An MOLP based procedure for finding efficient units in DEA models

In this paper a multiple objective linear programming (MOLP) problem whose feasible region is the production possibility set with variable returns to scale is proposed. By solving this MOLP problem by multicriterion simplex method, the extreme efficient Pareto points can be obtained. Then the extreme efficient units in data envelopment analysis (DEA) with variable returns to scale, considering the specified theorems and conditions, can be obtained. Therefore, by solving the proposed MOLP problem, the non-dominant units in DEA can be found. Finally, a numerical example is provided.     

Stochastic MOLP with Incomplete Information: An Interactive Approach with Recourse

Numerous multiobjective linear programming (MOLP) methods have been proposed in the last two decades, but almost all for contexts where the parameters of problems are deterministic. However, in many real situations, parameters of a stochastic nature arise. In this paper, we suppose that the decision-maker is confronted with a situation of partial uncertainty where he possesses incomplete information about the stochastic parameters of the problem, this information allowing him to specify only the limits of variation of these parameters and eventually their central values. For such situations, we propose a multiobjective stochastic linear programming methodology; it implies the transformation of the stochastic objective functions and constraints in order to obtain an equivalent deterministic MOLP problem and the solving of this last problem by an interactive approach derived from the STEM method. Our methodology is illustrated by a didactical example.     

An integrated FANP–MOLP for supplier evaluation and order allocation

In the face of acute global competition, supplier management is rapidly emerging as a crucial issue to any companies striving for business success and sustainable development. To optimize competitive advantages, a company should incorporate “suppliers” as an essential part of its core competencies. Supplier evaluation, the first step in supplier management, is a complex multi-criteria decision-making (MCDM) problem, and its complexity is further aggravated if the highly important interdependence among the selection criteria is taken into consideration. The objective of this paper is to suggest a comprehensive decision method for identifying top suppliers by considering the effects of interdependence among the selection criteria, as well as to achieve optimal allocation of orders among the selected suppliers.     

Demystifying DEA — A Visual Interactive Approach Based on Multiple Criteria Analysis

Both Data Envelopment Analysis (DEA) and Multiple Criteria Analysis (MCA) can be used to assess the efficiency with which units perform similar tasks. This paper describes an approach derived from the integration of data envelopment analysis and a multi-attribute value function. This approach is implemented as a visual interactive decision support system, the use of which is illustrated by a practical application. The authors feel that this approach overcomes some of the limitations of the original DEA approach and, in particular, increases users' understanding of DEA. The approach is particularly well suited to the analysis of the efficiency of a small number of units.     

Interactive scheme for a MOLP problem given two partial orders: One on variables and one on objectives

An interactive approach for solving a multiple objective linear programming (MOLP) problem is presented. This approach assumes that the decision maker (in contrast to the analyst) can establish a (preferential) partial order P_v on the decision variables and a partial order P_o on the objective functions. The solution approach presented in this paper requires minimal additional information in its interactive stage. Results are presented for a number of tests: both conceptual development and applicability in solving specific problems have been successfully tested.     

大学生就业扶持政策的有效性分析及改进:基于DEA方法的实证分析

鉴于数据包络分析(DEA)方法在评价多输入、多输出系统相对有效性方面所具有的优越性,基于DEA方法构建了C2R模型及相应投影分析模型和评价指标体系,对1999-2008年中国所实行的大学生就业扶持政策的有效性进行了评价分析,实证分析结果表明1999-2002年的大学生就业扶持政策在促进和解决大学生就业方面的效果显著,而2003年以后的大学生就业扶持政策在解决大学生就业问题上存在明显的效率损失,且政策效果逐年下降.为了提高大学生就业扶持政策的实施效果,就业扶持政策在未来的改进重点应着力从财政补贴、高等教育经费投入和贷款补助等政策内容入手,并提高政策的执行力度.     

An Extension Problem Related to the Fractional Laplacian

The operator square root of the Laplacian (? ?)^1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.     

An Interactive Aid to Financial Planning

The problem of producing financial plans for the subsidiary of a multinational corporation is one which is critical, especially in uncertain times. In addition there is always a pressing time constraint. This paper describes a suite of models which are in use by Caltex Oil South Africa to assist in this area. The approach adopted was to provide simple models which work interactively. The financial planning analysts were able to be very involved in the project because a high level modelling language was used which they could easily comprehend. The tremendous benefits of this type of approach in terms of user acceptance and in other areas are examined.     

Computationally Efficient Methods for Calculating the Ideal Solution for MOLP Problems

This paper presents the results of an investigation into computational considerations that are relevant to large-scale multiobjective linear programming (MOLP) problems. Four approaches to obtaining a representation of the ideal solution are compared. Statistics on the number of simplex iterations and CPU time required are analysed for a set of randomly generated multiobjective linear programming problems. Recommendations are made based on the analysis of these results which are applicable to many MOLP solution algorithms.     

An Extension of the Birkhoff Integrability for Multifunctions

A comparison between a set-valued Gould type and simple Birkhoff integrals of bf(X)-valued multifunctions with respect to a non-negative set function is given. Relationships among them and Mc Shane multivalued integrability is given under suitable assumptions.     

Lax等价定理在非线性方面的推广

本文证明了，用差分法求解非线性发展方程的初值问题，当方程适定，在差分格式相容的条件下，稳定性等价于收敛性和逐点Lipschitz条件。从而推广了对线性发展方程成立的Lax等价定理。     

An Extension of the Notion of Orthogonality to Banach Spaces

We extend the usual notion of orthogonality to Banach spaces. We show that the extension is quite rich in structure by establishing some of its main properties and consequences. Geometric characterizations and comparison results with other extensions are established. Also, we establish a characterization of compact operators on Banach spaces that admit orthonormal Schauder bases. Finally, we characterize orthogonality in the spaces l₂^p(C).     

Said型广义Ball基函数的拓展

在本文中,我们给出了构造Said型广义Ball基函数的新方法,该方法的优点在于,既可以推出奇次多项式的Said型广义Ball基函数表示,也可以推出偶次多项式的Said型广义Ball基函数表示;该方法的另一优点是,能很自然地定义Said型广义Ball基函数的对偶泛函; 给出了Said型广义Ball基函数的积分性质;定义了一种新的基函数, Said型广义Ball基函数是其特例; 给出了这种新的基函数的对偶泛函和类Marsden恒等式.     

An Interactive Approach for Project Selection

This paper describes an interactive method for presenting a sequence of feasible sets of indivisible projects to a decision-maker. For each set as a whole, the decision-maker evaluates its utilities with respect to each of several attributes; the utilities are then combined to give a single utility for the set.A sequence of zero-one programmes is used to ensure that the only sets presented are those which are feasible and which are not contained in larger feasible sets. The sets are presented in descending order of size, and the presentation can be terminated by the decision-maker or by supplementary rules.The method for presenting sets can be used in other contexts in which complete enumeration of possible sets would otherwise be required.     

规模收益分析的DEA方法

文章利用规模收益的几何意义得到不同规模收益的判别条件，并进一步由技术有效ＤＥＡ模型的最优值来分析边界点的规模收益。     

An Extension Theorem for Linear Codes

One of the first results one meets in coding theory is that a binary linear [n,k,d] code, whose minimum distance is odd, can be extended to an [n + 1, k, d + 1] code. This is one of the few elementary results about binary codes which does not obviously generalise to q-ary codes. The aim of this paper is to give a simple sufficient condition for a q-ary [n, k, d] code to be extendable to an [n + 1, k, d + 1] code. Applications will be given to the construction and classification of good codes, to proving the non- existence of certain codes, and also an application in finite geometry.     

An Extension of the Pizzetti Formula for Polyharmonic Functions

We represent the integral over the unit ball B in R ⁿ of any poly-harmonic function u(x) of degree m as a linear combination with constant coefficients of the integrals of its Laplacians ^j u (j = 0,...,m - 1) over any fixed(n - 1)-dimensional hypersphere S() of radius (0 1). In case = 0 theformula reduces to the classical Pizzetti formula. In particular, the cubature formula derived here integrates exactly all algebraic polynomials of degree 2m - 1.     

An Improved Solution Procedure for the Scheduling Problem

Given a set of n jobs to be processed on a single machine, the problem is to find an optimal job sequence that hierarchically minimizes a bi-criterion objective function. The primary criterion is the maximum value of a general non-decreasing penalty function of job completion time, while the secondary criterion is total job flow time. An extension of Emmons's result is presented on the basis of which an improved solution procedue is developed to reduce the computational effort to find the optimal solution.     

An Extension Principle for Fuzzy Logics

Let S be a set, P(S) the class of all subsets of S and F(S) the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P(S) into a fuzzy closure operator J* defined in F(S). This enables us to give the notion of canonical extension of a deduction system and to give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. Mathematics Subject Classification : 03B52.