On the derivation of the delta formulation for decision value

This paper contains decision analytical approaches, conditions and models for the quantification of decision values for built environment systems. Specifically, (1) delta formulations of objective functions for decision value quantification are introduced, (2) conditions for decision value are identified and (3) action value analysis formulations are further developed. The delta objective functions are formulated with differences in utility, cost, and probabilities for consistent decision identification by expected utility and value. The delta formulations facilitate the direct calculation of action and information values and the explication of conditions for a positive decision value. Action value objective functions are derived in delta formulation for the action types of utility and system state actions and with action implementation states and action uncertainty models. The delta formulations are exemplified for predicted information and predicted actions values. The paper closes with a synthesis and discussion of decision values and with findings encompassing a computational effort reduction and the identification of predicted information value mechanisms.