Interactive Procedure for Multiobjective Dynamic Programming with the Mixed Ordered Structure

• Authors: Nowak Maciej , Sitarz Sebastian , Trzaskalik Tadeusz
• Languages of publication: EN

Abstracts

EN

The paper presents a multiobjective dynamic programming problem with the values of the criteria function in ordered structures. The first problem is a model with deterministic values; the second, one with triangular fuzzy numbers; and the third, one with discrete random variables with the k-th absolute moment finite. The fourth model is a product of the three models listed above. The aim of the paper is to present an interactive procedure which uses trade-offs and which allows to determine the final solution in the mixed ordered structure. The ordered structures and the proposed procedure are illustrated by numerical examples.

Keywords

EN

Interactive procedures; Multiobjective dynamic programming

PL

Procedury interaktywne; Wielokryterialne programowanie dynamiczne

• Publisher: Uniwersytet Ekonomiczny w Katowicach
• Journal: Multiple Criteria Decision Making
• Year: 2017
• Volume: 12
• Pages: 168-184

Contributors

author

Nowak Maciej

• University of Economics in Katowice. Faculty of Informatics and Communication. Department of Operations Research. Katowice, Poland

author

Sitarz Sebastian

• University of Silesia. Institute of Mathematics. Katowice, Poland

author

Trzaskalik Tadeusz

• University of Economics in Katowice. Faculty of Informatics and Communication. Department of Operations Research. Katowice, Poland

References

• Bellman R.E. (1957), Dynamic Programming, Princeton University Press, Princeton.
• Benayoun R., De Montgolfier J., Tergny J., Laritchev O. (1971), Linear Programming with Multiple Objective Functions: Step Method (STEM), Mathematical Programming, 1(1), 366-375.
• Henig M.I. (1985), The Principle of Optimality in Dynamic Programming with Returns in Partially Ordered Sets, Mathematics of Operations Research, 10(3), 462-470.
• Korhonen P.J., Laakso J. (1986), A Visual Interactive Method for Solving the Multiple Criteria Problem, European Journal of Operational Research, 24(2), 277-287.
• Li D., Haimes Y.Y. (1989), Multiobjective Dynamic Programming: The State of the Art, Control Theory and Advanced Technology, 5(4), 471-483.
• Miettinen K., Makela M.M. (2000), Interactive Multiobjective Optimization System WWWNIMBUS on the Internet, Computers & Operations Research, 27(7), 709-723.
• Mitten L.G. (1974), Preference Order Dynamic Programming, Management Science, 21(1), 43-46.
• Nowak M. (2006), INSDECM – An Interactive Procedure for Discrete Stochastic Multicriteria Decision Making Problems, European Journal of Operational Research, 175(3), 1413-1430.
• Nowak M. (2007), Aspiration Level Approach in Stochastic MCDM Problems, European Journal of Operational Research, 177(3), 1626-1640.
• Nowak M. (2010), Trade-Off Analysis in Discrete Decision Making Problems Under Risk [in:] Jones D., Tamiz M., Ries J. (eds), New Developments in Multiple Objective and Goal Programming. Lecture Notes in Economics and Mathematical Systems, Vol. 638, Springer, Berlin, Heidelberg.
• Nowak M., Trzaskalik T. (2013), Interactive Procedure for a Multiobjective Stochastic Discrete Dynamic Problem, Journal of Global Optimization, 57(2), 315-330.
• Özpeynirci Ö., Özpeynirci S., Kaya A. (2017), An Interactive Approach for Multiple Criteria Selection Problem, Computers & Operations Research, 78, 154-162.
• Sobel M.M. (1975), Ordinal Dynamic Programming, Management Science, 21(9), 967-975.
• Steinberg E., Parks M.S. (1979), A Preference Order Dynamic Program for a Knapsack Problem with Stochastic Reward, Operational Research Society Journal, 30(2), 141-147.
• Steuer R.E. (1977), An Interactive Multiple Objective Linear Programming Procedure, TIMS Studies in the Management Sciences, 6, 225-239.
• Trzaskalik T. (1991), Wielokryterialne dyskretne programowanie dynamiczne. Teoria i zastosowania w praktyce gospodarczej, Wydawnictwo Akademii Ekonomicznej im. Karola Adamieckiego, Katowice.
• Trzaskalik T. (1998), Multiobjective Analysis in Dynamic Environment, Karol Adamiecki University of Economics Press, Katowice.
• Trzaskalik T., Hoa D.T. (1999), Wielokryterialne, wieloetapowe procesy decyzyjne w warunkach niepewności [in:] Trzaskalik T. (ed.), Modelowanie preferencji a ryzyko ’99. Część II, 409-423.
• Trzaskalik T., Sitarz S. (2002), Dynamic Discrete Programming with Partially Ordered Criteria Set [in:] Trzaskalik T., Michnik J. (eds.), Multiple Objective and Goal Programming. Recent Developments, Physica-Verlag, 186-195.
• Trzaskalik T., Sitarz S. (2004), Modele programowania dynamicznego w strukturach porządkowych [in:] Kulikowski R., Kacprzyk J. and Słowiński R. (eds.), Badania operacyjne i systemowe’04. Podejmowanie decyzji. Podstawy metodyczne i zastosowania, EXIT, Warszawa, 15-30.
• Trzaskalik T., Sitarz S. (2007), Discrete Dynamic Programming with Outcomes in Random Variable Structures, European Journal of Operational Research, 177(3), 1535-1548.
• Zaras K. (2004), Rough Approximation of a Preference Relation by a Multi-Attribute Dominance for Deterministic, Stochastic and Fuzzy Decision Problems, European Journal of Operational Research, 159(1), 196-206.

Identifiers

ISSN

2084-1531