ÇOK KRİTERLİ KARAR VERME PROBLEMLERİNDE FAYDA FONKSİYONU AĞIRLIKLARININ TAHMİN EDİLMESİ İÇİN MATEMATİKSEL MODEL TEMELLİ BİR YÖNTEM
Abstract
Çok Kriterli Karar Verme (ÇKKV) problemlerindeki
temel bir konu, karar vericinin (KV) tercihlerinin problem çözme sürecine dâhil
edilmesidir. Bu tercihler birçok yaklaşımda karar vermeye temel oluşturan
kriterlere atanan ağırlıklar şeklinde kullanılmaktadır. Ancak literatürdeki
çoğu ÇKKV yöntemi, ağırlıkların baştan bilindiğini kabul etmekte veya KV’nin bu
ağırlıkları doğru bir şekilde doğrudan ifade edebileceğini varsaymaktadır.
Kriter ağırlıklarını elde etmek için geliştirilen az sayıdaki yöntem,
genellikle kriterlerin direkt olarak birbirleriyle kıyaslanmasını gerektirmekte
ve KV’nin çok sayıda değerlendirme yapmasına ihtiyaç duymaktadır. Bu çalışmada
geliştirdiğimiz matematiksel programlama tabanlı yöntem, KV için bilişsel
zorluk yaratmayacak az sayıda tercih değerlendirmesi ile kriter ağırlıklarını
iyi bir şekilde tahmin etmektedir. KV’nin tercihlerini ağırlıklı toplam
şeklinde ifade edilen bir fayda fonksiyonuyla yaptığı varsayılmıştır. KV’den
direkt olarak kriterleri değerlendirmesi istenmemekte, sınırlı sayıda karar
alternatifini tercih sırasına sokması beklenmektedir. Geliştirilen yöntem, beş
kriterle değerlendirilen dünya üniversitelerinin sıralanması problemine
uygulanmıştır. Karşılaştırma yapmak amacıyla literatürde sıklıkla kullanılan
başka bir ağırlık tahmini yöntemi de (Swing yöntemi) aynı probleme
uygulanmıştır. Geliştirdiğimiz yaklaşımın bu yöntemden daha iyi sonuçlar
verdiği gözlemlenmiştir.
Keywords
Çok Kriterli Karar Verme Ağırlıklı toplam fayda fonksiyonu Ağırlık tahmini Üniversite sıralama Finansal portfolyo seçimi
References
- Brans, J. P., & Vincke, P., 1985. A Preference Ranking Organisation Method: The PROMETHEE Method for Multiple Criteria Decision-Making. Management science, 31(6), pp. 647-656.
- Hwang, C. L., Lai, Y. J., & Liu, T. Y., 1993. A new approach for multiple objective decision making. Computers & operations research, 20(8), pp. 889-899.
- Kahneman, D. & Tversky, A., 1974. Judgment under uncertainty: heuristics and biases. Science, 185(4157), pp.1124–1131.
- Kullback, S. 1959. Information theory and statistics, John Wiley and Sons, NY.
- Pekelman, D. & Sen, S.K., 1974. Mathematical Programming Models for the Determination of Attribute Weights. Management Science, 20(8), pp.1217–1229.
- Pomerol, J.-C. & Barba-Romero, S., 2012. Multicriterion decision in management: principles and practice, Springer Science & Business Media.
- Roy, B., 1968. Classement et choix en présence de points de vue multiples. Revue française d'informatique et de recherche opérationnelle, 2(8), pp. 57-75.
- Saaty, T.L., 2008. Decision making with the analytic hierarchy process. International Journal of Services Sciences, 1(1), p.83.
- Steuer, R.E., 1986. Multiple criteria optimization: theory, computation, and applications, John Wiley & Sons.
- Steuer, R.E. & Choo, E.-U., 1983. An Interactive Weighted Tchebycheff Procedure For Multiple Objective Programming. Mathematical Programming, 26, pp.326–344.
- Times Higher Education, 2015. World University Rankings 2015-2016 methodology. https://www.timeshighereducation.com/news/ranking-methodology-2016 [Erişim Tarihi: 20 Ekim 2017].
- Von Winterfeldt, D. & Edwards, W., 1986. Decision Analysis and Behavioural Research, Cambridge University Press.
- Zionts, S. & Wallenius, J., 1976. An Interactive Programming Method for Solving the Multiple Criteria Problem. Management Science, 22(6), pp.652–663. Available at: http://pubsonline.informs.org/doi/abs/10.1287/mnsc.22.6.652.
A Mathematical Modeling-based Method to Estimate Utility Function Weights in Multiple Criteria Decision Making Problems
Abstract
A basic issue in Multiple Criteria Decision Making (MCDM) problems is
to include the preferences of the decision maker (DM) in the problem solution
process. Many MCDM methods assume that DM preferences can be modeled in the
form of utility functions. The parameters of these functions represent varying
priorities of different DMs about the problem. Several approaches in the
literature assume that these parameters are already known or the DM can express
them directly and correctly. The approaches developed to derive preferential
parameters may require the DM to make many assessments and comparisons, and
involve complex procedures. The mathematical programming-based method developed
in this study estimates criteria weights in weighted sum utility functions by
few preference assessments without imposing cognitive difficulty on the DM. The
DM is not asked to directly evaluate criteria but to rank a limited number of alternatives
in preference order. The developed approach is applied to a financial portfolio
selection problem with three criteria and a university ranking problem with
five criteria. For comparison, the Swing method is also applied to the same
problems. The proposed method is observed to be more convenient, impose less
cognitive burden and provide superior results.
Keywords
Multiple Criteria Decision Making Weighted sum utility function Weight estimation University ranking Financial portfolio selection
References
- Brans, J. P., & Vincke, P., 1985. A Preference Ranking Organisation Method: The PROMETHEE Method for Multiple Criteria Decision-Making. Management science, 31(6), pp. 647-656.
- Hwang, C. L., Lai, Y. J., & Liu, T. Y., 1993. A new approach for multiple objective decision making. Computers & operations research, 20(8), pp. 889-899.
- Kahneman, D. & Tversky, A., 1974. Judgment under uncertainty: heuristics and biases. Science, 185(4157), pp.1124–1131.
- Kullback, S. 1959. Information theory and statistics, John Wiley and Sons, NY.
- Pekelman, D. & Sen, S.K., 1974. Mathematical Programming Models for the Determination of Attribute Weights. Management Science, 20(8), pp.1217–1229.
- Pomerol, J.-C. & Barba-Romero, S., 2012. Multicriterion decision in management: principles and practice, Springer Science & Business Media.
- Roy, B., 1968. Classement et choix en présence de points de vue multiples. Revue française d'informatique et de recherche opérationnelle, 2(8), pp. 57-75.
- Saaty, T.L., 2008. Decision making with the analytic hierarchy process. International Journal of Services Sciences, 1(1), p.83.
- Steuer, R.E., 1986. Multiple criteria optimization: theory, computation, and applications, John Wiley & Sons.
- Steuer, R.E. & Choo, E.-U., 1983. An Interactive Weighted Tchebycheff Procedure For Multiple Objective Programming. Mathematical Programming, 26, pp.326–344.
- Times Higher Education, 2015. World University Rankings 2015-2016 methodology. https://www.timeshighereducation.com/news/ranking-methodology-2016 [Erişim Tarihi: 20 Ekim 2017].
- Von Winterfeldt, D. & Edwards, W., 1986. Decision Analysis and Behavioural Research, Cambridge University Press.
- Zionts, S. & Wallenius, J., 1976. An Interactive Programming Method for Solving the Multiple Criteria Problem. Management Science, 22(6), pp.652–663. Available at: http://pubsonline.informs.org/doi/abs/10.1287/mnsc.22.6.652.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 24, 2018 |
| Submission Date | October 25, 2017 |
| Acceptance Date | April 10, 2018 |
| Published in Issue | Year 2018 Volume: 23 Issue: 1 |
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