IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v214y2011i1p85-90.html
   My bibliography  Save this article

An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Author

Listed:
  • Kirytopoulos, Konstantinos
  • Voulgaridou, Dimitra
  • Platis, Agapios
  • Leopoulos, Vrassidas

Abstract

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The 'power' matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss-Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.

Suggested Citation

  • Kirytopoulos, Konstantinos & Voulgaridou, Dimitra & Platis, Agapios & Leopoulos, Vrassidas, 2011. "An effective Markov based approach for calculating the Limit Matrix in the analytic network process," European Journal of Operational Research, Elsevier, vol. 214(1), pages 85-90, October.
  • Handle: RePEc:eee:ejores:v:214:y:2011:i:1:p:85-90
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711002803
    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. Cortés-Aldana, Félix Antonio & García-Melón, Mónica & Fernández-de-Lucio, Ignacio & Aragonés-Beltrán, Pablo & Poveda-Bautista, Rocío, 2009. "University objectives and socioeconomic results: A multicriteria measuring of alignment," European Journal of Operational Research, Elsevier, vol. 199(3), pages 811-822, December.
    2. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
    3. Yu, Jing-Rung & Cheng, Sheu-Ji, 2007. "An integrated approach for deriving priorities in analytic network process," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1427-1432, August.
    4. Raharjo, Hendry & Xie, Min & Brombacher, Aarnout C., 2009. "On modeling dynamic priorities in the analytic hierarchy process using compositional data analysis," European Journal of Operational Research, Elsevier, vol. 194(3), pages 834-846, May.
    5. Konstantinos Kirytopoulos & Dimitra Voulgaridou & Dimitrios Panopoulos & Vrassidas Leopoulos, 2009. "Project termination analysis in SMEs: making the right call," International Journal of Management and Decision Making, Inderscience Enterprises Ltd, vol. 10(1/2), pages 69-90.
    6. Saaty, Thomas L., 2006. "Rank from comparisons and from ratings in the analytic hierarchy/network processes," European Journal of Operational Research, Elsevier, vol. 168(2), pages 557-570, January.
    7. Saaty, Thomas L. & Shih, Hsu-Shih, 2009. "Structures in decision making: On the subjective geometry of hierarchies and networks," European Journal of Operational Research, Elsevier, vol. 199(3), pages 867-872, December.
    8. Zahir, Sajjad, 1999. "Geometry of decision making and the vector space formulation of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 112(2), pages 373-396, January.
    9. Meade, Laura & Sarkis, Joseph, 1998. "Strategic analysis of logistics and supply chain management systems using the analytical network process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 34(3), pages 201-215, September.
    10. Niemira, Michael P. & Saaty, Thomas L., 2004. "An Analytic Network Process model for financial-crisis forecasting," International Journal of Forecasting, Elsevier, vol. 20(4), pages 573-587.
    11. Jharkharia, Sanjay & Shankar, Ravi, 2007. "Selection of logistics service provider: An analytic network process (ANP) approach," Omega, Elsevier, vol. 35(3), pages 274-289, June.
    12. Koutras, V.P. & Platis, A.N. & Gravvanis, G.A., 2009. "Optimal server resource reservation policies for priority classes of users under cyclic non-homogeneous markov modeling," European Journal of Operational Research, Elsevier, vol. 198(2), pages 545-556, October.
    13. Aragones-Beltran, P. & Aznar, J. & Ferris-Onate, J. & Garcia-Melon, M., 2008. "Valuation of urban industrial land: An analytic network process approach," European Journal of Operational Research, Elsevier, vol. 185(1), pages 322-339, February.
    14. Hamalainen, Raimo P. & Seppalainen, Timo O., 1986. "The analytic network process in energy policy planning," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 399-405.
    15. Chin-Tsai Lin & Meng-Chuan Tsai, 2010. "Location choice for direct foreign investment in new hospitals in China by using ANP and TOPSIS," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(2), pages 375-390, February.
    16. Leung, Lawrence C. & Cao, Dong, 2001. "On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy," European Journal of Operational Research, Elsevier, vol. 132(1), pages 39-49, July.
    17. A. Platis & N. Limnios & M. Le Du, 1998. "Hitting time in a finite non‐homogeneous Markov chain with applications," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(3), pages 241-253, September.
    18. Demirtas, Ezgi Aktar & Üstün, Özden, 2008. "An integrated multiobjective decision making process for supplier selection and order allocation," Omega, Elsevier, vol. 36(1), pages 76-90, February.
    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. Jolanta Poplawska & Ashraf Labib & Deborah M. Reed, 2017. "From vicious to virtuous circles: problem structuring for quantified decision making in operationalization of corporate social responsibility," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 291-307, March.
    2. Kheybari, Siamak & Rezaie, Fariba Mahdi & Farazmand, Hadis, 2020. "Analytic network process: An overview of applications," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Liu, Qizhi, 2022. "Identifying and correcting the defects of the Saaty analytic hierarchy/network process: A comparative study of the Saaty analytic hierarchy/network process and the Markov chain-based analytic network ," Operations Research Perspectives, Elsevier, vol. 9(C).
    4. Chin-Yi Chen & Jih-Jeng Huang, 2019. "Deriving Fuzzy Weights of the Fuzzy Analytic Network Process via Fuzzy Inverse Matrix," Mathematics, MDPI, vol. 7(10), pages 1-14, October.

    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. Kheybari, Siamak & Rezaie, Fariba Mahdi & Farazmand, Hadis, 2020. "Analytic network process: An overview of applications," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Wen-Hsien Tsai & Pei-Ling Lee & Yu-Shan Shen & Elliott Hwang, 2014. "A combined evaluation model for encouraging entrepreneurship policies," Annals of Operations Research, Springer, vol. 221(1), pages 449-468, October.
    3. Erik Schulze-González & Juan-Pascual Pastor-Ferrando & Pablo Aragonés-Beltrán, 2021. "Testing a Recent DEMATEL-Based Proposal to Simplify the Use of ANP," Mathematics, MDPI, vol. 9(14), pages 1-23, July.
    4. Y H Yang & Y V Hui & L C Leung & G Chen, 2010. "An analytic network process approach to the selection of logistics service providers for air cargo," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1365-1376, September.
    5. Cortés-Aldana, Félix Antonio & García-Melón, Mónica & Fernández-de-Lucio, Ignacio & Aragonés-Beltrán, Pablo & Poveda-Bautista, Rocío, 2009. "University objectives and socioeconomic results: A multicriteria measuring of alignment," European Journal of Operational Research, Elsevier, vol. 199(3), pages 811-822, December.
    6. J P Pastor-Ferrando & P Aragonés-Beltrán & A Hospitaler-Pérez & M García-Melón, 2010. "An ANP- and AHP-based approach for weighting criteria in public works bidding," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(6), pages 905-916, June.
    7. Kayakutlu, Gulgun & Buyukozkan, Gulcin, 2011. "Assessing performance factors for a 3PL in a value chain," International Journal of Production Economics, Elsevier, vol. 131(2), pages 441-452, June.
    8. Wen‐Hsien Tsai & Yu‐Wei Chou & Kuen‐Chang Lee & Wan‐Rung Lin & Elliott T.Y. Hwang, 2013. "Combining Decision Making Trial and Evaluation Laboratory with Analytic Network Process to Perform an Investigation of Information Technology Auditing and Risk Control in an Enterprise Resource Planni," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(2), pages 176-193, March.
    9. Aragonés-Beltrán, P. & Chaparro-González, F. & Pastor-Ferrando, J.P. & Rodríguez-Pozo, F., 2010. "An ANP-based approach for the selection of photovoltaic solar power plant investment projects," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(1), pages 249-264, January.
    10. Mohd. Nishat Faisal & Bilal Mustafa Khan, 2008. "Selecting an Advertising Agency: A Multi-Criteria Decision Making Approach," Vision, , vol. 12(4), pages 13-22, October.
    11. Agnieszka Konys, 2019. "Green Supplier Selection Criteria: From a Literature Review to a Comprehensive Knowledge Base," Sustainability, MDPI, vol. 11(15), pages 1-41, August.
    12. J Aznar & J Ferrís-Oñate & F Guijarro, 2010. "An ANP framework for property pricing combining quantitative and qualitative attributes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 740-755, May.
    13. Zhu, Bin & Xu, Zeshui & Zhang, Ren & Hong, Mei, 2015. "Generalized analytic network process," European Journal of Operational Research, Elsevier, vol. 244(1), pages 277-288.
    14. Hsu, David W.L. & Shen, Yung-Chi & Yuan, Benjamin J.C. & Chou, Chiyan James, 2015. "Toward successful commercialization of university technology: Performance drivers of university technology transfer in Taiwan," Technological Forecasting and Social Change, Elsevier, vol. 92(C), pages 25-39.
    15. Aleksander Janeš & Armand Faganel, 2020. "Complementary Methods for Effective Decision Making," MIC 2020: The 20th Management International Conference,, University of Primorska Press.
    16. Jung-Jung Chang & Chia-Li Lin, 2023. "Determining the Sustainable Development Strategies and Adoption Paths for Public Bike-Sharing Service Systems (PBSSSs) under Various Users’ Considerations," Mathematics, MDPI, vol. 11(5), pages 1-30, February.
    17. Paweł Ziemba, 2019. "Inter-Criteria Dependencies-Based Decision Support in the Sustainable wind Energy Management," Energies, MDPI, vol. 12(4), pages 1-29, February.
    18. Bayazit, Ozden & Karpak, Birsen, 2007. "An analytical network process-based framework for successful total quality management (TQM): An assessment of Turkish manufacturing industry readiness," International Journal of Production Economics, Elsevier, vol. 105(1), pages 79-96, January.
    19. Saaty, Thomas L. & Shang, Jennifer S., 2011. "An innovative orders-of-magnitude approach to AHP-based mutli-criteria decision making: Prioritizing divergent intangible humane acts," European Journal of Operational Research, Elsevier, vol. 214(3), pages 703-715, November.
    20. Garbuzova-Schlifter, Maria & Madlener, Reinhard, 2016. "AHP-based risk analysis of energy performance contracting projects in Russia," Energy Policy, Elsevier, vol. 97(C), pages 559-581.

    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:214:y:2011:i:1:p:85-90. 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.