A multi-period output DEA model with consistent time lag effects

• Describe multi-period input (MPI) model and multi-period output (MPO) model.
• Modify the MPO model to consider consistent time lag effect.
• Some lemmas are given to describe some properties of the suggested model.
• Compare MPO and consistent time lag MPO using the data set of long term R&D projects.

Conventional data envelopment analysis (DEA) models assume that the inputs of a specific period are consumed to produce the outputs of the same period. However, in some applications, the inputs of a period can be thought to partially contribute to the outputs of several subsequent periods. This can be described as time lag effects for performance evaluation. A few researches have presented DEA models using the time lag weights of input or output factors to address the time lag effects. In those models, the weights for the time lag effects can vary by period. In this paper, we propose another DEA model with consistent weights for time lag effects throughout the periods. The proposed model is more realistic and more discriminative than the existing time lag model. We present the results of a case example for comparison of the proposed model and the existing time lag model.