An inverse DEA model for intermediate and output target setting in serially linked general two-stage processes

Abstract

Abstract In this paper, we formulate an inverse data envelopment analysis (DEA) model for a serially linked two-stage production process operating under constant returns to scale technology. The inverse DEA model determines a set of intermediate and output targets for an input augmented decision-making unit (DMU) to maintain its relative efficiency at a pre-specified level. We solve the inverse DEA model using the constraint method used in multi-objective optimization. The input augmented DMU with intermediate and output targets obtained in the inverse DEA model is a hypothetical DMU. Under our modelling framework, when such a hypothetical DMU established on an inefficient DMU is included in the observed DMU set, the frontier established with observed DMU set remains intact. This is important in practice as the intermediate and output targets of the hypothetical DMU would be feasible. When overall efficiency of the hypothetical DMU is decomposed, individual stages have the same efficiency level as that of the hypothetical DMU. This is important to DMU managers as sub-processes also maintain the desired overall efficiency level. We apply our inverse DEA model to a sample of Australian superannuation funds. We demonstrate that each unique Pareto optimal solution of the inverse DEA model obtained through the constraint method provides a specific set of intermediate and output targets and they may offer trade-off between intermediates and outputs. When fund managers anticipate expansion or growth in their funds, choice of targets allows comparison of different trade-off scenarios and makes informed decisions.