Stochastic Multiplicative DEA for Estimating Most Productive Scale Size

Document Type: Research Articles


Department of Statistics, Faculty of Science, Arak-Branch, Islamic Azad University, Arak, Iran.


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