IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v39y2011i2p159-167.html
   My bibliography  Save this article

Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences

Author

Listed:
  • Hinojosa, M.A.
  • Mármol, A.M.

Abstract

In this paper we introduce the class of axial solutions for multiple objective optimization problems in contexts in which partial information on preference weights is available. These solutions combine the use of an improvement axis to direct the search of the most preferred result with the concept of efficiency with respect to preference information. In addition, we show how this solution is used in data envelopment analysis in order to set realistic targets in accordance with either the partially specified preferences of a single decision maker, or the different individual preference information provided by the members of a group of decision makers.

Suggested Citation

  • Hinojosa, M.A. & Mármol, A.M., 2011. "Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences," Omega, Elsevier, vol. 39(2), pages 159-167, April.
    • Handle: RePEc:eee:jomega:v:39:y:2011:i:2:p:159-167
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305-0483(10)00069-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. V V Podinovski, 2004. "Production trade-offs and weight restrictions in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1311-1322, December.
    3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    4. Doyle, J & Green, R, 1993. "Data envelopment analysis and multiple criteria decision making," Omega, Elsevier, vol. 21(6), pages 713-715, November.
    5. Merja Halme & Tarja Joro & Pekka Korhonen & Seppo Salo & Jyrki Wallenius, 1999. "A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis," Management Science, INFORMS, vol. 45(1), pages 103-115, January.
    6. Richard E. Wendell, 1985. "The Tolerance Approach to Sensitivity Analysis in Linear Programming," Management Science, INFORMS, vol. 31(5), pages 564-578, May.
    7. Weber, Martin, 1987. "Decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 28(1), pages 44-57, January.
    8. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    9. Halme, Merja & Korhonen, Pekka, 2000. "Restricting weights in value efficiency analysis," European Journal of Operational Research, Elsevier, vol. 126(1), pages 175-188, October.
    10. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    11. André, Francisco J., 2009. "Indirect elicitation of non-linear multi-attribute utility functions. A dual procedure combined with DEA," Omega, Elsevier, vol. 37(4), pages 883-895, August.
    12. Marmol, Amparo M. & Puerto, Justo & Fernandez, Francisco R., 2002. "Sequential incorporation of imprecise information in multiple criteria decision processes," European Journal of Operational Research, Elsevier, vol. 137(1), pages 123-133, February.
    13. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    14. Russell G. Thompson & F. D. Singleton & Robert M. Thrall & Barton A. Smith, 1986. "Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas," Interfaces, INFORMS, vol. 16(6), pages 35-49, December.
    15. Hansen, Pierre & Labbe, Martine & Wendell, Richard E., 1989. "Sensitivity analysis in multiple objective linear programming: The tolerance approach," European Journal of Operational Research, Elsevier, vol. 38(1), pages 63-69, January.
    16. André, Francisco J. & Herrero, Inés & Riesgo, Laura, 2010. "A modified DEA model to estimate the importance of objectives with an application to agricultural economics," Omega, Elsevier, vol. 38(5), pages 371-382, October.
    17. Stewart, Theodor J., 2010. "Goal directed benchmarking for organizational efficiency," Omega, Elsevier, vol. 38(6), pages 534-539, December.
    18. Richard E. Wendell, 2004. "Tolerance Sensitivity and Optimality Bounds in Linear Programming," Management Science, INFORMS, vol. 50(6), pages 797-803, June.
    19. Marmol, A. M. & Puerto, J., 1997. "Special cases of the tolerance approach in multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 98(3), pages 610-616, May.
    20. Yang, Jian-Bo & Wong, Brandon Y.H. & Xu, Dong-Ling & Stewart, Theodor J., 2009. "Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods," European Journal of Operational Research, Elsevier, vol. 195(1), pages 205-222, May.
    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. Mustapha Daruwana Ibrahim & Sahand Daneshvar & Hüseyin Güden & Bela Vizvari, 2020. "Target setting in data envelopment analysis: efficiency improvement models with predefined inputs/outputs," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1319-1336, December.
    2. Tavana, Madjid & Ebrahimnejad, Ali & Santos-Arteaga, Francisco J. & Mansourzadeh, Seyed Mehdi & Matin, Reza Kazemi, 2018. "A hybrid DEA-MOLP model for public school assessment and closure decision in the City of Philadelphia," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 70-89.
    3. Yu, Ming-Miin & Rakshit, Ipsita, 2024. "How to establish input and output targets for airlines with heterogeneous production technologies: A nash bargaining DEA approach within the meta-frontier framework," Journal of Air Transport Management, Elsevier, vol. 116(C).
    4. Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2019. "Extending the bargaining approach to DEA target setting," Omega, Elsevier, vol. 85(C), pages 94-102.
    5. Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2015. "Set-valued DEA production games," Omega, Elsevier, vol. 52(C), pages 92-100.
    6. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    7. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    8. Zhu, Qingyuan & Wu, Jie & Ji, Xiang & Li, Feng, 2018. "A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity," Omega, Elsevier, vol. 79(C), pages 1-8.
    9. Ahn, Heinz & Neumann, Ludmila & Vazquez Novoa, Nadia, 2012. "Measuring the relative balance of DMUs," European Journal of Operational Research, Elsevier, vol. 221(2), pages 417-423.
    10. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.

    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. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    2. Tavana, Madjid & Ebrahimnejad, Ali & Santos-Arteaga, Francisco J. & Mansourzadeh, Seyed Mehdi & Matin, Reza Kazemi, 2018. "A hybrid DEA-MOLP model for public school assessment and closure decision in the City of Philadelphia," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 70-89.
    3. M. A. Hinojosa & A. M. Mármol, 2011. "Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information," Group Decision and Negotiation, Springer, vol. 20(6), pages 707-724, November.
    4. Giannis Karagiannis & Panagiotis Ravanos, 2023. "On Value Efficiency Analysis and Cone-Ratio Data Envelopment Analysis models," Discussion Paper Series 2023_03, Department of Economics, University of Macedonia, revised Mar 2023.
    5. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
    6. Dyckhoff, Harald & Souren, Rainer, 2022. "Integrating multiple criteria decision analysis and production theory for performance evaluation: Framework and review," European Journal of Operational Research, Elsevier, vol. 297(3), pages 795-816.
    7. Gerami, Javad & Mozaffari, Mohammad Reza & Wanke, Peter F. & Correa, Henrique L., 2022. "Improving information reliability of non-radial value efficiency analysis: An additive slacks based measure approach," European Journal of Operational Research, Elsevier, vol. 298(3), pages 967-978.
    8. T Joro & E-J Viitala, 2004. "Weight-restricted DEA in action: from expert opinions to mathematical models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 814-821, August.
    9. Ahti Salo & Antti Punkka, 2011. "Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis," Management Science, INFORMS, vol. 57(1), pages 200-214, January.
    10. Santos, Sérgio P. & Belton, Valerie & Howick, Susan & Pilkington, Martin, 2018. "Measuring organisational performance using a mix of OR methods," Technological Forecasting and Social Change, Elsevier, vol. 131(C), pages 18-30.
    11. Peter Nijkamp & Soushi Suzuki, 2009. "A Generalized Goals-achievement Model in Data Envelopment Analysis: an Application to Efficiency Improvement in Local Government Finance in Japan," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(3), pages 249-274.
    12. Pereira, Miguel Alves & Camanho, Ana Santos & Figueira, José Rui & Marques, Rui Cunha, 2021. "Incorporating preference information in a range directional composite indicator: The case of Portuguese public hospitals," European Journal of Operational Research, Elsevier, vol. 294(2), pages 633-650.
    13. Yang, J.B. & Wong, B.Y.H. & Xu, D.L. & Liu, X.B. & Steuer, R.E., 2010. "Integrated bank performance assessment and management planning using hybrid minimax reference point - DEA approach," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1506-1518, December.
    14. V V Podinovski, 2004. "Production trade-offs and weight restrictions in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1311-1322, December.
    15. HOSSEINZADEH LOTFI, Farhad & HATAMI-MARBINI, Adel & AGRELL, Per & GHOLAMI, Kobra, 2013. "Centralized resource reduction and target setting under DEA control," LIDAM Discussion Papers CORE 2013005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Maarit Kallio & Markku Kallio, 2002. "Nonparametric Methods for Evaluating Economic Efficiency and Imperfect Competition," Journal of Productivity Analysis, Springer, vol. 18(2), pages 171-189, September.
    17. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    18. Perrigot, Rozenn & Barros, Carlos Pestana, 2008. "Technical efficiency of French retailers," Journal of Retailing and Consumer Services, Elsevier, vol. 15(4), pages 296-305.
    19. Barros, Carlos Pestana & Peypoch, Nicolas, 2008. "Technical efficiency of thermoelectric power plants," Energy Economics, Elsevier, vol. 30(6), pages 3118-3127, November.
    20. Khalili, M. & Camanho, A.S. & Portela, M.C.A.S. & Alirezaee, M.R., 2010. "The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs," European Journal of Operational Research, Elsevier, vol. 203(3), pages 761-770, June.

    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:jomega:v:39:y:2011:i:2:p:159-167. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.