Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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A Mixed-Integer Programming Model to Draw the Concordance Level and the Kernel Set for the Implementation of ELECTRE IS

ELECTRE IS의 구현 시 일치판정 기준비율 도출과 핵심대안 선정을 위한 혼합정수계획 모형

  • Park, Seokyoung (Department of Industrial Systems and Information Engineering, Korea University) ;
  • Kim, Jaehee (School of Business Administration and Accounting, Kunsan National University) ;
  • Kim, Sheung-Kown (Department of Industrial Systems and Information Engineering, Korea University)
  • 박석영 (고려대학교 산업시스템정보공학과) ;
  • 김재희 (군산대학교 경영회계학부) ;
  • 김승권 (고려대학교 산업시스템정보공학과)
  • Published : 2005.12.30
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Abstract

ELECTRE IS requires the decision maker (DM) to specify several parameters such as weights, pseudo-criteria thresholds and the concordance level. Among these parameters, the concordance level has a significant effect on the outranking relation. And the number of alternatives selected may be sensitive to the value of these parameters. Therefore the DM may have to perform many iterations to obtain the desired number of alternatives in the kernel set. In this study, we developed a mixed-integer programming (MIP) model to elicit the concordance level and thereby to choose the desired number of alternatives in the kernel set. The MIP model can be applied in the interactive process so that the pseudo-criteria thresholds are adjusted according to the results of MIP model. Using the MIP model in the interactive process, we can reduce the number of iterations needed to perform ELECTRE IS.

Keywords

References

  1. Brans, J. P. and Vincke, Ph. (1985), A Preference Ranking Organisation Method : (The PROMETHEE Method for Multiple Criteria Decision-Making), Management Science, 31(6), 647-656 https://doi.org/10.1287/mnsc.31.6.647
  2. Hokkanen, J. and Salminen, P. (1997), ELECTRE III and IV Decision Aids in an Environmental Problem, Journal of Multi-Criteria Decision Analysis, 6, 215-226 https://doi.org/10.1002/(SICI)1099-1360(199707)6:4<215::AID-MCDA139>3.0.CO;2-P
  3. ILOG (2003), ILOG CPLEX C+ + API 9.0 Reference Manual
  4. Keeney, R. L. and Raiffa, H. (1976), Decisions with Multiple Objective : Preferences and Value Tradeoff, John Wiley & Sons, New York
  5. Lourenco, R. P. and Costa, J. P (2004), Using ELECTRE TRI Outranking Method to Sort MOMILP Nondominated Solutions, European Journal of Operational Research, 153(2), 271-289 https://doi.org/10.1016/S0377-2217(03)00150-4
  6. Maystre, L. Y. (1999), ELECTRE and Decision Support: Methods and Applications in Engineering and Infrastructure Investment, Kluwer Academic, Boston
  7. Mousseau, V. and Slowinski, R. (1998), Inferring an ELECTRE TRI Model from Assignment Examples, Journal of Global Optimization, 12(2), 157-174 https://doi.org/10.1023/A:1008210427517
  8. Roy, B. (1990), Decision-aid and Decision-making, European Journal of Operational Research, 45(2/3), 324-331 https://doi.org/10.1016/0377-2217(90)90196-I
  9. Roy, B. (1991). The Outranking Approach and the Foundations of ELECTRE Methods, Theory and Decision, 31, 49-73 https://doi.org/10.1007/BF00134132
  10. Roy, B. and Hugonnard, J. C. (1982), Ranking of Suburban Line Extension Projects on the Paris Metro System by a Multicriteria Method, Transportation Research, 16(4), 301-312 https://doi.org/10.1016/0191-2607(82)90057-7
  11. Roy, B., Present, M, and Silhol, D. (1986), A Programming Method for Determining which Paris Metro Stations Should be Renovated, European Journal of Operational Research, 24(2), 318-334 https://doi.org/10.1016/0377-2217(86)90054-8
  12. Roy, B. and Vincke, Ph. (1984), Relational Systems of Preferences with One or More Pseudo-Criteria: Some New Concepts and Results, Management Science, 30(11), 1245-1254
  13. Saaty, T. L. (1980), The Analytic Hierarchy Process, McGraw-Hill, New York
  14. Saaty, T. L. (1996), Decision Making with Dependence and Feedback: the Analytic Network Process, RWS publisher, Pittsburgh