IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v311y2023i2p777-788.html
   My bibliography  Save this article

Design of water quality policies based on proportionality in multi-issue problems with crossed claims

Author

Listed:
  • Acosta-Vega, Rick K.
  • Algaba, Encarnación
  • Sánchez-Soriano, Joaquín

Abstract

Water pollutants can be classified into three categories, each of which includes several classifications of substances. In this paper, we present a methodology based on bankruptcy models to determine the emission limits of polluting substances belonging to more than one category. We model the problem as a multi-issue allocation problem with crossed claims and introduce the constrained proportional awards rule to obtain the emission limits. This rule is based on the concept of proportionality and extends the proportional rule for bankruptcy problems. We also provide an axiomatic characterization of this rule. Moreover, this allocation rule is illustrated by means of a numerical example based on real-world data. Finally, managerial and policy implications of this approach for water pollution control are given.

Suggested Citation

  • Acosta-Vega, Rick K. & Algaba, Encarnación & Sánchez-Soriano, Joaquín, 2023. "Design of water quality policies based on proportionality in multi-issue problems with crossed claims," European Journal of Operational Research, Elsevier, vol. 311(2), pages 777-788.
    • Handle: RePEc:eee:ejores:v:311:y:2023:i:2:p:777-788
    DOI: 10.1016/j.ejor.2023.05.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723004083
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.05.029?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. Mohammad Nikoo & Reza Kerachian & Mohammad Niksokhan, 2012. "Equitable Waste Load Allocation in Rivers Using Fuzzy Bi-matrix Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(15), pages 4539-4552, December.
    2. Peter Borm & Luisa Carpente & Balbina Casas-Méndez & Ruud Hendrickx, 2005. "The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions," Annals of Operations Research, Springer, vol. 137(1), pages 211-227, July.
    3. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    4. Timo Kuosmanen & Marita Laukkanen, 2011. "(In)Efficient Environmental Policy with Interacting Pollutants," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(4), pages 629-649, April.
    5. José-Manuel Giménez-Gómez & Jordi Teixidó-Figueras & Cori Vilella, 2016. "The global carbon budget: a conflicting claims problem," Climatic Change, Springer, vol. 136(3), pages 693-703, June.
    6. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    7. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
    8. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    9. Wenzhong Li & Genjiu Xu & Rene van den Brink, 2021. "Sharing the cost of cleaning up a polluted river," Tinbergen Institute Discussion Papers 21-028/II, Tinbergen Institute.
    10. Algaba, Encarnación & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Horizontal cooperation in a multimodal public transport system: The profit allocation problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 659-665.
    11. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 973-988, November.
    12. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    13. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    14. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    15. M. Pulido & P. Borm & R. Hendrickx & N. Llorca & J. Sánchez-Soriano, 2008. "Compromise solutions for bankruptcy situations with references," Annals of Operations Research, Springer, vol. 158(1), pages 133-141, February.
    16. María Gómez-Rúa, 2012. "Sharing a polluted river network through environmental taxes," Economics Bulletin, AccessEcon, vol. 32(1), pages 992-1000.
    17. María Gómez-Rúa, 2013. "Sharing a polluted river through environmental taxes," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(2), pages 137-153, June.
    18. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    19. Joaquín Sánchez-Soriano & Natividad Llorca & Encarnación Algaba, 2016. "Valuing managerial flexibility: An application of real-option theory to steel industry investments," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 127-145.
    20. Bergantiños, Gustavo & Gómez-Rúa, María & Llorca, Natividad & Pulido, Manuel & Sánchez-Soriano, Joaquín, 2020. "Allocating costs in set covering problems," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1074-1087.
    21. Duro, Juan Antonio & Giménez-Gómez, José-Manuel & Vilella, Cori, 2020. "The allocation of CO2 emissions as a claims problem," Energy Economics, Elsevier, vol. 86(C).
    22. Dinar, Ariel & Hogarth, Margaret, 2015. "Game Theory and Water Resources Critical Review of its Contributions, Progress and Remaining Challenges," Foundations and Trends(R) in Microeconomics, now publishers, vol. 11(1-2), pages 1-139, June.
    23. Long He & Guangrui Ma & Wei Qi & Xin Wang, 2021. "Charging an Electric Vehicle-Sharing Fleet," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 471-487, March.
    24. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    25. Fioravante Patrone & Joaquin Sanchez-Soriano & Ariel Dinar, 2008. "Does Game Theory Have A Role To Play In Policy Making In Natural Resources And The Environment?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 221-228.
    26. Manuel Pulido & Joaquín Sánchez-Soriano & Natividad Llorca, 2002. "Game Theory Techniques for University Management: An Extended Bankruptcy Model," Annals of Operations Research, Springer, vol. 109(1), pages 129-142, January.
    27. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    28. Baomin Dong & Debing Ni & Yuntong Wang, 2012. "Sharing a Polluted River Network," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(3), pages 367-387, November.
    29. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.
    30. Jorge Alcalde-Unzu & María Gómez-Rúa & Elena Molis, 2021. "Allocating the costs of cleaning a river: expected responsibility versus median responsibility," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 185-214, March.
    31. Hamed Poorsepahy-Samian & Reza Kerachian & Mohammad Nikoo, 2012. "Water and Pollution Discharge Permit Allocation to Agricultural Zones: Application of Game Theory and Min-Max Regret Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4241-4257, November.
    32. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Constrained multi-issue rationing problems," UB School of Economics Working Papers 2016/347, University of Barcelona School of Economics.
    33. Bloemhof-Ruwaard, Jacqueline M. & van Beek, Paul & Hordijk, Leen & Van Wassenhove, Luk N., 1995. "Interactions between operational research and environmental management," European Journal of Operational Research, Elsevier, vol. 85(2), pages 229-243, September.
    34. Mishra, Mukesh Kumar, 2020. "Application of Operational Research in Sustainable Environmental Management and Climate Change," EconStor Preprints 215782, ZBW - Leibniz Information Centre for Economics.
    35. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
    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. Algaba, E. & Márquez, G. & Martínez-Lozano, J. & Sánchez-Soriano, J., 2023. "A novel methodology for public management of annual greenhouse gas emissions in the European Union," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).

    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. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.
    2. Rick K. Acosta-Vega & Encarnaci'on Algaba & Joaqu'in S'anchez-Soriano, 2022. "On proportionality in multi-issue problems with crossed claims," Papers 2202.09877, arXiv.org.
    3. Algaba, E. & Márquez, G. & Martínez-Lozano, J. & Sánchez-Soriano, J., 2023. "A novel methodology for public management of annual greenhouse gas emissions in the European Union," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    4. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    5. M. Hinojosa & A. Mármol & F. Sánchez, 2012. "A consistent talmudic rule for division problems with multiple references," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 661-678, October.
    6. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    7. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    8. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.
    9. M. Hinojosa & A. Mármol & F. Sánchez, 2013. "Extended proportionality in division problems with multiple references," Annals of Operations Research, Springer, vol. 206(1), pages 183-195, July.
    10. Gustavo Bergantiños & Jose María Chamorro & Leticia Lorenzo & Silvia Lorenzo‐Freire, 2018. "Mixed rules in multi‐issue allocation situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 66-77, February.
    11. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    12. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    13. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing with baselines: the composition extension operator," Annals of Operations Research, Springer, vol. 211(1), pages 179-191, December.
    14. Cano-Berlanga, Sebastián & Giménez-Gómez, José-Manuel & Vilella, Cori, 2017. "Enjoying cooperative games: The R package GameTheory," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 381-393.
    15. Silvia Lorenzo-Freire & Balbina Casas-Méndez & Ruud Hendrickx, 2010. "The two-stage constrained equal awards and losses rules for multi-issue allocation situations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 465-480, December.
    16. Hinojosa Ramos, Miguel Ángel & López Sánchez, Ana Dolores, 2011. "Regla de reparto proporcional con referencias múltiples: aplicación al caso de agregación y actualización de probabilidades || A Proportional Rule for the Division Problems with Multiple References: A," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 12(1), pages 65-80, December.
    17. Sinan Ertemel & Rajnish Kumar, 2018. "Proportional rules for state contingent claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 229-246, March.
    18. Andrea Gallice, 2019. "Bankruptcy problems with reference-dependent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 311-336, March.
    19. Gutiérrez, E. & Llorca, N. & Sánchez-Soriano, J. & Mosquera, M., 2018. "Sustainable allocation of greenhouse gas emission permits for firms with Leontief technologies," European Journal of Operational Research, Elsevier, vol. 269(1), pages 5-15.
    20. Yuzhi Yang & Erik Ansink & Jens Gudmundsson, 2023. "How to Pollute a River If You Must," Tinbergen Institute Discussion Papers 23-036/VIII, Tinbergen Institute, revised 01 Jun 2024.

    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:ejores:v:311:y:2023:i:2:p:777-788. 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/eor .

    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.