[Article] Counterfactual Analysis in Benchmarking
Peter Bogetoft Jasone Ramirez-Ayerbe Dolores Romero Morales
Description: Traditional benchmarking based on simple key performance indicators is widely used and easy to understand. Unfortunately, such indicators cannot fully capture the complex relationship between multiple inputs and outputs in most firms. Data Envelopment Analysis (DEA) offers an attractive alternative. It builds an activity analysis model of best practices considering the multiple inputs used and products and services produced. This allows more substantial evaluations and also offers a framework that can support many other operational, tactical and strategic planning efforts. Unfortunately, a DEA model may be hard to understand by managers. In turn, this may lead to mistrust in the model, and to difficulties in deriving actionable information from the model beyond the efficiency scores. In this paper, we propose the use of counterfactual analysis to overcome these problems. We define DEA counterfactual instances as alternative combinations of inputs and outputs that are close to the original inputs and outputs of the firm and lead to desired improvements in its performance. We formulate the problem of finding counterfactual explanations in DEA as a bilevel optimization model. For a rich class of cost functions, reflecting the effort an inefficient firm will need to spend to change to its counterfactual, finding counterfactual explanations boils down to solving Mixed Integer Convex Quadratic Problems with linear constraints. We illustrate our approach using both a small numerical example and a real-world dataset on banking branches.