Time-staged outputs in DEA

• In DEA outputs generally occur at the same point in time.
• Sometimes outputs occur earlier than others, impacting those others.
• A new methodology is developed to handle such “time-staged outputs”.
• Methodology is applied to efficiency of a set of business schools.

This paper examines the issue of handling outputs in DEA that occur at different stages in time. As a backdrop for the research we examine a data set involving the evaluation of efficiencies of business schools. The data focuses explicitly on a particular institution, namely the business school ENCSH (Escuela de Negocios, Ciencias Sociales y Humanidades) at ITESM (Instituto Tecnologico y de Estudios Superiores Monterrey) in Mexico. This school of business is evaluated relative to 41 peer institutions in the USA, using data envelopment analysis as the principal evaluation instrument. Using internships and jobs as outputs, and various quality measures as inputs, we demonstrate that this problem setting gives rise to the phenomenon of time-staged outputs. Specifically, the two outputs occur at different points in time, meaning that one of them plays a dual role. While this problem might potentially be viewed as a type of network DEA model, we demonstrate that a modification of the conventional DEA methodology is a more appropriate structure to handle this situation.