Skip to main content
SpringerLink
Log in

Optimal location with equitable loads

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and for the special cases of the problem on a tree or on a path. The complexity of the problem is analyzed, O(n) algorithms and an O(pn 3) dynamic programming algorithm are proposed for the problem on a path respectively for p=2 and p>2 facilities. Heuristic algorithms (two types of a steepest descent approach and tabu search) are proposed for its solution. Extensive computational results are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alp, O., Drezner, Z., & Erkut, E. (2003). An efficient genetic algorithm for the p-median problem. Annals of Operations Research, 122, 21–42.

    Article  Google Scholar 

  • Azar, Y., Epstein, L., Richter, Y., & Woeginger, G. (2004). All-norm approximation algorithms. Journal of Algorithms, 52, 120–133.

    Article  Google Scholar 

  • Baron, O., Berman, O., Krass, D., & Wang, Q. (2007). The equitable location problem on the plane. European Journal of Operational Research, 183, 578–590.

    Article  Google Scholar 

  • Baron, O., Berman, O., & Krass, D. (2008, accepted). Facility location with stochastic demand and constraints on waiting time. Manufacturing and Service Operations Management.

  • Beasley, J. E. (1990). OR-library—distributing test problems by electronic mail. Journal of the Operational Research Society, 41, 1069–1072. Also available at http://mscmga.ms.ic.ac.uk/jeb/orlib/pmedinfo.html.

    Article  Google Scholar 

  • Berman, O., & Larson, R. C. (1985). Optimal 2-facility network districting in the presence of queuing. Transportation Science, 19, 261–277.

    Article  Google Scholar 

  • Berman, O., & Drezner, Z. (2007). The multiple server location problem. Journal of the Operational Research Society, 58, 91–99.

    Article  Google Scholar 

  • Berman, O., Larson, R. C., & Parkan, C. (1987). The stochastic queue p-median problem. Transportation Science, 21, 207–216.

    Article  Google Scholar 

  • Chiyoshi, F., & Galvao, R. D. (2000). A statistical analysis of simulated annealing applied to the p-median problem. Annals of Operations Research, 96, 61–74.

    Article  Google Scholar 

  • Dear, R., & Drezner, Z. (2000). Applying combinatorial optimization metaheuristics to the golf scramble problem. International Transactions of Operations Research, 7, 331–347.

    Article  Google Scholar 

  • Drezner, Z. (Ed.). (1995). Facility location: a survey of applications and methods. New York: Springer.

    Google Scholar 

  • Drezner, T., & Drezner, Z. (2001). A note on applying the gravity rule to the airline hub problem. Journal of Regional Science, 41, 67–73.

    Article  Google Scholar 

  • Drezner, T., & Drezner, Z. (2006). Multiple facilities location in the plane using the gravity model. Geographical Analysis, 38, 391–406.

    Article  Google Scholar 

  • Frederickson, G. N., & Johnson, D. B. (1984). Generalized selection and ranking: sorted matrices. SIAM Journal on Computing, 13, 14–30.

    Article  Google Scholar 

  • Gallo, G., Grigoriadis, M., & Tarjan, R. E. (1989). A fast parametric network flow problem. SIAM Journal on Computing, 18, 30–55.

    Article  Google Scholar 

  • Garey, M. R., & Johnson, D. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: Freeman.

    Google Scholar 

  • Garfinkel, R. S., & Nemhauser, G. L. (1970). Optimal political districting by implicit enumeration techniques. Management Science, 16(8), B-495–B-508.

    Article  Google Scholar 

  • Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers and Operations Research, 13, 533–549.

    Article  Google Scholar 

  • Glover, F., & Laguna, M. (1997). Tabu search. Boston: Kluwer Academic.

    Google Scholar 

  • Goldman, A. J. (1971). Optimal center location in simple networks. Transportation Science, 5, 212–221.

    Article  Google Scholar 

  • Hansen, P., & Mladenovic, N. (1997). Variable neighborhood search for the p-median. Location Science, 5, 207–226.

    Article  Google Scholar 

  • Hess, S., Weaver, J., Siegfeldt, H., Whelan, J., & Zitlau, P. (1965). Non-partisan political redistricting by computer. Operations Research, 13, 993–1006.

    Article  Google Scholar 

  • Horowitz, E., & Sahni, S. (1976). Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM, 23, 317–327.

    Article  Google Scholar 

  • Kalcsics, J., Melo, T., & Nickel, S. (2002). Planning sales territories—a facility location approach. In ISOLDE IX Conference, Fredericton, New Brunswick, Canada, June 2002.

  • Kariv, O., & Hakimi, L. S. (1979). An algorithmic approach to network location problems. Part 2. The p-medians. SIAM Journal on Applied Mathematics, 37, 539–560.

    Article  Google Scholar 

  • Kirpatrick, S., Gelat, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680.

    Article  Google Scholar 

  • Lenstra, J. K., Shmoys, D. B., & Tardos, E. (1990). Approximation algorithms for scheduling unrelated machines. Mathematical Programming, 46, 259–271.

    Article  Google Scholar 

  • Meholtra, A. A., Johnson, E. L., & Nemhauser, G. L. (1998). An optimization based heuristic for political districting. Management Science, 44, 1100–1114.

    Article  Google Scholar 

  • Mirchandani, P. B., & Francis, R. L. (Eds.). (1990). Discrete location theory. New York: Wiley.

    Google Scholar 

  • Mladenovic, N., Labbe, M., & Hansen, P. (2003). Solving the p-center problem with tabu search and variable neighborhood search. Networks, 42, 48–64.

    Article  Google Scholar 

  • Mladenovic, N., Brimberg, J., Hansen, P., & Moreno-Perez, J. A. (2007). The p-median problem: a survey of metaheuristic approaches. European Journal of Operational Research, 179, 927–939.

    Article  Google Scholar 

  • Murray, A. T., & Church, R. L. (1996). Applying simulated annealing to location-planning models. Journal of Heuristics, 2, 31–53.

    Article  Google Scholar 

  • Rolland, E., Schilling, D. A., & Current, J. R. (1997). An efficient tabu search procedure for the p-median problem. European Journal of Operational Research, 96, 329–342.

    Article  Google Scholar 

  • Suzuki, A., & Drezner, Z. (2008, in press). The minimum equitable radius location problem with continuous demand. European Journal of Operational Research.

  • Teitz, M. B., & Bart, P. (1968). Heuristic methods for estimating the generalized vertex median of a weighted graph. Operations Research, 16, 955–961.

    Article  Google Scholar 

  • van Roy, T. J. (1986). A cross decomposition algorithm for capacitated facility location. Operations Research, 34, 145–163.

    Article  Google Scholar 

  • Wang, Q., Batta, R., & Rump, C. M. (2002). Algorithms for a facility location problems with stochastic customer demand and immobile servers. In O. Berman & D. Krass (Eds.), Annals of operations research : Vol. 111. Recent developments in the theory and applications of location models part II (pp. 17–34). Dordrecht: Kluwer Academic.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, ON, M5S 3E6, Canada

    Oded Berman

  2. Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner

  3. Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Arie Tamir

  4. Faculty of Business, McMaster University, Hamilton, ON, L8S 4M4, Canada

    George O. Wesolowsky

Authors
  1. Oded Berman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zvi Drezner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arie Tamir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. George O. Wesolowsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zvi Drezner.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berman, O., Drezner, Z., Tamir, A. et al. Optimal location with equitable loads. Ann Oper Res 167, 307–325 (2009). https://doi.org/10.1007/s10479-008-0339-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-008-0339-9

Keywords

Search

Navigation