Data Envelopment Analysis with Reverse Inputs and Outputs

Data envelopment analysis (DEA) assumes that inputs and outputs are measured on scales in which larger numerical values correspond to greater consumption of inputs and greater production of outputs. We present a class of DEA problems in which one or more of the inputs or outputs are naturally measured on scales in which higher numerical values represent lower input consumption or lower output production. We refer to such quantities as reverse inputs and reverse outputs. We propose to incorporate reverse inputs and outputs into a DEA model by returning to the basic principles that lead to the DEA model formulation. We compare our method to reverse scoring, the most commonly used approach, and demonstrate the relative advantages of our proposed technique. We use this concept to analyze all 30 Major League Baseball (MLB) organizations during the 1999 regular season to determine their on-field and front office relative efficiencies. Our on-field DEA model employs one output and two symmetrically defined inputs, one to measure offense and one to measure defense. The defensive measure is such that larger values correspond to worse defensive performance, rather than better, and hence is a reverse input. The front office model uses one input. Its outputs, one of which is a reverse output, are the inputs to the on-field model. We discuss the organizational implications of our results.