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2007 | 2 | 117--136
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On Multicriteria Problems with Modification of Attributes

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In this paper we propose a mathematical model for multicriteria decision problems with alternatives which may change their properties in a direct response to external actions. We assume that the change of attributes may be controlled by the decision-maker taking into account that an improvement of the criteria values bears certain cost. Thus we get a bi-level multicriteria optimization problem: an optimal allocation of resources at the lower level, and finding the related nondominated outputs surpassing a reference point q at the higher level. A concrete problem of this type, motivated by technological, ecological and socio-economical applications, will be discussed in more detail, namely optimizing the structure of a finite population X by assuring that after a fixed time T a maximal number of its elements is characterized by nondominated values of criteria. Assuming that X consists of N elements, the solution to this problem is equivalent to solving in parallel N discrete dynamic programming problems sharing the same resources. (original abstract)
Opis fizyczny
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