IDEAS home Printed from https://ideas.repec.org/a/wsi/ijitdm/v16y2017i02ns0219622017500043.html
   My bibliography  Save this article

A New Compromise Solution Model Based on Dantzig–Wolfe Decomposition for Solving Belief Multi-Objective Nonlinear Programming Problems with Block Angular Structure

Author

Listed:
  • Behnam Vahdani

    (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran)

  • Meghdad Salimi

    (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran)

  • Seyed Meysam Mousavi

    (#x2020;Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran)

Abstract

This paper presents an integrated model based on a compromised solution method to solve fuzzy belief multi-objective large-scale nonlinear programming (FBMOLSNLP) problem with block angular structure. A new method is proposed to transfer each belief decision-making problem into some fuzzy problems. Furthermore, we propose a new compromise method of decision-making as one of the most efficient methods based on the particular measure of closeness to the ideal solution to aggregate multi-objective decision-making (MODM) problems into a single problem. The decomposition algorithm based on Dantzig–Wolfe is utilized to reduce the large-dimensional objective space into a two-dimensional space. Then, Zimmerman method is applied to transfer each bi-objective to a single-objective. Moreover, TOPSIS and VIKOR are utilized as two independent solution methods to aggregate each multi-objective sub-problem. Finally, a new single-objective nonlinear programming problem is solved to find the final solution. To justify the proposed model, two illustrative examples are provided, and the results of three decision methods are compromised.

Suggested Citation

  • Behnam Vahdani & Meghdad Salimi & Seyed Meysam Mousavi, 2017. "A New Compromise Solution Model Based on Dantzig–Wolfe Decomposition for Solving Belief Multi-Objective Nonlinear Programming Problems with Block Angular Structure," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 333-387, March.
    • Handle: RePEc:wsi:ijitdm:v:16:y:2017:i:02:n:s0219622017500043
    DOI: 10.1142/S0219622017500043
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219622017500043
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219622017500043?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. Gang Kou & Yanqun Lu & Yi Peng & Yong Shi, 2012. "Evaluation Of Classification Algorithms Using Mcdm And Rank Correlation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 197-225.
    2. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    3. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    4. de Sá, Elisangela Martins & de Camargo, Ricardo Saraiva & de Miranda, Gilberto, 2013. "An improved Benders decomposition algorithm for the tree of hubs location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 185-202.
    5. Fu, Chao & Yang, Shan-Lin, 2010. "The group consensus based evidential reasoning approach for multiple attributive group decision analysis," European Journal of Operational Research, Elsevier, vol. 206(3), pages 601-608, November.
    6. Sakawa, Masatoshi & Sawada, Kazuya & Inuiguchi, Masahiro, 1995. "A fuzzy satisficing method for large-scale linear programming problems with block angular structure," European Journal of Operational Research, Elsevier, vol. 81(2), pages 399-409, March.
    7. Lai, Young-Jou & Liu, Ting-Yun & Hwang, Ching-Lai, 1994. "TOPSIS for MODM," European Journal of Operational Research, Elsevier, vol. 76(3), pages 486-500, August.
    8. Wang, Reay-Chen & Liang, Tien-Fu, 2005. "Applying possibilistic linear programming to aggregate production planning," International Journal of Production Economics, Elsevier, vol. 98(3), pages 328-341, December.
    9. Yang, Jian-Bo, 2001. "Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties," European Journal of Operational Research, Elsevier, vol. 131(1), pages 31-61, May.
    10. Xu, Dong-Ling & Yang, Jian-Bo & Wang, Ying-Ming, 2006. "The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1914-1943, November.
    11. Wang, Ying-Ming & Yang, Jian-Bo & Xu, Dong-Ling, 2006. "Environmental impact assessment using the evidential reasoning approach," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1885-1913, November.
    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. Hua Zhu & Jianbin Zhao & Yang Xu & Limin Du, 2016. "Interval-Valued Belief Rule Inference Methodology Based on Evidential Reasoning-IRIMER," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1345-1366, November.
    2. Fu, Chao & Yang, Jian-Bo & Yang, Shan-Lin, 2015. "A group evidential reasoning approach based on expert reliability," European Journal of Operational Research, Elsevier, vol. 246(3), pages 886-893.
    3. Dong-Ling Xu, 2012. "An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis," Annals of Operations Research, Springer, vol. 195(1), pages 163-187, May.
    4. Kun Chen & Gang Kou & J. Michael Tarn & Yan Song, 2015. "Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices," Annals of Operations Research, Springer, vol. 235(1), pages 155-175, December.
    5. Kuang-Hua Hu & Wei Jianguo & Gwo-Hshiung Tzeng, 2017. "Risk Factor Assessment Improvement for China’s Cloud Computing Auditing Using a New Hybrid MADM Model," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 737-777, May.
    6. Eleonora Bottani & Piera Centobelli & Teresa Murino & Ehsan Shekarian, 2018. "A QFD-ANP Method for Supplier Selection with Benefits, Opportunities, Costs and Risks Considerations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 911-939, May.
    7. J-B Yang & D-L Xu & X Xie & A K Maddulapalli, 2011. "Multicriteria evidential reasoning decision modelling and analysis—prioritizing voices of customer," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1638-1654, September.
    8. Viral Gupta & P. K. Kapur & Deepak Kumar, 2019. "Prioritizing and Optimizing Disaster Recovery Solution using Analytic Network Process and Multi Attribute Utility Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 171-207, January.
    9. Fu, Chao & Yang, Shanlin, 2011. "An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context," European Journal of Operational Research, Elsevier, vol. 212(1), pages 179-189, July.
    10. Qian Qian & Yang Yang & Zong-Fang Zhou, 2019. "Research on Trade Credit Spreading and Credit Risk within the Supply Chain," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 389-411, January.
    11. Fu, Chao & Yang, Shanlin, 2012. "An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements," European Journal of Operational Research, Elsevier, vol. 223(1), pages 167-176.
    12. Wenshuai Wu & Yi Peng, 2016. "Extension of grey relational analysis for facilitating group consensus to oil spill emergency management," Annals of Operations Research, Springer, vol. 238(1), pages 615-635, March.
    13. Wenshuai Wu & Yi Peng, 2016. "Extension of grey relational analysis for facilitating group consensus to oil spill emergency management," Annals of Operations Research, Springer, vol. 238(1), pages 615-635, March.
    14. Akshay Hinduja & Manju Pandey, 2019. "An Integrated Intuitionistic Fuzzy MCDM Approach to Select Cloud-Based ERP System for SMEs," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1875-1908, November.
    15. Emre Çalişkan & Erdem Aksakal & Saliha Çetinyokuş & Tahsin Çetinyokuş, 2019. "Hybrid Use of Likert Scale-Based AHP and PROMETHEE Methods for Hazard Analysis and Consequence Modeling (HACM) Software Selection," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1689-1715, September.
    16. Shouzhen Zeng & Jianping Chen & Xingsen Li, 2016. "A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 403-422, March.
    17. Aiiad Albeshri & Vijey Thayananthan, 2018. "Analytical Techniques for Decision Making on Information Security for Big Data Breaches," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 527-545, March.
    18. Fu, Chao & Yang, Shan-Lin, 2010. "The group consensus based evidential reasoning approach for multiple attributive group decision analysis," European Journal of Operational Research, Elsevier, vol. 206(3), pages 601-608, November.
    19. Guo, Min & Yang, Jian-Bo & Chin, Kwai-Sang & Wang, Hongwei, 2007. "Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1294-1312, November.
    20. Peide Liu & Lili Zhang & Xi Liu & Peng Wang, 2016. "Multi-Valued Neutrosophic Number Bonferroni Mean Operators with their Applications in Multiple Attribute Group Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1181-1210, 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:wsi:ijitdm:v:16:y:2017:i:02:n:s0219622017500043. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijitdm/ijitdm.shtml .

    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.