Optimistic and pessimistic performance and congestion analysis in fuzzy data envelopment analysis

Abstract

The notion of input congestion in data envelopment analysis (DEA) is analogous to the 'law of diminishing returns' in the classical economic theory of production which states that if a single input is increased while other inputs are held constant, the marginal product of the variable input diminishes. Congestion has been an under-researched topic in economic theory especially when there is a need for augmenting inputs to serve important objectives besides output maximisation. We propose a fuzzy DEA model and represent the imprecise and ambiguous input and output data with fuzzy numbers. We solve the model with an α-cut approach and obtain the value of input congestion for the optimistic and pessimistic cases. The fundamental idea in this paper is to transform the fuzzy DEA model into a crisp linear programming 2 M Khodabakhshi et al. model using the α-cut approach. Two auxiliary crisp models are solved to obtain optimistic and pessimistic values of congestion for evaluating the decision-making units (DMUs). We use a numerical example from the literature to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.

Data envelopment analysis with neutrosophic inputs and outputs

“…Kao and Liu (, ), Smirlis et al (), and Khodabakhshi, Tavana, and Abootaleb () suggested that, when the inputs and outputs vary in an interval, the minimum efficiency of a DMU k occurs when the outputs of this DMU and the inputs of other DMUs are set to their lower bounds, whereas the inputs of the DMU k and the outputs of other DMUs are set to their upper bounds. On the contrary, the maximum efficiency of a DMU k occurs when the outputs of this DMU and the inputs of other DMUs are set to their upper bounds, whereas the inputs of this DMU and the outputs of other DMUs are set to their lower bounds.…”