Efficiency of two-stage systems in stochastic DEA

Abstract

In the present world, there are many of two-stage systemsthat their information of inputs, outputs, and intermediate measuresare imprecise (like stochastic, fuzzy, interval, etc). In these conditions,two-stage data envelopment analysis (two-stage DEA) cannot evaluatethe efficiencies of these systems. In many two-stage systems, the simultaneouspresence of the stages is necessary for the final product.Hence, in this paper, firstly we shall propose the stochastic multiplicativemodel and the deterministic equivalent to measure the efficiencies ofthese systems in presence of stochastic data under the constant returnsto scale (CRS) assumption by using the non-compensatory property ofthe multiplication operator. Then, we will use the reparative property ofadditive operation to propose the additive models and the deterministicequivalents to calculate the efficiencies of two-stage systems in presenceof stochastic data under the constant returns to scale (CRS) and variablereturns to scale (VRS) assumptions that the simultaneous presenceof the stages is not necessary for the final product and one stage compensatesthe another stage’s shortcomings. Likewise, we shall converteach of these deterministic equivalents to quadratic programming problems.Based on the proposed stochastic models, the whole system isefficient if and only if the first and the second stages are efficient. Atlast, we will illustrate in the proposed multiplicative model by using thedata of Taiwanese non-life insurance companies that extracted from theextant literature.