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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...
Non-negative linear combinations of -norms and their conorms are used to formulate some decision making problems using systems of max-separable equations and inequalities and optimization problems under constraints described by such systems. The systems have the left hand sides equal to the maximum of increasing functions of one variable and on the right hand sides are constants. Properties of the systems are studied as well as optimization problems with constraints given by the systems and appropriate...
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...
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...
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.
In this paper, we consider the fixed-cost transportation problem. This problem is known to be NP-hard. Therefore, various heuristic and metaheuristic approaches have been proposed to find an approximate optimal solution. In this paper, we propose three hybrid algorithms that combine the ideas of metaheuristic and heuristic approaches in different ways. Two of the proposed algorithms consist of the sequential implementation of metaheuristic and heuristic algorithms, while the third one is a full...
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.
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...
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 -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
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].
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).
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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