IDEAS home Printed from https://ideas.repec.org/a/eee/soceps/v82y2022ipbs0038012122000970.html
   My bibliography  Save this article

Revisiting Gini for equitable humanitarian logistics

Author

Listed:
  • Alem, Douglas
  • Caunhye, Aakil M.
  • Moreno, Alfredo

Abstract

Modeling equity in the allocation of scarce resources is a fast-growing concern in the humanitarian logistics field. The Gini coefficient is one of the most widely recognized measures of inequity and it was originally characterized by means of the Lorenz curve, which is a mathematical function that links the cumulative share of income to rank-ordered groups in a population. So far, humanitarian logistics models that have approached equity using the Gini coefficient do not actually optimize its original formulation, but they use alternative definitions that do not necessarily replicate that original Gini measure. In this paper, we derive the original Gini coefficient via the Lorenz curve to optimize the effectiveness-equity trade-off in a humanitarian location-allocation problem. We also propose new valid inequalities based on a bounding Lorenz curve to tighten the linear relaxation of our model and develop a clustering-based construction of the Lorenz curve that requires fewer additional constraints and variables than the original one. The computational study, based on the floods and landslides in Rio de Janeiro state, Brazil, reveals that while alternative Gini definitions have interesting properties, they can generate vastly different decisions compared to the original Gini coefficient. In addition, viewed from the perspective of the original Gini coefficient, these decisions can be significantly less equitable.

Suggested Citation

  • Alem, Douglas & Caunhye, Aakil M. & Moreno, Alfredo, 2022. "Revisiting Gini for equitable humanitarian logistics," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    • Handle: RePEc:eee:soceps:v:82:y:2022:i:pb:s0038012122000970
    DOI: 10.1016/j.seps.2022.101312
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0038012122000970
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.seps.2022.101312?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. Mahdi Mostajabdaveh & Walter J. Gutjahr & F. Sibel Salman, 2019. "Inequity-averse shelter location for disaster preparedness," IISE Transactions, Taylor & Francis Journals, vol. 51(8), pages 809-829, August.
    2. Li, Xiaoping & Batta, Rajan & Kwon, Changhyun, 2017. "Effective and equitable supply of gasoline to impacted areas in the aftermath of a natural disaster," Socio-Economic Planning Sciences, Elsevier, vol. 57(C), pages 25-34.
    3. 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.
    4. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    5. Enayati, Shakiba & Özaltın, Osman Y., 2020. "Optimal influenza vaccine distribution with equity," European Journal of Operational Research, Elsevier, vol. 283(2), pages 714-725.
    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. Chong Hyun Park & Gemma Berenguer, 2020. "Supply Constrained Location‐Distribution in Not‐for‐Profit Settings," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2461-2483, November.
    8. Dönmez, Zehranaz & Kara, Bahar Y. & Karsu, Özlem & Saldanha-da-Gama, Francisco, 2021. "Humanitarian facility location under uncertainty: Critical review and future prospects," Omega, Elsevier, vol. 102(C).
    9. Ghasemi, Peiman & Khalili-Damghani, Kaveh & Hafezalkotob, Ashkan & Raissi, Sadigh, 2020. "Stochastic optimization model for distribution and evacuation planning (A case study of Tehran earthquake)," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    10. Abazari, Seyed Reza & Aghsami, Amir & Rabbani, Masoud, 2021. "Prepositioning and distributing relief items in humanitarian logistics with uncertain parameters," Socio-Economic Planning Sciences, Elsevier, vol. 74(C).
    11. Alem, Douglas & Bonilla-Londono, Hector F. & Barbosa-Povoa, Ana Paula & Relvas, Susana & Ferreira, Deisemara & Moreno, Alfredo, 2021. "Building disaster preparedness and response capacity in humanitarian supply chains using the Social Vulnerability Index," European Journal of Operational Research, Elsevier, vol. 292(1), pages 250-275.
    12. Ohad Eisenhandler & Michal Tzur, 2019. "The Humanitarian Pickup and Distribution Problem," Operations Research, INFORMS, vol. 67(1), pages 10-32, January.
    13. Gutjahr, Walter J. & Fischer, Sophie, 2018. "Equity and deprivation costs in humanitarian logistics," European Journal of Operational Research, Elsevier, vol. 270(1), pages 185-197.
    14. Amartya K. Sen, 1997. "From Income Inequality to Economic Inequality," Southern Economic Journal, John Wiley & Sons, vol. 64(2), pages 384-401, October.
    15. Nilay Noyan & Gökçe Kahvecioğlu, 2018. "Stochastic last mile relief network design with resource reallocation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 187-231, January.
    16. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    17. Marvin B. Mandell, 1991. "Modelling Effectiveness-Equity Trade-Offs in Public Service Delivery Systems," Management Science, INFORMS, vol. 37(4), pages 467-482, April.
    18. Cao, Wenwei & Çelik, Melih & Ergun, Özlem & Swann, Julie & Viljoen, Nadia, 2016. "Challenges in service network expansion: An application in donated breastmilk banking in South Africa," Socio-Economic Planning Sciences, Elsevier, vol. 53(C), pages 33-48.
    19. 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.
    20. Philip D. Leclerc & Laura A. McLay & Maria E. Mayorga, 2012. "Modeling Equity for Allocating Public Resources," International Series in Operations Research & Management Science, in: Michael P. Johnson (ed.), Community-Based Operations Research, chapter 0, pages 97-118, Springer.
    21. Ece Aslan & Melih Çelik, 2019. "Pre-positioning of relief items under road/facility vulnerability with concurrent restoration and relief transportation," IISE Transactions, Taylor & Francis Journals, vol. 51(8), pages 847-868, August.
    22. Alem, Douglas & Clark, Alistair & Moreno, Alfredo, 2016. "Stochastic network models for logistics planning in disaster relief," European Journal of Operational Research, Elsevier, vol. 255(1), pages 187-206.
    Full references (including those not matched with items on IDEAS)

    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. Dönmez, Zehranaz & Kara, Bahar Y. & Karsu, Özlem & Saldanha-da-Gama, Francisco, 2021. "Humanitarian facility location under uncertainty: Critical review and future prospects," Omega, Elsevier, vol. 102(C).
    2. Ohad Eisenhandler & Michal Tzur, 2019. "A Segment-Based Formulation and a Matheuristic for the Humanitarian Pickup and Distribution Problem," Transportation Science, INFORMS, vol. 53(5), pages 1389-1408, September.
    3. Sarid, Adi S. & Glynn, Peter W. & Tzur, Michal, 2024. "Power distribution in developing countries — Planning for effectiveness and equity," Omega, Elsevier, vol. 123(C).
    4. Yoon Ha Lee & Ji Soo Lee & Seung Chan Baek & Won Hwa Hong, 2020. "Spatial Equity with Census Population Data vs. Floating Population Data: The Distribution of Earthquake Evacuation Shelters in Daegu, South Korea," Sustainability, MDPI, vol. 12(19), pages 1-17, September.
    5. Tanzid Hasnain & Irem Sengul Orgut & Julie Simmons Ivy, 2021. "Elicitation of Preference among Multiple Criteria in Food Distribution by Food Banks," Production and Operations Management, Production and Operations Management Society, vol. 30(12), pages 4475-4500, December.
    6. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    7. 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.
    8. Chong Hyun Park & Gemma Berenguer, 2020. "Supply Constrained Location‐Distribution in Not‐for‐Profit Settings," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2461-2483, November.
    9. Gutjahr, Walter J., 2021. "Inequity-averse stochastic decision processes," European Journal of Operational Research, Elsevier, vol. 288(1), pages 258-270.
    10. Wang, Qingyi & Nie, Xiaofeng, 2023. "A location-inventory-routing model for distributing emergency supplies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    11. Mohammadmehdi Hakimifar & Vera C. Hemmelmayr & Fabien Tricoire, 2023. "A lexicographic maximin approach to the selective assessment routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 205-249, March.
    12. Chen, Violet Xinying & Hooker, J.N., 2022. "Combining leximax fairness and efficiency in a mathematical programming model," European Journal of Operational Research, Elsevier, vol. 299(1), pages 235-248.
    13. Spencer Leitch & Zhiyuan Wei, 2024. "Improving spatial access to healthcare facilities: an integrated approach with spatial analysis and optimization modeling," Annals of Operations Research, Springer, vol. 341(2), pages 1057-1074, October.
    14. Ohad Eisenhandler & Michal Tzur, 2019. "The Humanitarian Pickup and Distribution Problem," Operations Research, INFORMS, vol. 67(1), pages 10-32, January.
    15. Rodríguez-Espíndola, Oscar & Ahmadi, Hossein & Gastélum-Chavira, Diego & Ahumada-Valenzuela, Omar & Chowdhury, Soumyadeb & Dey, Prasanta Kumar & Albores, Pavel, 2023. "Humanitarian logistics optimization models: An investigation of decision-maker involvement and directions to promote implementation," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    16. Li Zhu & Yeming Gong & Yishui Xu & Jun Gu, 2019. "Emergency relief routing models for injured victims considering equity and priority," Annals of Operations Research, Springer, vol. 283(1), pages 1573-1606, December.
    17. Breugem, Thomas & Van Wassenhove, Luk N., 2022. "The price of imposing vertical equity through asymmetric outcome constraints," Other publications TiSEM b6e85652-c54a-4597-a32e-d, Tilburg University, School of Economics and Management.
    18. Gang Wang, 2024. "Disaster relief supply chain network planning under uncertainty," Annals of Operations Research, Springer, vol. 338(2), pages 1127-1156, July.
    19. Jon M. Stauffer & Manoj Vanajakumari & Subodha Kumar & Theresa Mangapora, 2022. "Achieving equitable food security: How can food bank mobile pantries fill this humanitarian need," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1802-1821, April.
    20. Afshin Kamyabniya & Antoine Sauré & F. Sibel Salman & Noureddine Bénichou & Jonathan Patrick, 2024. "Optimization models for disaster response operations: a literature review," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 737-783, September.

    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:eee:soceps:v:82:y:2022:i:pb:s0038012122000970. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/seps .

    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.