Abstract
This paper is concerned with the upgrading selective obnoxious p-median location problem on tree networks in which the existing customer points and the candidate facility locations are assumed to be two selective subsets of the vertex set of the underlying tree. The task is to augment the edge lengths within associated bounds and a budget constraint on the overall modification cost so that the optimal selective obnoxious p-median objective value is maximized under the new edge lengths. Exact optimal algorithms with polynomial time complexities are developed for cases \(p=1 \) and \(p\ge 2\). Moreover, it is shown that if the bound constraints are dropped, then the problems under investigation can be solved in lower times.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alizadeh, B., Afrashteh, E., & Baroughi, F. (2018). Combinatorial algorithms for some variants of inverse obnoxious \( p \)-median location problem on tree networks. Journal of Optimization Theory and Applications, 178, 914–934.
Alizadeh, B., Afrashteh, E., & Baroughi, F. (2019). Inverse obnoxious \( p \)-median location problems on trees with edge length modifications under different norms. Theoretical Computer Science, 772, 73–87.
Alizadeh, B., & Burkard, R. E. (2013). A linear time algorithm for inverse obnoxious center location problems on networks. Central European Journal of Operations Research, 21, 585–594.
Alizadeh, B., Burkard, R. E., & Pferschy, U. (2009). Inverse 1-center location problems with edge length augmentation on trees. Computing, 86, 331–343.
Alizadeh, B., & Etemad, R. (2016). Linear time optimal approaches for reverse obnoxious center location problems on networks. Optimization, 65, 2025–2036.
Alizadeh, B., & Etemad, R. (2018). Optimal algorithms for inverse vertex obnoxious center location problems on graphs. Theoretical Computer Science, 707, 36–45.
Balas, E., & Zemel, E. (1980). An algorithm for large zero-one knapsack problems. Operations Research, 28, 1130–1154.
Burkard, R. E., Fathali, J., & Kakhki, H. T. (2007). The \( p \)-maxian problem on a tree. Operations Research Letters, 35, 331–335.
Burkard, R. E., Lin, Y., & Zhang, J. (2004). Weight reduction problems with certain bottleneck objectives. European Journal of Operational Research, 153, 191–199.
Cappanera, P., Gallo, G., & Maffioli, F. (2003). Discrete facility location and routing of obnoxious activities. Discrete Applied Mathematics, 133, 3–28.
Chepoi, V., Noltemeier, H., & Vaxes, Y. (2003). Upgrading trees under diameter and budget constraints. Networks, 41, 24–35.
Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2001). Introduction to Algorithms (2nd ed.). Cambridge: MIT Press.
Drangmeister, K. U., Krumke, S. O., Marathe, M. V., Noltemeier, H., & Ravi, S. S. (1998). Modifying edges of a network to obtain short subgraphs. Theoretical Computer Science, 203, 91–121.
Etemad, R., & Alizadeh, B. (2017). Combinatorial algorithms for reverse selective undesirable center location problems on cycle graphs. Journal of the Operations Research Society of China, 5, 347–361.
Etemad, R., & Alizadeh, B. (2018). Reverse selective obnoxious center location problems on tree graphs. Mathematical Methods of Operations Research, 87, 431–450.
Frederickson, G. N., & Solis-Oba, R. (1999). Increasing the weight of minimum spanning trees. Journal of Algorithms, 33, 244–266.
Fulkerson, D. R., & Harding, G. C. (1977). Maximizing the minimum source–sink path subject to a budget constraint. Mathematical Programming, 13, 116–118.
Gassner, E. (2007). Up- and downgrading the 1-median in a network, Technical report 2007–2016, Graz University of Technology
Gassner, E. (2008a). The inverse 1-maxian problem with edge length modification. Journal of Combinatorial Optimization, 16, 50–67.
Gassner, E. (2008b). Up- and downgrading the 1-center in a network. European Journal of Operational Research, 198, 370–377.
Gassner, E. (2009). A game-theoretic approach for downgrading the 1-median in the plane with Manhattan metric. Annals of Operations Research, 172, 393–404.
Goldman, A. J. (1971). Optimal center location in simple networks. Transportation Science, 5, 212–221.
Hambrusch, S. E., & Tu, H. Y. (1997). Edge weight reduction problems in directed acyclic graphs. Journal of Algorithms, 24, 66–93.
Handler, G. Y. (1973). Minimax location of a facility in an undirected tree graph. Transportation Science, 7, 287–293.
Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack Problems. Berlin: Springer.
Krumke, S. O., Marathe, M. V., Noltemeier, H., Ravi, R., & Ravi, S. S. (1998). Approximation algorithms for certain network improvement problems. Journal of Combinatorial Optimization, 2, 257–288.
Nguyen, K. T., & Vui, P. T. (2016). The invere \( p \)-maxian problem on trees with variable edge lengths. Taiwanese Journal of Mathematics, 20, 1437–1449.
Plastria, F. (1996). Optimal location of undesirable facilities: A selective overview. Belgian Journal of Operations Research, Statistics and Computer Science, 36, 109–127.
Plastria, F. (2016). Up- and downgrading the euclidean 1-median problem and knapsack Voronoi diagrams. Annals of Operations Research, 246, 227–251.
Sepasian, A. R. (2018). Upgrading the 1-center problem with edge length variables on a tree. Discrete Optimization, 29, 1–17.
Sepasian, A. R., & Rahbarnia, F. (2015). Upgrading \( p \)-median problem on a path. Journal of Mathematical Modelling and Algorithms, 14, 145–157.
Ting, S. S. (1984). A linear time algorithm for maxisum facility location on tree networks. Transportation Science, 18, 76–84.
Zanjirani, R., & Hekmatfar, M. (2009). Facility Location: Concepts, Models, Algorithms and Case Studies. Berlin: Physica-Verlag.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Afrashteh, E., Alizadeh, B. & Baroughi, F. Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks. Ann Oper Res 289, 153–172 (2020). https://doi.org/10.1007/s10479-020-03561-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-020-03561-4