Analytic Network Process With Feedback Influence: A New Approach to Impact Study *

This paper introduces a network model (Analytic Network Process) for impact study incorporating feedback influences, capable of capturing and combining tangible and intangible factors by using ratio scales. Contrasting it with a hierarchy model, some distinct features are identified. While the two rely on pair-wise comparison matrix and its corresponding eigenvector, the dependence of elements between clusters (outer dependence) and within cluster (inner dependence) in the network model necessitates the use of a stochastic supermatrix. Although there are different possibilities regarding the maximum eigen-value being equal to unity, i.e., multiple root or non-multiple root, the final priorities can be obtained by raising the supermatrix to large powers. Applying the model to an integrated impact and planning analysis of a highway construction, the results of the two models are found to be considerably different. It is revealed from sensitivity analysis that the outcomes of the network model are more stable and robust than those of the hierarchy model. A time dependent case is subsequently shown by using a numerical example. The model and its contrast with hierarchy models is discussed in the next Section. An example of application on an integrated impact and planning analysis using the case of a post-project evaluation of a highway construction is shown in the subsequent Section, followed by sensitivity analysis and the discussions on dynamic time dependent case. The sensitivity analysis shows that the results of the proposed model are not only different from those obtained from a hierarchy model but they are also more stable and robust.