Concurrent estimation of efficiency, effectiveness and returns to scale

In recent years, data envelopment analysis (DEA) has been widely used to assess both efficiency and effectiveness. Accurate measurement of overall performance is a product of concurrent consideration of these measures. There are a couple of well-known methods to assess both efficiency and effectiveness. However, some issues can be found in previous methods. The issues include non-linearity problem, paradoxical improvement solutions, efficiency and effectiveness evaluation in two independent environments: dividing an operating unit into two autonomous departments for performance evaluation and problems associated with determining economies of scale. To overcome these issues, this paper aims to develop a series of linear DEA methods to estimate efficiency, effectiveness, and returns to scale of decision-making units (DMUs), simultaneously. This paper considers the departments of a DMU as a united entity to recommend consistent improvements. We first present a model under constant returns to scale (CRS) assumption, and examine its relationship with one of existing network DEA model. We then extend model under variable returns to scale (VRS) condition, and again its relationship with one of existing network DEA models is discussed. Next, we introduce a new integrated two-stage additive model. Finally, an in-depth analysis of returns to scale is provided. A case study demonstrates applicability of the proposed models.