Prepared under Contract no. EX-76-A-01-2295, Task order 37.

[In large and complicated management systems, solutions with the same indices, but with different degrees of aggregation, are used and coordinated. For example, in hierarchical systems, those in higher management levels make decisions with more aggregated indices than those in lower management levels. Managers of an individual subsystem within a large and complicated system use detailed information about their own subsystem and aggregated information (in some degree or other) about other subsystems. The principal idea of the iterative aggregation method is to consecutively recompute the aggregated indices characterizing the activities of the whole system, followed by a recomputation of the detailed indices characterizing each of its subsystems. From a theoretical point of view these methods are generalizations of some classes of iterative and decomposition methods.]

Finite horizon sequential decision problems with a temporal von NeumannMorgenstern criterion are analyzed. This criterion, as developed in [7], is a generalization of von Neumann-Morgenstern (expected) utility of the vector of rewards, wherein an individual's preferences concerning the timing of the resolution of uncertainty are taken into account. The preference theory underlying this criterion is reviewed and then extended in natural fashion to yield preferences for strategies in sequential decision problems. The main result is that value functions for sequential decision problems can be defined by a dynamic programming recursion using the functions which represent the original preferences, and these value functions represent the preferences defined on strategies. This permits citation of standard results from the dynamic programming literature, concerning the existence of (memoryless) strategies which are optimal with respect to the given preference relation.