A Computational Method for Solving DEA Problems with Infinitely Many DMUs

Semi-infinite programs as related to DEA with infinitely many DMUs will be solved by bisections within the framework of LPs. No gradient Information Is needed, contrary to the usual Newton-Raphson type methods for solving semi-Infinite programs.The rate of convergence is linear. The method has a stable convergency feature derived from the bisection rule.Reprinted from Research Report CCS 561, Center for Cybernetic Studies, The University of Texas, at Austin

Existence and representation of diophantine and mixed diophantine solutions to linear equations and inequalities

AbstractIn this paper we present necessary and sufficient conditions for the existence of solutions to more general systems of linear diophantine equations and inequalities than have previously been considered. We do this in terms of variants and extensions of generalized inverse concepts which also permit us to give representation of the set of all solutions to the systems. The results are further extended to mixed integer systems

Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them

Asymptotic duality over closed convex sets

AbstractThe asymptotic duality theory of linear programming over closed convex cones [4] is extended to closed convex sets, by embedding such sets in appropriate cones. Applications to convex programming and to approximation theory are given

Some models of organization response to budgeted multiple goals

At head of title: Research paper no.1

The role of duality in optimization problems involving entropy functionals with applications to information theory

We consider infinite-dimensional optimization problems involving entropy-type functionals in the objective function as well as as in the constraints. A duality theory is developed for such problems and applied to the reliability rate function problem in information theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45233/1/10957_2004_Article_BF00939682.pd

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach:the need to assess evolving units

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a Multiobjective Mixed Integer Linear Programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development

Proceedings: November 15, 1962, Ambassador East Hotel, Chicago, Illinois

https://egrove.olemiss.edu/aicpa_comm/1441/thumbnail.jp

Evaluating Greek equity funds using data envelopment analysis

This study assesses the relative performance of Greek equity funds employing a non-parametric method, specifically Data Envelopment Analysis (DEA). Using an original sample of cost and operational attributes we explore the e¤ect of each variable on funds' operational efficiency for an oligopolistic and bank-dominated fund industry. Our results have significant implications for the investors' fund selection process since we are able to identify potential sources of inefficiencies for the funds. The most striking result is that the percentage of assets under management affects performance negatively, a conclusion which may be related to the structure of the domestic stock market. Furthermore, we provide evidence against the notion of funds' mean-variance efficiency