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Bounds on integrals with respect to multivariate copulas

Michael Preischl (2016)

Dependence Modeling

In this paper, we present a method to obtain upper and lower bounds on integrals with respect to copulas by solving the corresponding assignment problems (AP’s). In their 2014 paper, Hofer and Iacó proposed this approach for two dimensions and stated the generalization to arbitrary dimensons as an open problem. We will clarify the connection between copulas and AP’s and thus find an extension to the multidimensional case. Furthermore, we provide convergence statements and, as applications, we consider...

Flexible measures in production process: A DEA-based approach

Alireza Amirteimoori, Ali Emrouznejad (2011)

RAIRO - Operations Research

Data envelopment analysis (DEA) has been proven as an excellent data-oriented efficiency analysis method for comparing decision making units (DMUs) with multiple inputs and multiple outputs. In conventional DEA, it is assumed that the status of each measure is clearly known as either input or output. However, in some situations, a performance measure can play input role for some DMUs and output role for others. Cook and Zhu [Eur. J. Oper. Res.180 (2007) 692–699] referred to these variables...

Flexible measures in production process: A DEA-based approach

Alireza Amirteimoori, Ali Emrouznejad (2011)

RAIRO - Operations Research

Data envelopment analysis (DEA) has been proven as an excellent data-oriented efficiency analysis method for comparing decision making units (DMUs) with multiple inputs and multiple outputs. In conventional DEA, it is assumed that the status of each measure is clearly known as either input or output. However, in some situations, a performance measure can play input role for some DMUs and output role for others. Cook and Zhu [Eur. J. Oper. Res.180 (2007) 692–699] referred to these variables...

Fuzzy linear programming via simulated annealing

Rita Almeida Ribeiro, Fernando Moura Pires (1999)

Kybernetika

This paper shows how the simulated annealing (SA) algorithm provides a simple tool for solving fuzzy optimization problems. Often, the issue is not so much how to fuzzify or remove the conceptual imprecision, but which tools enable simple solutions for these intrinsically uncertain problems. A well-known linear programming example is used to discuss the suitability of the SA algorithm for solving fuzzy optimization problems.

Improved interval DEA models with common weight

Jiasen Sun, Yajun Miao, Jie Wu, Lianbiao Cui, Runyang Zhong (2014)

Kybernetika

The traditional data envelopment analysis (DEA) model can evaluate the relative efficiencies of a set of decision making units (DMUs) with exact values. But it cannot handle imprecise data. Imprecise data, for example, can be expressed in the form of the interval data or mixtures of interval data and exact data. In order to solve this problem, this study proposes three new interval DEA models from different points of view. Two examples are presented to illustrate and validate these models.

Linear optimization with multiple equitable criteria

Michael M. Kostreva, Wodzimierz Ogryczak (2010)

RAIRO - Operations Research

The standard multiple criteria optimization starts with an assumption that the criteria are incomparable. However, there are many applications in which the criteria express ideas of allocation of resources meant to achieve some equitable distribution. This paper focuses on solving linear multiple criteria optimization problems with uniform criteria treated in an equitable way. An axiomatic definition of equitable efficiency is introduced as an refinement of Pareto-optimality. Various generation...

Linear programming interpretations of Mather’s variational principle

L. C. Evans, D. Gomes (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].

Linear programming interpretations of Mather's variational principle

L. C. Evans, D. Gomes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We discuss some implications of linear programming for Mather theory [13-15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [5-8].

Maximization of distances of regular polygons on a circle

Filip Guldan (1980)

Aplikace matematiky

This paper presents the solution of a basic problem defined by J. Černý which solves a concrete everyday problem in railway and road transport (the problem of optimization of time-tables by some criteria).

On cycling in the simplex method of the transportation problem

Włodzimierz Szwarc (2009)

Applicationes Mathematicae

This paper shows that cycling of the simplex method for the m × n transportation problem where k-1 zero basic variables are leaving and reentering the basis does not occur once it does not occur in the k × k assignment problem. A method to disprove cycling for a particular k is applied for k=2,3,4,5 and 6.

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