Abstract
The multicriteria Bipolar method can be extended and used to control multicriteria, multistage decision processes. In this extension, at each stage of the given multistage process two sets of reference points are determined, constituting a reference system for the evaluation of stage alternatives. Multistage alternatives, which are compositions of stage alternatives, are assigned to one of six predefined hierarchical classes and then ranked. The aim of this paper is to show the possibility of finding the best multistage alternative, using Bellman’s optimality principle and optimality equations. Of particular importance is a theorem on the non-dominance of the best multistage alternative, proven here. The methodology proposed allows to avoid reviewing each multistage alternative, which is important in large-size problems. The method is illustrated by a numerical example and a brief description of the sustainable regional development problem. The problem can be solved by means of the proposed procedure.
Highlights
The reference point methodology is one of the most important concepts in multiple criteria decision making and has been extensively studied in the past
Almost simultaneously with the introduction of the classic Bipolar method, the question arose: is it possible to apply this approach to the analysis of multistage, multicriteria decision processes (Trzaskalik 1987)
The question arises: In order to find the best multistage alternative, is it necessary to examine all such alternatives? The present paper aims at showing that it is possible to find the best alternative using Bellman’s vector Principle of Optimality and optimality equations
Summary
The reference point methodology is one of the most important concepts in multiple criteria decision making and has been extensively studied in the past. Based on the concept of bipolar reference sets, Konarzewska-Gubała (1987, 1989) proposed a single-stage method, called Bipolar In her method, the author noticed that the motivation to achieve success and the motivation to avoid failure are not equivalent, the final evaluation of the decision alternatives is based on their position with respect to two segments of the reference system: ideal and nadir. The present paper is an attempt to reformulate this problem and to solve it using multiobjective dynamic programming. The present paper aims at showing that it is possible to find the best alternative using Bellman’s vector Principle of Optimality and optimality equations. Of importance is here the theorem on the non-domination of the best multistage alternative, proven in the paper. Applying that theorem and the vector version of Bellman’s Principle of Optimality, it is shown how multiobjective dynamic programming can be used to find the best multistage alternative.
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