Ranking units by target-direction-set value efficiency analysis and mixed integer programming

Büyükbaşaran, Tayyar
In this thesis, two methods are proposed in order to rank units: Target-direction-set value efficiency analysis (TDSVEA) and mixed integer programming (MIP) technique. Besides its ranking ability based on preferences of a decision maker (DM), TDSVEA, which modifies the targeted projection approach of Value Efficiency Analysis (VEA) and Data Envelopment Analysis (DEA), provides important information to analyzer: targets and distances of units from these targets, proposed input allocations in order to project these targets, the lack of harmony between the DM and the manager of the unit etc. In MIP technique, units select weights of the criteria from a feasible weight space in order to outperform maximum number of other units. Units are then ranked according to their outperforming ability. Mixed integer programs in this technique are simplified by domination and weight-domination relations. This simplification procedure is further simplified using transitivity between relations. Both TDSVEA and MIP technique are applied to rank research universities and these rankings are compared to those of other ranking techniques.


Derivative free multilevel optimization methods
Pekmen, Bengisen; Karasözen, Bülent; Department of Scientific Computing (2009)
Derivative free optimization algorithms are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. These are designed to minimize smooth functions whose derivatives are not available or costly to compute. The trust region based multilevel optimization algorithms for solving large scale unconstrained optimization problems resulting by discretization of partial differential equations (PDEs), make use of different discretization levels to reduce the computati...
Image segmentation and smoothing via partial differential equations
Özmen, Neslihan; Leblebicioğlu, Mehmet Kemal; Department of Scientific Computing (2009)
In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical i...
Betti Numbers of Smooth Schubert Varieties and the Remarkable Formula of Kostant, Macdonald, Shapiro, and Steinberg
Akyıldız, Ersan (2012-01-01)
The purpose of this note is to give a refinement of the product formula proved in [1] for the Poincare polynomial of a smooth Schubert variety in the flag variety of an algebraic group G over C. This yields a factorization of the number of elements in a Bruhat interval [e,w] in the Weyl group W of G provided the Schubert variety associated to w is smooth. This gives an elementary necessary condition for a Schubert variety in the flag variety to be smooth.
Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems
Bozkaya, Canan (Elsevier BV, 2007-01-01)
Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which ar...
Generating functions and their applications
Bilgin, Begül; Doğanaksoy, Ali; Department of Cryptography (2010)
Generating functions are important tools that are used in many areas of mathematics and especially statistics. Besides analyzing the general structure of sequences and their asymptotic behavior; these functions, which can be roughly thought as the transformation of sequences into functions, are also used effciently to solve combinatorial problems. In this thesis, the effects of the transformations of generating functions on their corresponding sequences and the effects of the change in sequences on the gene...
Citation Formats
T. Büyükbaşaran, “Ranking units by target-direction-set value efficiency analysis and mixed integer programming,” M.S. - Master of Science, Middle East Technical University, 2005.