Skip to main content
SpringerLink
Log in

Balancing the arrival times of users in a two-stage location problem

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

Abstract

There has been a number of facility location problems dealing with the introduction of the equity issue in the travel distances distribution. In this paper we analyze a new aspect of equity concerning the distribution of the arrival times of customers. Given a depot and a set of demand points generating flow which also represent potential locations, we consider a discrete two-stage location problem whose aim is to locate a given number of facilities and to allocate the demand points to a facility. We assume as objective the maximization of the minimum difference between two consecutive arrival times of flows to the depot through the patronized facility. This particular equity measure is introduced in order to reduce risks of congestion in the dynamic of flow arrivals at the common destination. The problem is described through two Integer Programming formulations. Computational results for solution methods based on both formulations are then shown and analyzed.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Baron, O., Berman, O., & Krass, D. (2008). Facility location with stochastic demand and constraints on waiting time. Manufacturing & Service Operations Management, 10(3), 484–505.

    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(2), 578–590.

    Article  Google Scholar 

  • Batta, R., Lejeune, M., & Prasad, S. (2014). Public facility location using dispersion, population, and equity criteria. European Journal of Operational Research, 234(3), 819–829.

    Article  Google Scholar 

  • Berman, O., Drezner, Z., Tamir, A., & Wesolowsky, G. O. (2009). Optimal location with equitable loads. Annals of Operations Research, 167(1), 307–325.

    Article  Google Scholar 

  • Berman, O., Drezner, Z., & Wesolowsky, G. O. (2002). The collection depots location problem on networks. Naval Research Logistics, 49(1), 15–24.

    Article  Google Scholar 

  • Berman, O., & Huang, R. (2004). Minisum collection depots location problem with multiple facilities on a network. Journal of the Operational Research Society, 55(7), 769–779.

    Article  Google Scholar 

  • Berman, O., & Huang, R. (2008). The minimum weighted covering location problem with distance constraints. Computers & Operations Research, 35(2), 356–372.

    Article  Google Scholar 

  • Berman, O., & Kaplan, E. H. (1990). Equity maximizing facility location schemes. Transportation Science, 24(2), 137–144.

    Article  Google Scholar 

  • Burkey, M. L., Bhadury, J., & Eiselt, H. A. (2012). A location-based comparison of health care services in four U.S. states with efficiency and equity. Socio-Economic Planning Sciences, 46(2), 157–163.

    Article  Google Scholar 

  • Drezner, T. (2004). Location of casualty collection points. Environment and Planning C: Government and Policy, 22(6), 899–912.

    Article  Google Scholar 

  • Drezner, T., & Drezner, Z. (2006). Multiple facilities location in the plane using the gravity model. Geographical Analysis, 38(4), 391–406.

    Article  Google Scholar 

  • Drezner, T., Drezner, Z., & Guyse, J. (2009). Equitable service by a facility: Minimizing the Gini coefficient. Computers & Operations Research, 36(12), 3240–3246.

    Article  Google Scholar 

  • Drezner, T., Drezner, Z., & Salhi, S. (2006). A multi-objective heuristic approach for the casualty collection points location problem. Journal of the Operational Research Society, 57(6), 727–734.

    Article  Google Scholar 

  • Drezner, Z., & Wesolowsky, G. O. (2001). On the collection depots location problem. European Journal of Operational Research, 130(3), 510–518.

    Article  Google Scholar 

  • Eiselt, H. A., & Laporte, G. (1995). Objectives in location problems. In Z. Drezner (Ed.), Facility location: A survey of applications and methods (pp. 151–180). New York: Springer.

    Chapter  Google Scholar 

  • Erkut, E. (1993). Inequality measures for location problems. Location Science, 1(3), 199–217.

    Google Scholar 

  • Espejo, I., Marín, A., Puerto, J., & Rodríguez-Chía, A. M. (2009). A comparison of formulations and solution methods for the minimum-envy location problem. Computers & Operations Research, 36(6), 1966–1981.

    Article  Google Scholar 

  • Espejo, I., Marín, A., & Rodríguez-Chía, A. M. (2012). Closest assignment constraints in discrete location problems. European Journal of Operational Research, 219(1), 49–58.

    Article  Google Scholar 

  • Galvão, R. D., Acosta Espejo, L. G., Boffey, B., & Yates, D. (2006). Load balancing and capacity constraints in a hierarchical location model. European Journal of Operational Research, 172(2), 631–646.

    Article  Google Scholar 

  • García, S., Labbé, M., & Marín, A. (2011). Solving large \(p\)-median problems with a radius formulation. INFORMS Journal on Computing, 23(4), 546–556.

    Article  Google Scholar 

  • López-de-los-Mozos, M. C., & Mesa, J. A. (2001). The maximum absolute deviation measure in location problems on networks. European Journal of Operational Research, 135(1), 184–194.

    Article  Google Scholar 

  • López-de-los-Mozos, M. C., Mesa, J. A., & Puerto, J. (2008). A generalized model of equality measures in network location problems. Computers & Operations Research, 35(3), 651–660.

    Article  Google Scholar 

  • Maimon, O. (1986). The variance equity measure in locational decision theory. Annals of Operations Research, 6(5), 147–160.

    Article  Google Scholar 

  • Maimon, O. (1988). An algorithm for the Lorenz measure in locational decisions on trees. Journal of Algorithms, 9(4), 583–596.

    Article  Google Scholar 

  • Marín, A. (2011). The discrete facility location problem with balanced allocation of customers. European Journal of Operational Research, 210(1), 27–38.

    Article  Google Scholar 

  • Marín, A., Nickel, S., Puerto, J., & Velten, S. (2009). A flexible model and efficient solution strategies for discrete location problems. Discrete Applied Mathematics, 157(5), 1128–1145.

    Article  Google Scholar 

  • Marín, A., Nickel, S., & Velten, S. (2010). An extended covering model for flexible discrete and equity location problems. Mathematical Methods of Operations Research, 71(1), 125–163.

    Article  Google Scholar 

  • Marsh, M. T., & Schilling, D. A. (1994). Equity measurement in facility location analysis: A review and framework. European Journal of Operational Research, 74(1), 1–17.

    Article  Google Scholar 

  • McAllister, D. M. (1976). Equity and efficiency in public facility location. Geographical Analysis, 8(1), 47–63.

    Article  Google Scholar 

  • Mesa, J. A., Puerto, J., & Tamir, A. (2003). Improved algorithms for several network location problems with equality measures. Discrete Applied Mathematics, 130(3), 437–448.

    Article  Google Scholar 

  • Ohsawa, Y., Ozaki, N., & Plastria, F. (2008). Equity-efficiency bicriteria location with squared Euclidean distances. Operations Research, 56(1), 79–87.

    Article  Google Scholar 

  • Prokopyev, O. A., Kong, N., & Martínez-Torres, D. L. (2009). The equitable dispersion problem. European Journal of Operational Research, 197(1), 59–67.

    Article  Google Scholar 

  • Tamir, A., & Halman, N. (2005). One-way and round-trip center location problems. Discrete Optimization, 2(2), 168–184.

    Article  Google Scholar 

Download references

Acknowledgments

Alfredo Marín acknowledges that research reported here was partially supported by Ministerio de Economía y Competitividad, Project MTM2012-36163-C06-04, and Fundación Séneca Project 08716/PI/08.

Author information

Authors and Affiliations

  1. Centre of Operations Research and Logistics, Portsmouth Business School, University of Portsmouth, Richmond Building, Portland Street, Portsmouth, PO1 3DE, UK

    Maria Barbati

  2. Department of Industrial Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 , Naples, Italy

    Giuseppe Bruno

  3. Departamento de Estadística e Investigación Operativa, Universidad de Murcia, Campus de Espinardo, 30071 , Murcia, Spain

    Alfredo Marín

Authors
  1. Maria Barbati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giuseppe Bruno
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alfredo Marín
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria Barbati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barbati, M., Bruno, G. & Marín, A. Balancing the arrival times of users in a two-stage location problem. Ann Oper Res 246, 273–288 (2016). https://doi.org/10.1007/s10479-015-1886-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-015-1886-5

Keywords

Search

Navigation