General network production theory for good and bad inputs and outputs

Abstract

The paper systematically extends a recently developed general production theory for networks of arbitrarily complex structure by utilising multi-criteria analysis to include undesirable objects as inputs and outputs. By embedding Koopmans’ linear activity analysis into the broader framework the approach is generic in that it requires rather weak technological properties, thus allowing non-convex and even discrete production possibilities without any disposability property. The modelling approach can often be more appropriate than conventional ones and can be easily extended to dynamic analyses, since its network flow equations are based on balances that can integrate inventories in cases of material inputs and outputs. Theorems are proved that relate important properties of whole networks (e.g. convexity) or of their activities (e.g. efficiency) to those of their individual production units. Common methods of efficiency measurement are integrated in such a way that network data envelopment analysis for bads as inputs or outputs is embedded as the special case focusing specifically on polyhedral technologies. By applying different types of efficiency measures, a systematic procedure for evaluating the performance of network activities is demonstrated for the example of a two-stage production and abatement network and its subsystem with parallel units.