility location using vehicle routing. Ann Oper Res 167, 287–296 (2009). https://doi.org/10.1007/s10479-007-0223-z
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DOI: https://doi.org/10.1007/s10479-007-0223-z