Weak congestion in output additive data envelopment analysis

Our earlier work [Wei QL, Yan H. Congestion and returns to scale in data envelopment analysis. European Journal of Operational Research 2004;153:641-60] discussed necessary and sufficient conditions for the existence of congestion together with aspects of returns to scale under an output-oriented DEA framework. In line with this work, the current paper investigates the issue of "weak congestion", wherein congestion occurs when the reduction of selected inputs causes some, rather than all, outputs to increase, without a worsening of others. We define output efficiency for decision making units under a series of typical DEA output additive models. Based on this definition, we offer necessary and sufficient conditions for the existence of weak congestion. Numerical examples are provided for purposes of illustration.