Embedding Best-Worst Method into Data Envelopment Analysis

Abstract

In real-life applications, there generally exist Decision Makers (DMs) who have preferences over outputs and inputs. Choosing appropriate weights for different criteria by DMs often arises as a problem. The Best-Worst Method (BWM) in Multiple Criteria Decision-Making (MCDM) depends on very few pairwise comparisons and just needs DMs to identify the most desirable and the least desirable criteria. Unlike MCDM, Data Envelopment Analysis (DEA) does not generally assume a priority for an output (an input) over any other outputs (inputs). The link between DEA and MCDM can be introduced by considering Decision-Making Units (DMUs) as alternatives, outputs as criteria to be maximized, and inputs as criteria to be minimized. In this study, we propose a linear programming model to embed DEA and BWM appropriately. We first propose a modified BWM linear programming model to satisfy all conditions that DMs can assume. We then illustrate how a conventional DEA model can be developed to include the BWM conditions. From our approach, the MCDM problem to obtain the optimal weights of different criteria are measured. At the same time, the relative efficiency scores of DMUs corresponding to the MCDM criteria are also calculated. We provide the foundation of measuring the efficiency scores when most desirable and the least desirable inputs and outputs are known. To show the process of the proposed approach, a numerical example (including 17 DMUs with seven inputs and outputs) is also discussed.