Estimating Marginal Rates of Substitution in Two-Stage Processes with Undesirable Factors

Trade-offs between production factors such as marginal rates of substitution are significant aspects for decision makers and managers. Due to the complexity of processes and the presence of undesirable measures in many real world applications, in this study, the relative efficiency and marginal rates of substitution are calculated in two-stage structures including weakly disposable undesirable intermediate measures. Actually, an approach based on the directional distance function is provided for this purpose. Therefore, the effect of the changes of a measure in other measures such as the effect of changes of intermediate factors on the output of the first stage and second stage is measured by maintaining efficiency, and the rate of these changes is calculated. To elaborate in details, marginal rates of substitution in two-stage processes are dealt with using the proposed two-stage data envelopment analysis (DEA) approach while undesirable intermediate components are presented. A real data set is also used to clarify the proposed method herein.