An Analytical Framework for the Multiplicative Best-Worst Method

The Best-Worst Method (BWM) is a well-known Multi-Criteria Decision-Making (MCDM) method. Numerous models of BWM have been developed by integrating various distance functions with the core principles of the method. This article addresses the multiplicative model of BWM. We first formulate an optimization model that is equivalent to the existing multiplicative model. This model provides a robust foundation for deriving analytical forms of optimal interval-weights, the Consistency Index (CI) and the Consistency Ratio (CR). The proposed approach eliminates the need for optimization software, enhancing its ease of implementation and time efficiency. Moreover, the derived analytical form of CR enables it to function as an input-based consistency measure. We then introduce a secondary objective function to select the best optimal weight set from the collection of all optimal weight sets. Finally, we present numerical examples to illustrate the proposed approach.