A dynamic multi-stage slacks-based measure data envelopment analysis model with knowledge accumulation and technological evolution

Abstract

Dynamic data envelopment analysis (DEA) models are built on the idea that single period optimization is not fully appropriate to evaluate the performance of decision making units (DMUs) through time. As a result, these models provide a suitable framework to incorporate the different cumulative processes determining the evolution and strategic behavior of firms in the economics and business literatures. In the current paper, we incorporate two distinct complementary types of sequentially cumulative processes within a dynamic slacks-based measure DEA model. In particular, human capital and knowledge, constituting fundamental intangible inputs, exhibit a cumulative effect that goes beyond the corresponding factor endowment per period. At the same time, carry-over activities between consecutive periods will be used to define the pervasive effect that technology and infrastructures have on the productive capacity and efficiency of DMUs. The resulting dynamic DEA model accounts for the evolution of the knowledge accumulation and technological development processes of DMUs when evaluating both their overall and per period efficiency. Several numerical examples and a case study are included to demonstrate the applicability and efficacy of the proposed method.