Stochastic Multiplicative DEA for Estimating Most Productive Scale Size

Abstract

In this paper, stochastic multiplicative data envelopment analysis<br />(MDEA) model under variable return to scale (VRS) technology in<br />the presence of log-normal distribution is proposed for estimating<br />most productive scale size (MPSS). Banker and Maindiratta [Banker,<br />R. D., and Maindiratta, A., Piecewise log-linear estimation of<br />efficient production surfaces. Management Science 1986, 32,<br />126--135.] introduced MPSS pattern in MDEA model. The MDEA model<br />requires that the values for all inputs and outputs be known<br />exactly. But this assumption is not always correct, because data<br />in many practical situations cannot be precisely measured. One of<br />the most important methods, when we're dealing with imprecise data<br />is considering stochastic data. Therefore, in the present study,<br />stochastic input-output orientation MDEA model is introduced for<br />estimating MPSS pattern in the presence of inputs and outputs<br />having log-normal distributions. Moreover, for solving stochastic<br />model, a deterministic equivalent is obtained and also stochastic<br />alpha-MPSS is defined for decision making units (DMUs).<br />Finally, an example of the systems reliability is presented to<br />demonstrate our proposed modeling idea and its efficiency.