Marginal rates of technical changes and impact in stochastic data envelopment analysis: An application in power industry

Abstract

Marginal rates of technical changes and marginal impact are useful tools to calculate the trade-offs between production factors in a production process. In the data envelopment analysis (DEA) framework, the calculation of these trade-offs (marginal rates of technical substitution, marginal rates of transformation, marginal productivity and marginal costs) using the existing deterministic approaches may be sensitive to uncertainty and variability of the input and output data. Therefore, in this contribution, we introduce a stochastic DEA model based on chance-constrained programming to develop a measure of the marginal rates of firms facing data uncertainty. In this contribution, chance-constrained programming is used to develop a procedure to calculate these trade-offs. Our proposed stochastic procedure is applied to sample data on 31 power plants. The empirical results on marginal rates obtained from our proposed stochastic programs revealed that the results are different at various tolerance levels of chance constraints.