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A dimension-reduction algorithm for multi-stage decision problems with returns in a partially ordered set

Teodros GetachewMichael M. Kostreva — 2002

RAIRO - Operations Research - Recherche Opérationnelle

In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming via the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real” valued...

A Dimension-Reduction Algorithm for Multi-Stage Decision Problems with Returns in a Partially Ordered Set

Teodros GetachewMichael M. Kostreva — 2010

RAIRO - Operations Research

In this paper a two-stage algorithm for finding non- dominated subsets of partially ordered sets is established. A connection is then made with dimension reduction in time-dependent dynamic programming the notion of a bounding label, a function that bounds the state-transition cost functions. In this context, the computational burden is partitioned between a time-independent dynamic programming step carried out on the bounding label and a direct evaluation carried out on a subset of “real" valued...

Linear optimization with multiple equitable criteria

Michael M. KostrevaWodzimierz Ogryczak — 2010

RAIRO - Operations Research

The standard multiple criteria optimization starts with an assumption that the criteria are incomparable. However, there are many applications in which the criteria express ideas of allocation of resources meant to achieve some equitable distribution. This paper focuses on solving linear multiple criteria optimization problems with uniform criteria treated in an equitable way. An axiomatic definition of equitable efficiency is introduced as an refinement of Pareto-optimality. Various generation...

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