a b s t r a c tIn this paper, additive model is used to provide an alternative approach for estimating returns to scale in data envelopment analysis. The proposed model is developed in both stochastic and fuzzy data envelopment analysis. Deterministic (crisp) equivalents are obtained which correspond to the stochastic and fuzzy models. Numerical examples are, also, used to illustrate the proposed approaches.

This article developed an approached model of congestion, based on relaxed combination of inputs, in stochastic data envelopment analysis (SDEA) with chance constrained programming approaches. Classic data envelopment analysis models with deterministic data have been used by many authors to identify congestion and estimate its levels; however, data envelopment analysis with stochastic data were rarely used to identify congestion. This article used chance constrained programming approaches to replace stochastic models with ‘‘deterministic equivalents”. This substitution leads us to non-linear problems that should be solved. Finally, the proposed method based on relaxed combination of inputs was used to identify congestion input in six Iranian hospital with one input and two outputs in the period of 2009 to 2012.

Abstract. This paper develops a BCC input relaxation model for identifying input congestion as a severe form of inefficiency of decision-making units in fuzzy data envelopment analysis. The possibility approach is presented to obtain the models equivalent to fuzzy models. We use a one-model approach to determine input congestion based on the BCC input relaxation model. A numerical example is given to illustrate the proposed model and identify the congestion with precise and imprecise data. The proposed model is also used to determine the congestion in 16 hospitals using four fuzzy inputs and two fuzzy outputs with a symmetrical triangular membership function.

This paper develops a non-radial model, unified additive model approach, for evaluating decision making units in data envelopment analysis. Based on the proposed additive input relaxation model, two approaches, a two model approach and a one model approach are provided for determining input congestion. It is shown that the proposed two model approach determines the amount of congestion and, simultaneously, identifies factors responsible for congestion and distinguishes congestion amounts from other components of inefficiency. These amounts are all obtainable from non-zero slacks in a slightly altered version of the additive input relaxation model which we further extend and modify to obtain additional details. One model approach, also, determines input congestion, and is preferred from computational point of view. Numerical and empirical examples are used to illustrate the proposed non-radial methods.