A Robust Model for the Best-Worst Method (BWM) Based on Goal Programming

The utilization of effective decision-making methodologies has historically captured the attention of decision-makers. The Best-Worst Method (BWM) is a prominent and extensively utilized technique in Multi Attribute Decision Making (MADM), owing to its simplicity, reduced number of pairwise comparisons, and high consistency of results. However, the original BWM operates under the assumption that decision-makers' judgments are precise and certain. In real-world conditions, uncertainty is prevalent. Furthermore, when addressing MADM problems that are not fully consistent and involve more than three criteria, the BWM technique may not result in a unique optimal solution. To address these limitations, this study proposes a Robust BWM approach based on goal programming and formulated as a linear optimization model. This approach incorporates interval preferences to model uncertainty in judgments. Additionally, a methodology is put forward to assess the Consistency Ratio (CR) of input data in the presence of uncertainty, thereby ensuring the reliability of the results obtained. The performance of the model has been examined through six numerical examples, and its validity has been evaluated. The findings suggest that the proposed method exhibits adequate efficiency and performance in addressing MADM problems and managing uncertain data. Consequently, the proposed method can serve as an effective solution for decision-making problems in real-world and uncertainty-based environments.