An Analytical Framework for the Linear Best-Worst Method

Abstract The Best-Worst Method (BWM) has emerged as a prominent multi-criteria decision-making method for determining the weights of the decision criteria. Among various BWM models, this research focuses on the linear model of the BWM. This model generates a unique weight set by solving an optimization problem, which traditionally necessitates the use of optimization software. However, its claim of uniqueness has thus far been observation-based rather than mathematically proven. In this article, we present a novel framework that solves this optimization model analytically, deriving a closed-form expression for the resultant weights. This approach eliminates the dependency on optimization software while simultaneously providing a rigorous mathematical proof of uniqueness. Based of this framework, we demonstrate the model’s limited response to data variations, i.e., its lower data sensitivity. We also compute the values of consistency index for the linear BWM, which are required to calculate the consistency ratio—a consistency indicator used for assessing inconsistency in input data. The proposed approach is illustrated through five numerical examples. Extensive computational experiments are then conducted to confirm the correctness of the proposed approach and establish its superior efficiency over traditional optimization software-based methods. We demonstrate its applicability through a real-world case study that ranks eighteen drivers across three categories—Industry 4.0, sustainability, and circular economy—in relation to sustainable development goals—-driven agri-food supply chains. From an implementation perspective, the proposed framework enhances the model’s practical accessibility for non-expert practitioners and supports its deployment in real-time decision-making across dynamic environments and large-scale strategic contexts.