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

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 decisions. A computational application to time-dependent fuzzy dynamic programming is presented.