Stochastic decision making using multiplicative AHP. (English) Zbl 0920.90002
Summary: The Analytic Hierarchy Process (AHP) has found a number of applications in decision making problems. Its multiplicative version, called the Multiplicative AHP (MAHP), has been proposed to overcome some of the criticisms of the conventional version. Both these methodologies operate by obtaining expert judgements on the ratios of perceived importance of objects under consideration. The literature on MAHP in dealing with these judgements, when they are specified without uncertainty, is well developed. However, stochastic aspects of these judgements have not received much consideration in the literature so far. Stochastic judgements are considered in this paper for use in MAHP. The fact that weight derivation in MAHP can be handled using mathematical programming is exploited and the literature on stochastic programming is adapted to the MAHP context.
MSC:
| 91B06 | Decision theory |
| 90C90 | Applications of mathematical programming |
| 90C15 | Stochastic programming |
Keywords:
maximum likelihood weights; analytic hierarchy process; multiplicative AHP; stochastic judgements; decision makingReferences:
| [1] | Barzilai, J., On the use of the eigenvector in the AHP, (Proceedings of the Tenth International Conference on MCDM, Volume I (1992)), 291-300, Taipei |
| [2] | Barzilai, J.; Cook, W. D.; Golany, B., Consistent weights for judgements matrices of the relative importance of alternatives, Operations Research Letters, 6, 3, 131-134 (1987) · Zbl 0622.90004 |
| [3] | Belton, V.; Gear, T., On a shortcoming of Saaty’s method of analytical hierarchies, Omega, 11, 3, 228-230 (1983) |
| [4] | Contini, B., A stochastic approach to goal programming, Operations Research, 16, 576-586 (1968) · Zbl 0211.22501 |
| [5] | Crawford, G.; Williams, C., A note on the analysis of subjective judgment matrices, Journal of Mathematical Psychology, 29, 387-405 (1985) · Zbl 0585.62183 |
| [6] | Dyer, J. S., Remarks of the Analytic Hierarchy Process, Management Science, 36, 3, 249-258 (1990) |
| [7] | Gass, S. I., A process for determining priorities for large scale linear goal programs, Journal of the Operational Research Society, 37, 8, 779-785 (1986) · Zbl 0598.90055 |
| [8] | Golden, B. L.; Wasil, E. A.; Levy, D. E., Applications of the Analytic Hierarchy Process: A categorized, annotated bibliography, (Golden, B. L.; Wasil, E. A.; Harker, P. T., The Analytic Hierarchy Process: Applications and Studies (1989), Springer-Verlag: Springer-Verlag Berlin), 37-58 |
| [9] | Honert, R. C.van den, Stochastic group preference modelling in the Multiplicative AHP: A model of group consensus, (Technical Reports of the Faculty of Technical Mathematics and Informatics No. 95-87 (1995), Delft University of Technology: Delft University of Technology Delft, The Netherlands) · Zbl 0936.91014 |
| [10] | Ijiri, Y., Management Goals and Accounting for Control (1964), Rand McNally: Rand McNally Chicago, IL |
| [11] | Kall, P.; Wallace, S. W., Stochastic Programming (1994), Wiley: Wiley Chichester · Zbl 0812.90122 |
| [12] | Kataoka, S., A stochastic programming model, Econometrica, 31, 1-2, 181-196 (1963) · Zbl 0125.09601 |
| [13] | Khorramshahgol, R.; Moustakis, V. S., Delphic Hierarchic Process (DHP): A methodology derived from the Delphi method and Analytic Hierarchy Process, European Journal of Operational Research, 37, 347-354 (1988) · Zbl 0652.90065 |
| [14] | Kolbin, V. V., Stochastic Programming (1977), D. Reidel: D. Reidel Dordrecht · Zbl 0359.90043 |
| [15] | Korhonen, P.; Wallenius, J., Using qualitative data in multiple objective linear programming, European Journal of Operational Research, 46, 81-87 (1990) |
| [16] | Lootsma, F. A., Numerical scaling of human judgement in pairwise-comparison methods for fuzzy multi-criteria decision analysis, (Mitra, G., Mathematical Models for Decision Support (1988), Springer-Verlag: Springer-Verlag Berlin), 57-88 |
| [17] | Lootsma, F. A., Scale sensitivity in the Multiplicative AHP and SMART, Journal of Multi-Criteria Decision Analysis, 2, 87-110 (1993) · Zbl 0838.90009 |
| [18] | Olson, D. L.; Fliedner, G.; Currie, K., Comparison of the REMBRANDT system with analytic hierarchy process, European Journal of Operational Research, 82, 522-539 (1995) · Zbl 0905.90112 |
| [19] | Ramanathan, R., A note on the use of Goal Programming for Multiplicative AHP, (Technical Reports of the Faculty of Technical Mathematics and Informatics No. 95-106 (1995), Delft University of Technology: Delft University of Technology Delft, The Netherlands) · Zbl 0889.90009 |
| [20] | Ramanathan, R.; Ganesh, L. S., Energy resource allocation incorporating quantitative and qualitative criteria: An integrated model using Goal Programming and AHP, Socio-Economic Planning Sciences, 29, 197-218 (1995) |
| [21] | Sengupta, J. K., Stochastic Programming: Methods and Applications (1972), North-Holland: North-Holland Amsterdam · Zbl 0262.90049 |
| [22] | Saaty, T. L., The Analytic Hierarchy Process: Planning, Priority Setting and Resource Allocation (1980), McGraw-Hill: McGraw-Hill New York · Zbl 0587.90002 |
| [23] | Saaty, T. L., Multicriteria Decision Making: The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, (The Analytic Hierarchy Process Series: Volume I (1990), RWS Publications: RWS Publications Pittsburgh, PA) · Zbl 1176.90315 |
| [24] | Saaty, T. L., Fundamentals of Decision Making and Priority Theory with the Analytic Hierarchy Process, (The Analytic Hierarchy Process Series: Volume VI (1994), RWS Publications: RWS Publications Pittsburgh, PA) · Zbl 1176.90315 |
| [25] | Shim, J. P., Bibliographical research on the Analytic Hierarchy Process (AHP), Socio-Economic Planning Sciences, 23, 3, 161-167 (1989) |
| [26] | Stewart, T. J., A critical survey on the status of multicriteria decision making theory and practice, Omega, 20, 569-586 (1992) |
| [27] | Wets, R. J.-B., Stochastic programming: Solution techniques and approximation schemes, (Bachem, A.; Grotschel, M.; Korte, B., Mathematical Programming: The State of the Art, Bonn, 1982 (1983), Springer-Verlag: Springer-Verlag Berlin), 566-603 · Zbl 0551.90070 |
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