An Analytical Framework for the Linear Best-Worst Method and its Application to Achieve Sustainable Development Goals--Oriented Agri-Food Supply Chains

TL;DR

This paper introduces an analytical framework for the linear Best-Worst Method, providing explicit weight calculations that improve clarity and efficiency, and demonstrates its application to sustainable agri-food supply chains.

Contribution

The paper presents a novel mathematical solution for the linear BWM, removing the need for optimization software and enhancing computational efficiency and conceptual understanding.

Findings

The analytical framework simplifies weight calculation in linear BWM.

The method shows lower sensitivity to data variations.

It effectively ranks drivers related to sustainability goals in agri-food chains.

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 calculates weights by solving an optimization problem, necessitating optimization software. In this article, we present a novel framework that solves this optimization model mathematically, yielding an analytical expression for the resultant weights, thus eliminating the requirement for an optimization software. The proposed approach enhances both the conceptual clarity of the underlying optimization process and the computational efficiency of the model. 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. Finally, we illustrate the validity and applicability of the proposed approach through five numerical examples and 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.