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Inequity-averse shelter location for disaster preparedness

Author

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  • Mahdi Mostajabdaveh
  • Walter J. Gutjahr
  • F. Sibel Salman

Abstract

We study the problem of selecting a set of shelter locations in preparation for natural disasters. Shelters provide victims of a disaster both a safe place to stay and relief necessities such as food, water and medical support. Individuals from the affected population living in a set of population points go to, or are transported to the assigned open shelters. We aim to take both efficiency and inequity into account, thus we minimize a linear combination of: (i) the mean distance between opened shelter locations and the locations of the individuals assigned to them; and (ii) Gini’s Mean Absolute Difference of these distances. We develop a stochastic programming model with a set of scenarios that consider uncertain demand and disruptions in the transportation network. A chance constraint is defined on the total cost of opening the shelters and their capacity expansion. In this stochastic context, a weighted mean of the so-called ex ante and ex post versions of the inequity-averse objective function under uncertainty is optimized. Since the model can be solved to optimality only for small instances, we develop a tailored Genetic Algorithm (GA) that utilizes a mixed-integer programming subproblem to solve this problem heuristically for larger instances. We compare the performance of the mathematical program and the GA via benchmark instances where the model can be solved to optimality or near optimality. It turns out that the GA yields small optimality gaps in much shorter time for these instances. We run the GA also on Istanbul data to drive insights to guide decision-makers for preparation.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uiiexx:v:51:y:2019:i:8:p:809-829
    DOI: 10.1080/24725854.2018.1496372
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    Citations

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    Cited by:

    1. 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.
    2. Bian Liang & Dapeng Yang & Xinghong Qin & Teresa Tinta, 2019. "A Risk-Averse Shelter Location and Evacuation Routing Assignment Problem in an Uncertain Environment," IJERPH, MDPI, vol. 16(20), pages 1-28, October.
    3. Violet Xinying Chen & J. N. Hooker, 2023. "A guide to formulating fairness in an optimization model," Annals of Operations Research, Springer, vol. 326(1), pages 581-619, July.
    4. 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.
    5. 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).
    6. Alem, Douglas & Caunhye, Aakil M. & Moreno, Alfredo, 2022. "Revisiting Gini for equitable humanitarian logistics," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    7. Eghbal Akhlaghi, Vahid & Campbell, Ann Melissa & de Matta, Renato E., 2021. "Fuel distribution planning for disasters: Models and case study for Puerto Rico," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    8. 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.
    9. Liu, Kanglin & Zhang, Hengliang & Zhang, Zhi-Hai, 2021. "The efficiency, equity and effectiveness of location strategies in humanitarian logistics: A robust chance-constrained approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    10. Liu, Kanglin & Liu, Changchun & Xiang, Xi & Tian, Zhili, 2023. "Testing facility location and dynamic capacity planning for pandemics with demand uncertainty," European Journal of Operational Research, Elsevier, vol. 304(1), pages 150-168.

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