On modeling dynamic priorities in the analytic hierarchy process using compositional data analysis

In a rapidly changing environment, the priorities derived using the analytic hierarchy process (AHP) approach at one point in time might very likely change in the near future. Thus, in order to adapt to such ever-changing environment, it is of primary importance to be able to follow the change over time as to enable the system to respond differently and continuously over time of its operation. This paper proposes the use of a time-based compositional forecasting method, which is based on the idea of exponential smoothing, to deal with the AHP priority dynamics. The proposed method is particularly useful when there is a limited number of historical data, and might be considered to be more effective and time-efficient compared to that of multivariate time series method. It was also shown that the proposed method provides much greater adaptability in modeling the AHP priorities change over time compared to that of recently developed methods in compositional data research field. The shortcoming of Saaty's dynamic judgment approach and some limitations of the other existing methods will be discussed. Finally, to substantiate the validity of the proposed method and to give some practical insights, an illustrative case study is provided.