Abstract: Congestion is an unfavorable economic phenomenon where the production efficiency is damaged by excessive increase of inputs. As a main source of inefficiency, congestion has been widely explored in both academia and industry. A common assumption in existing studies is that all inputs and outputs of decision making units (DMUs) are desirable. However, bunches of situations where output indices are undesirable exist in real applications. In this paper, the congestion measurement for DMUs with undesirable outputs is explored. First, the definition of congestion for DMUs with undesirable outputs is developed. Then, based on the input relaxation model, a one-model approach is established to measure the congestion in the presence of both desirable and undesirable outputs. By applying the proposed model, not only the existence of congestion is determined, but also the amount of congestion in each input is measured. Furthermore, the relationship between congestion and technical inefficiency is demonstrated. Finally, an empirical study of listed commercial banks in China is employed to test the congestion performance via the proposed approach. The results show that a high degree of congestion is detected for most commercial banks and the congestion varies among state-owned banks, stock banks and urban commercial banks. Some practical policy suggestions are provided to relieve bank congestions. To some extent, the proposed approach enriches the theoretical research on the congestion of DMUs with undesirable outputs. Empirically, feasible improvement strategies are provided for decision makers who face congestion problems.

Key words: undesirable outputs, congestion, technical inefficiency, commercial banks