IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v167y2009i1p61-8610.1007-s10479-007-0234-9.html
   My bibliography  Save this article

Inequality measures and equitable locations

Author

Listed:
  • Włodzimierz Ogryczak

Abstract

While making location decisions, the distribution of distances (outcomes) among the service recipients (clients) is an important issue. In order to comply with the minimization of distances as well as with an equal consideration of the clients, mean-equity approaches are commonly used. They quantify the problem in a lucid form of two criteria: the mean outcome representing the overall efficiency and a scalar measure of inequality of outcomes to represent the equity (fairness) aspects. The mean-equity model is appealing to decision makers and allows a simple trade-off analysis. On the other hand, for typical dispersion indices used as inequality measures, the mean-equity approach may lead to inferior conclusions with respect to the distances minimization. Some inequality measures, however, can be combined with the mean itself into optimization criteria that remain in harmony with both inequality minimization and minimization of distances. In this paper we introduce general conditions for inequality measures sufficient to provide such an equitable consistency. We verify the conditions for the basic inequality measures thus showing how they can be used in location models not leading to inferior distributions of distances. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Włodzimierz Ogryczak, 2009. "Inequality measures and equitable locations," Annals of Operations Research, Springer, vol. 167(1), pages 61-86, March.
    • Handle: RePEc:spr:annopr:v:167:y:2009:i:1:p:61-86:10.1007/s10479-007-0234-9
    DOI: 10.1007/s10479-007-0234-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-007-0234-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-007-0234-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. William J. Abernathy & John C. Hershey, 1972. "A Spatial-Allocation Model for Regional Health-Services Planning," Operations Research, INFORMS, vol. 20(3), pages 629-642, June.
    2. labbe, M. & Peeters, D. & Thisse, J.F., 1992. "Location on Networks," Papers 9216, Universite Libre de Bruxelles - C.E.M.E..
    3. Oded Berman & Edward H. Kaplan, 1990. "Equity Maximizing Facility Location Schemes," Transportation Science, INFORMS, vol. 24(2), pages 137-144, May.
    4. Current, John & Min, Hokey & Schilling, David, 1990. "Multiobjective analysis of facility location decisions," European Journal of Operational Research, Elsevier, vol. 49(3), pages 295-307, December.
    5. Kostreva, Michael M. & Ogryczak, Wlodzimierz & Wierzbicki, Adam, 2004. "Equitable aggregations and multiple criteria analysis," European Journal of Operational Research, Elsevier, vol. 158(2), pages 362-377, October.
    6. Marvin B. Mandell, 1991. "Modelling Effectiveness-Equity Trade-Offs in Public Service Delivery Systems," Management Science, INFORMS, vol. 37(4), pages 467-482, April.
    7. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    8. J Malczewski & W Ogryczak, 1988. "A Multiobjective Approach to the Reorganization of Health-Service Areas: A Case Study," Environment and Planning A, , vol. 20(11), pages 1461-1470, November.
    9. L D Mayhew & G Leonardi, 1982. "Equity, Efficiency, and Accessibility in Urban and Regional Health-Care Systems," Environment and Planning A, , vol. 14(11), pages 1479-1507, November.
    10. Oded Berman, 1990. "Mean-Variance Location Problems," Transportation Science, INFORMS, vol. 24(4), pages 287-293, November.
    11. Malczewski, Jacek & Jackson, Marlene, 2000. "Multicriteria spatial allocation of educational resources: an overview," Socio-Economic Planning Sciences, Elsevier, vol. 34(3), pages 219-235, September.
    12. Cruz Lopez-de-los-Mozos, M. & Mesa, Juan A., 2001. "The maximum absolute deviation measure in location problems on networks," European Journal of Operational Research, Elsevier, vol. 135(1), pages 184-194, November.
    13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    14. Marsh, Michael T. & Schilling, David A., 1994. "Equity measurement in facility location analysis: A review and framework," European Journal of Operational Research, Elsevier, vol. 74(1), pages 1-17, April.
    15. Ogryczak, Wlodzimierz, 1997. "On the lexicographic minimax approach to location problems," European Journal of Operational Research, Elsevier, vol. 100(3), pages 566-585, August.
    16. Ogryczak, Wlodzimierz, 2000. "Inequality measures and equitable approaches to location problems," European Journal of Operational Research, Elsevier, vol. 122(2), pages 374-391, April.
    17. Alonso, M. A. Benito & Devaux, P., 1981. "Location and size of day nurseries-- a multiple goal approach," European Journal of Operational Research, Elsevier, vol. 6(2), pages 195-198, February.
    18. Włodzimierz Ogryczak & Mariusz Zawadzki, 2002. "Conditional Median: A Parametric Solution Concept for Location Problems," Annals of Operations Research, Springer, vol. 110(1), pages 167-181, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amy Givler Chapman & John E. Mitchell, 2018. "A fair division approach to humanitarian logistics inspired by conditional value-at-risk," Annals of Operations Research, Springer, vol. 262(1), pages 133-151, March.
    2. Drezner, Tammy & Drezner, Zvi & Hulliger, Beat, 2014. "The Quintile Share Ratio in location analysis," European Journal of Operational Research, Elsevier, vol. 238(1), pages 166-174.
    3. Núñez Ares, José & de Vries, Harwin & Huisman, Dennis, 2016. "A column generation approach for locating roadside clinics in Africa based on effectiveness and equity," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1002-1016.
    4. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    5. Olender, Paweł & Ogryczak, Włodzimierz, 2019. "A revised Variable Neighborhood Search for the Discrete Ordered Median Problem," European Journal of Operational Research, Elsevier, vol. 274(2), pages 445-465.
    6. Ortega, Emilio & López, Elena & Monzón, Andrés, 2012. "Territorial cohesion impacts of high-speed rail at different planning levels," Journal of Transport Geography, Elsevier, vol. 24(C), pages 130-141.
    7. Piotr Żebrowski & Ulf Dieckmann & Åke Brännström & Oskar Franklin & Elena Rovenskaya, 2022. "Sharing the Burdens of Climate Mitigation and Adaptation: Incorporating Fairness Perspectives into Policy Optimization Models," Sustainability, MDPI, vol. 14(7), pages 1-24, March.
    8. Gutjahr, Walter J., 2021. "Inequity-averse stochastic decision processes," European Journal of Operational Research, Elsevier, vol. 288(1), pages 258-270.
    9. Cavallaro, Federico & Bruzzone, Francesco & Nocera, Silvio, 2020. "Spatial and social equity implications for High-Speed Railway lines in Northern Italy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 135(C), pages 327-340.
    10. Chen, Qingxin & Fu, Chenyi & Zhu, Ning & Ma, Shoufeng & He, Qiao-Chu, 2023. "A target-based optimization model for bike-sharing systems: From the perspective of service efficiency and equity," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 235-260.
    11. Karsu, Özlem & Morton, Alec & Argyris, Nikos, 2018. "Capturing preferences for inequality aversion in decision support," European Journal of Operational Research, Elsevier, vol. 264(2), pages 686-706.
    12. Rongbing Huang, 2016. "A short note on locating facilities on a path to minimize load range equity measure," Annals of Operations Research, Springer, vol. 246(1), pages 363-369, November.
    13. Luo, Weicong & Yao, Jing & Mitchell, Richard & Zhang, Xiaoxiang & Li, Wenqiang, 2022. "Locating emergency medical services to reduce urban-rural inequalities," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    14. Jesús Sánchez-Oro & Ana D. López-Sánchez & Anna Martínez-Gavara & Alfredo G. Hernández-Díaz & Abraham Duarte, 2021. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k -Balanced Center Location Problem," Mathematics, MDPI, vol. 9(8), pages 1-21, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ogryczak, Wlodzimierz, 1997. "On the lexicographic minimax approach to location problems," European Journal of Operational Research, Elsevier, vol. 100(3), pages 566-585, August.
    2. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2021. "On single-source capacitated facility location with cost and fairness objectives," European Journal of Operational Research, Elsevier, vol. 289(3), pages 959-974.
    3. Drezner, Tammy & Drezner, Zvi & Hulliger, Beat, 2014. "The Quintile Share Ratio in location analysis," European Journal of Operational Research, Elsevier, vol. 238(1), pages 166-174.
    4. Ogryczak, Wlodzimierz, 2000. "Inequality measures and equitable approaches to location problems," European Journal of Operational Research, Elsevier, vol. 122(2), pages 374-391, April.
    5. Jesús Sánchez-Oro & Ana D. López-Sánchez & Anna Martínez-Gavara & Alfredo G. Hernández-Díaz & Abraham Duarte, 2021. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k -Balanced Center Location Problem," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    6. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    7. Kostreva, Michael M. & Ogryczak, Wlodzimierz & Wierzbicki, Adam, 2004. "Equitable aggregations and multiple criteria analysis," European Journal of Operational Research, Elsevier, vol. 158(2), pages 362-377, October.
    8. Fang Lei & Li Hecheng, 2014. "Pluralistic Efficiency-Equity Tradeoffs in Locating Public Services," Journal of Systems Science and Information, De Gruyter, vol. 2(2), pages 130-143, April.
    9. P. Matl & R. F. Hartl & T. Vidal, 2018. "Workload Equity in Vehicle Routing Problems: A Survey and Analysis," Transportation Science, INFORMS, vol. 52(2), pages 239-260, March.
    10. Karsu, Özlem & Morton, Alec & Argyris, Nikos, 2018. "Capturing preferences for inequality aversion in decision support," European Journal of Operational Research, Elsevier, vol. 264(2), pages 686-706.
    11. Mandell, Marvin B. & Becker, Les R., 1996. "A model for locating automatic external defibrillators," Socio-Economic Planning Sciences, Elsevier, vol. 30(1), pages 51-66, March.
    12. Gutjahr, Walter J., 2021. "Inequity-averse stochastic decision processes," European Journal of Operational Research, Elsevier, vol. 288(1), pages 258-270.
    13. Cruz Lopez-de-los-Mozos, M. & Mesa, Juan A., 2001. "The maximum absolute deviation measure in location problems on networks," European Journal of Operational Research, Elsevier, vol. 135(1), pages 184-194, November.
    14. Antreas D. Athanassopoulos, 1998. "Decision Support for Target-Based Resource Allocation of Public Services in Multiunit and Multilevel Systems," Management Science, INFORMS, vol. 44(2), pages 173-187, February.
    15. Kasin Ransikarbum & Scott J. Mason, 2016. "Multiple-objective analysis of integrated relief supply and network restoration in humanitarian logistics operations," International Journal of Production Research, Taylor & Francis Journals, vol. 54(1), pages 49-68, January.
    16. Mut, Murat & Wiecek, Margaret M., 2011. "Generalized equitable preference in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 212(3), pages 535-551, August.
    17. Perugia, Alessandro & Moccia, Luigi & Cordeau, Jean-François & Laporte, Gilbert, 2011. "Designing a home-to-work bus service in a metropolitan area," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1710-1726.
    18. Bélanger, V. & Ruiz, A. & Soriano, P., 2019. "Recent optimization models and trends in location, relocation, and dispatching of emergency medical vehicles," European Journal of Operational Research, Elsevier, vol. 272(1), pages 1-23.
    19. Yoshiaki Ohsawa & Naoya Ozaki & Frank Plastria, 2008. "Equity-Efficiency Bicriteria Location with Squared Euclidean Distances," Operations Research, INFORMS, vol. 56(1), pages 79-87, February.
    20. Akoluk, Damla & Karsu, Özlem, 2022. "Ensuring multidimensional equality in public service," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:167:y:2009:i:1:p:61-86:10.1007/s10479-007-0234-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.