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Fire hazard analysis often includes the use of mathematical models of the egress of the individual occupants of a structure which is involved in a fire. In this paper, we introduce some mathematical optimization models which produce as output at least one path for each occupant which is optimal with respect to some measurement. Network based models of increasing levels of complexity and realism are demonstrated by means of a sequence of examples. These examples include single attribute constant costs, single attribute timevarying costs, two attribute constant costs, and finally two attribute time-varying costs imposed on network links. Dynamic programming functional equations which are based on the principle of optimality are presented. A multi-attribute analysis is proposed to evaluate a building design with respect to evacuation paths.

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In this paper a two-stage algorithm for finding nondominated 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.