Further Studies of Scale Elasticity in Multi-input Multi-output Production Technologies: Network DEA Modelling and Applications

Scale properties, including scale elasticity (SE) and returns to scale (RTS), are important characteristics of the production frontier and play an essential role in analyzing the productivity of strongly efficient decision-making units (DMU). For multi-input multi-output production technologies, scale elasticity (SE) has been defined as the largest proportional change in outputs in response to a marginal proportional change of inputs. Given the network data envelopment analysis (DEA), existing research focused on estimating SE for each sub-technology to locate the sources of scale economies in network technologies. However, the relationship between the overall SE and the SE in each sub-technology is unclear since the existing methods of estimating SE in sub-technologies rely on separately extracting the transformation function of each sub-technology. Moreover, the existing research on estimating SE in network production technologies ignored the non-proportional changes and undesirable outputs. This thesis, therefore, will develop methods of estimating and decomposing SE based on the response function defined by various network production technologies. The main contributions of this thesis are as follows.

• For multi-activity and multi-stage technologies, two DEA-based methods of decomposing SE are proposed, respectively. The first method automatically allocates weights of SE in each activity, and the second method can yield a unique solution for each sub-stage while reflecting the special scale status of the points that cannot further increase the intermediate products.

• It develops directional scale elasticity (DSE) in multi-activity and multistage technologies, respectively, followed by exploring the potential directions to maximise the value of DSE by using heuristic searching.

• Considering the assumptions of strong and selective weak disposability in undesirable outputs, it proposes novel multi-activity and two-stage production technologies with undesirable measures, and develops the corresponding methods to estimated SE.

• It develops a novel method of estimating and decomposing SE in a proposed network technology with two-stage parallel structures. A case study in the context of the sustainability evaluation of commercial banks illustrates the method.