Stochastic Multiplicative DEA for Estimating Most Productive Scale Size
Subject Areas : Applied Mathematics
1 - Department of Statistics, Faculty of Science, Arak-Branch, Islamic Azad University, Arak, Iran.
Keywords: Log-normal distribution, Multiplicative data envelopment analysis(MDEA), Systems reliability, Stochastic MDEA, Stochastic alpha-MPSS,
Abstract :
In this paper, stochastic multiplicative data envelopment analysis(MDEA) model under variable return to scale (VRS) technology inthe presence of log-normal distribution is proposed for estimatingmost productive scale size (MPSS). Banker and Maindiratta [Banker,R. D., and Maindiratta, A., Piecewise log-linear estimation ofefficient production surfaces. Management Science 1986, 32,126--135.] introduced MPSS pattern in MDEA model. The MDEA modelrequires that the values for all inputs and outputs be knownexactly. But this assumption is not always correct, because datain many practical situations cannot be precisely measured. One ofthe most important methods, when we're dealing with imprecise datais considering stochastic data. Therefore, in the present study,stochastic input-output orientation MDEA model is introduced forestimating MPSS pattern in the presence of inputs and outputshaving log-normal distributions. Moreover, for solving stochasticmodel, a deterministic equivalent is obtained and also stochasticalpha-MPSS is defined for decision making units (DMUs).Finally, an example of the systems reliability is presented todemonstrate our proposed modeling idea and its efficiency.