Abstract
This work considers the problem of locating \(p\) facilities on the nodes of a path such that the range of the weights assigned to facilities will be as small as possible. We present a polynomial progressive search algorithm to solve the problem.
Similar content being viewed by others
References
Balinski, M. L., & Young, H. P. (2001). Fair representation, meeting the ideal of one man, one vote (2nd ed.). Washington, DC: Brookings Institution Press.
Baron, O., Berman, O., & Krass, D. (2008). Facility location with stochastic demand and constraints on waiting time. Manufacturing and Service Operations Management, 10(3), 484–505.
Baron, O., Berman, O., Krass, D., & Wang, Q. (2007). The equitable location problem on the plane. European Journal of Operational Research, 183, 578–590.
Berman, O., Drezner, Z., Tamir, A., & Wesolowsky, G. O. (2009). Optimal location with equitable loads. Annals of Operations Research, 167, 307–325.
Cavalier, T., Conner, W., Delcastillo, E., & Brown, S. (2007). A heuristic algorithm for minimax sensor location in the plane. European Journal of Operational Research, 183(1), 42–55.
Drezner, Z., Thisse, J.-F., & Wesolowsky, G. O. (1986). The minimax-min location problem. Journal of Regional Science, 26, 87–101.
Edelman, P. H. (2006). Minimum total deviation apportionments. In B. Simeone & F. Pukelsheim (Eds.), Mathematics and democracy. Berlin: Springer.
Lucertini, M., & Simeone, B. (1993). Most uniform path partitioning its use in image processing. Discrete Applied Mathematics, 42, 227–256.
Marsh, M., & Schilling, D. (1994). Equity measurement in facility location analysis: A review and framework. European Journal of Operational Research, 74, 1–17.
Mesa, J. A., & Puerto, J. (2003). Improved algorithms for several network location problems with equality measures. Discrete Applied Mathematics, 130, 437–448.
Ogryczak, W. (2009). Inequality measures and equitable locations. Annals of Operations Research, 167(1), 61–86.
Suzuki, A., & Drezner, Z. (2009). The minimum equitable radius location problem with continuous demand. European Journal of Operational Research, 195, 17–30.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, R. A short note on locating facilities on a path to minimize load range equity measure. Ann Oper Res 246, 363–369 (2016). https://doi.org/10.1007/s10479-014-1617-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-014-1617-3