Abstract The emissions trading system allows organizations to transact emission permits fit their production practice. This paper develops a new nonparametric methodology for performance evaluation of (or decision-making units, DMUs) considering carbon permit trading. Explicit axioms are discussed, and technology is proposed. Models based on the established evaluating reduction potential DMUs. ...

In this lecture we learn to solve nonhomogeneous equations of the form ay′′ + by′ + cy = g(t) using the “method of undetermined coefficients”. In previous lectures we learned to how to solve any equation of the form ay′′ + by′ + cy = 0. We will apply these techniques to help us solve the nonhomogeneous equation ay′′ + by′ + cy = g(t) by understanding the connection between solutions to homogene...

In some data envelopment analysis (DEA) applications, some inputs of DMUs have negative values with positive cost. This paper generalizes the global cost Malmquist productivity index to compare the productivity of different DMUs with negative inputs in any two periods of times under variable returns to scale (VRS) technology, and then the generalized index is decomposed to several components. T...

In original data envelopment analysis (DEA) models, the data for all inputs and outputs are known exactly. When some inputs and outputs are unknown decision variables, such as interval data, ordinal data, and ratio bounded data, the DEA model is called imprecise DEA (IDEA). In this paper, We develop an alternative approach based upon slacksbased measure of efficiency (SBM) for dealing with inte...

In this paper, we have developed a heuristic that uses Data Envelopment Analysis (DEA) to rank Decision Making Units (DMUs) with fuzzy input and output values in the order of their probable efficiency. The heuristic is designed to be used with the raw samples of the fuzzy data, and does not require knowledge of the fuzzy data’s probability distribution. It is meant to be a simple method of diff...

Data envelopment analysis (DEA) is a linear programming problem approach for evaluating the relative efficiency of peer decision making units (DMUs) that have multiple inputs and outputs. DMUs can have a two-stage structure where all the outputs from the first stage are the only inputs to the second stage, in addition to the inputs to the first stage and the outputs from the second stage. The o...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

Data envelopment analysis (DEA) is a non-parametric data-driven approach for evaluating the efficiency of set homogeneous decision-making units (DMUs) with multiple inputs and outputs. The number performance factors (inputs outputs) plays crucial role when applying DEA to real-world applications. In other words, if significantly greater than DMUs, it highly possible arrive at large portion effi...

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there ar...