Taxicab distance based best-worst method for multi-criteria decision-making: An analytical approach

TL;DR

This paper introduces an analytical framework for the taxicab distance based Best-Worst Method in multi-criteria decision-making, revealing multiple optimal solutions and improving computational efficiency without relying on optimization software.

Contribution

It develops an analytical solution for the taxicab BWM, demonstrating multiple optimal weights and providing a mathematical foundation that enhances understanding and efficiency.

Findings

Multiple optimal weight sets can occur in taxicab BWM.

The framework eliminates the need for optimization software.

Numerical examples validate the proposed approach.

Abstract

The Best-Worst Method (BWM) is a well-known distance based multi-criteria decision-making method used for computing the weights of decision criteria. This article examines a taxicab distance based model of the BWM, with the objective of developing a framework for deriving the model's optimal weights by solving its associated optimization problem analytically. To achieve this, an optimal modification based optimization problem, equivalent to the original one, is first formulated. This reformulated problem is then solved analytically, and the optimal weight sets are derived from its solutions. Contrary to existing literature that asserts the uniqueness of optimal weight sets based on numerical examples, our findings reveal that, in some cases, the taxicab BWM leads to multiple optimal weight sets. A mixed-integer linear programming model is then employed to compute the consistency index. This framework provides a solid mathematical foundation that enhances understanding of the model. It also eliminates the requirement for optimization software, improving the model's precision and efficiency. Finally, the effectiveness of the proposed framework is demonstrated through numerical examples.