In this paper, we re-examine Data Envelopment Analysis models from perspectives of preference order, production set and performance measure. we investigate the relationship between Data Envelopment Analysis (DEA) and Multiple Criteria Decision Making Theory. There are three key building blocks in a DEA model: preference order, production possibility set and performance measure. It is shown in t...

Process Synthesis seeks to develop systematically process flowsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process flowsheets. The mathematical model...

This study introduces a revised data envelopment analysis (DEA) model to explore a new use of DEA for the environmental assessment in which outputs are classified into desirable (good) and undesirable (bad). Such an output separation is important in the DEA-based environmental assessment. We used a Range-Adjusted Measure (RAM) DEA model that is a kind of non-radial DEA model for combining the t...

Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixed-integer region S and a collection of valid \base" mixed-integer inequalities , we develop a procedure for generating new val...

NK landscapes (NKL) are stochastically generated pseudoboolean functions with N bits (genes) and K interactions between genes. By means of the parameter K ruggedness as well as the epistasis can be controlled. NKL are particularly useful to understand the dynamics of evolutionary search. We extend NKL from the traditional binary case to a mixed variable case with continuous, nominal discrete, a...

data envelopment analysis (dea) is a mathematical programming method in operations research that can be used to distinguish between efficient and inefficient decision making units (dmus). however, the conventional dea models do not have the ability to rank the efficient dmus. this article suggests bootstrapping method for ranking measures of technical efficiency as calculated via non-radial mod...

the non-differentiability and implicit definition of boundary of production possibility set (pps) in data envelopment analysis (dea) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. also, imposing weight restrictions in dea models have some shortcomings and misunderstandings. in this paper we ut...

data envelopment analysis (dea) models with interval inputs and outputs have been rarely discussed in dea literature. this paper, using the enhanced russell measurement proposes an extended model which permits the presence of interval scale variables which can take both negative and positive values. the model is compared with most well-known dea models of which include the ccr model, the bcc mo...

We present a set of exactly solvable Ising models, with half-odd-integer spinS on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spinS lattice....

We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer assignments is finite. We develop a characterization for the more general case of unbounded integer variables together with a simple necessary condition for re...