One of the important issues in data envelopment analysis (DEA) is sensitivity analysis. Heretofore the existent studies have considered the data modification of inputs and outputs in one or multiple DMUs. In this paper the number of DMUs is increased and a stability region is obtained in  by applying defining hyperplanes in which if the added DMU (only one DMU) is in this region then all of the...

The Spherical Frontier DEA Model (SFM) (Avellar et al., 2007) was developed to be used when one wants to fairly distribute a new and fixed input to a group of Decision Making Units (DMU’s). SFM’s basic idea is to distribute this new and fixed input in such a way that every DMU will be placed on an efficiency frontier with a spherical shape. We use SFM to analyze the problems that appear when on...

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distributi...

Performance assessment often has to be conducted under uncertainty. This paper proposes a ‘‘fuzzy expected value approach’’ for data envelopment analysis (DEA) in which fuzzy inputs and fuzzy outputs are first weighted, respectively, and their expected values then used to measure the optimistic and pessimistic efficiencies of decision making units (DMUs) in fuzzy environments. The two efficienc...

Data envelopment analysis (DEA) is a non-parametric technique to measure the efficiencies of a set of decision making units (DMUs) with common crisp inputs and outputs. In real-world problems, however, inputs and outputs typically have some levels of fuzziness. To analyze a DMU with fuzzy input/output data, previous studies provided the fuzzy DEA (FDEA) model and proposed an associated evaluati...

In this paper, we consider the following Yamabe type problem of polyharmonic operator : { Dmu = |u| 4m N−2m u on S u ∈ H(S ), (P ) where N ≥ 2m + 1,m ∈ N+, S is the unit sphere with the induced Riemannian metric g = gSN , and Dm is the elliptic differential operator of 2m order given by Dm = m ∏ k=1 (−∆g + 14(N − 2k)(N + 2k − 2)) where ∆g is the Laplace-Beltrami operator on S . We will show tha...

in models of data envelopment analysis (dea), an optimal set of weights is generally assumed to represent the assessed decision making unit (dmu) in the best light in comparison to all the other dmus, and so there is an optimal set of weights corresponding to each dmu. the present paper, proposes a three stage method to determine one common set of weights for decision making units. then, we use...