We develop a new Data Envelopment Analysis (DEA)-based methodology for measuring the efficiency of Decision Making Units (DMUs) characterized by multiple inputs and multiple outputs. The distinguishing feature of our method is that it explicitly includes information about output-specific inputs and joint inputs in the efficiency evaluation. This contributes to opening the “black box” of efficiency measurement in two different ways. First, including information on the input allocation substantially increases the discriminatory power of the efficiency measurement. Second, it allows us to decompose the efficiency value of a DMU into output-specific efficiency values which facilitates the identification of the outputs the manager should focus on to remedy the observed inefficiency. We demonstrate the usefulness and managerial implications of our methodology by means of a unique data set collected from the Activity Based Costing (ABC) system of a large service company with 290 DMUs.