International Journal of Information Engineering and Electronic Business(IJIEEB)

ISSN: 2074-9023 (Print), ISSN: 2074-9031 (Online)

Published By: MECS Press

IJIEEB Vol.7, No.1, Jan. 2015

Compromise Hypersphere for Multi-Criteria Dynamic Programming

Full Text (PDF, 532KB), PP.1-7

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Sebastian Sitarz

Index Terms

Dynamic programming;multi-criteria decision making;compromise hypersphere


The paper considers multi-criteria dynamic decision process. We focus on the efficient realizations of the dynamic process which are characterized by non-dominated values of the multi-period criteria function. The aim of the paper is to use the compromise hypersphere method to rank the efficient realizations. The presented method allows us to take into account the risk aversion of the decision maker. Moreover, we apply the presented theory in the market model taken from microeconomic theory.

Cite This Paper

Sebastian Sitarz,"Compromise Hypersphere for Multi-Criteria Dynamic Programming", IJIEEB, vol.7, no.1, pp.1-7, 2015. DOI: 10.5815/ijieeb.2015.01.01


[1]Sitarz S., "Pareto Optimal Allocations and Dynamic Programming", Annals of Operations Research, 172/1, 203-219, 2009. 

[2]Sitarz S., "Dynamic Programming with Ordered Structures: Theory, Examples and Applications", Fuzzy Sets and Systems, 161, 2623–2641, 2010.

[3]Bazgan C, Hugot H., Vanderpooten D., "Solving efficiently the 0–1 multi-objective knapsack problem", Computers and Operations Research, 36, 260-279, 2009.

[4]Sitarz S., "Multiple Criteria Dynamic Programming and Multiple Knapsack Problem", Applied Mathematics and Computation, 228, 598-605, 2014.

[5]Woerner S., Laumanns R., Fertis A., "Approximate dynamic programming for stochastic linear control problems on compact state spaces", European Journal of Operational Research, 241, 85-98, 2015.

[6]Gass S. I., Roy P. G., "The compromise hypersphere for multiobjective linear programming", European Journal of Operational Research 144, 459–479, 2003.

[7]Charnes A., Cooper W. W., "Goal Programming and Mulitple Objective Optimiaztion", European Journal of Operation Research, 1, 39-45, 1957.

[8]Zeleny M., "Multiple Criteria Decision Making", McGraw-Hill Book Company, New York, 1982.

[9]Trzaskalik T., Sitarz S., "Discrete dynamic programming with outcomes in random variable structures", European Journal of Operational Research, 177/3, 1535-1548, 2007. 

[10]Sitarz S., "Hybrid methods in multi-criteria dynamic programming", Applied Mathematics and Computation, 180/1, 38-45, 2006.

[11]Sitarz S., "Discrete dynamic programming in ordered structures and its applications". Ph. D., University of Lodz, Poland, (in polish), 2003.

[12]Ballestero E., "Selecting the CP metric: A risk aversion approach", European Journal of Operational Research, 97, 593–596, 1996.

[13]Ekeland I., "Elements d'economic mathematic", Hermann, Paris, 1979.

[14]Opricovic S., Tzeng G.H., "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS", European Journal of Operational Research, 156, 445-455, 2004.

[15]Sitarz S., "Approaches to sensitivity analysis in MOLP", International Journal of Information Technology and Computer Science, 6 (3), 54-60, 2014.