DEA for non-homogenous parallel networks

In practice, systems are often composed of a group of sub-units. Each sub-unit has a set of performance metrics that are classified as inputs and outputs in data envelopment analysis (DEA). Conventional DEA views such a system as a “black-box”, other DEA-based models are developed to investigate the inner structure, either with a serial structure where components are connected by intermediate products, or with a parallel system under the key assumption that all sub-units are associated with the same type of inputs and outputs (in differing amounts) without the links. In many applications, however, this property of identical input/output factors may not hold. For example, factories may have various manufacturing lines whose inputs and outputs differ from one another. The current paper proposes a series of DEA models to accommodate settings where non-homogenous sub-units operate in parallel network structures with intermediate measures or links. Both the overall performance of the entire parallel network system and efficiency decomposition for each sub-unit can be evaluated through our method.     

Efficiency decomposition in network data envelopment analysis with slacks-based measures

Conventional data envelopment analysis (DEA) treats the production system as a black box when measuring efficiency, ignoring its internal structure. By taking the operations of the component processes of the system into consideration, several network DEA models have been developed. Of these, the slacks-based measure (SBM) approach has attracted much attention for its ability to provide suitable efficiency measures, especially for weakly efficient production units. This paper proposes a general SBM model for network systems, and is able to decompose the system efficiency into a weighted average of the process efficiencies. This relationship holds for all types of network structure. An example shows that the network model has stronger discriminating power than the conventional black-box model, and the system efficiency is indeed a weighted average of the process efficiencies. The decomposition of the system efficiency helps identify key factors to improve the performance of a production unit.     

A slacks-based measure model for calculating cross efficiency in data envelopment analysis

Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.     

并联结构决策单元的DEA效率评价研究

对复杂生产系统进行效率评价,是改善其运作性能的重要工具.并联结构生产系统是一类有代表性的复杂生产系统,现有研究已经提出了若干针对并联结构生产系统的效率评价问题.然而,现有研究均未考察并联生产系统的前沿生产能力.本文分析了并联生产系统的前沿生产能力,提出了评价并联生产系统的乘数模型和包络模型,证明了这两个模型与有关文献的等价性.与传统CCR模型相比较,本文模型具有更强的鉴别能力,可更大程度挖掘系统整体性能改善的潜力.最后,一个农业评价的实证研究验证了有关结论.     

Efficiency measurement for hierarchical network systems

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for systems with a hierarchical structure. It is shown that the hierarchical structure is equivalent to a parallel structure, with the components being the units at the bottom of the hierarchy. Due to the characteristics of a parallel system, the efficiency of a hierarchical system is thus a weighted average of those of the units at the bottom of the hierarchy. A hypothetic example shows that the proposed model is able to distinguish the order of the efficient DMUs evaluated by the conventional DEA model. Moreover, it provides the efficiencies of the functions of the DMU, which enables managers to identify areas of weakness, and thus better focus efforts to improve overall performance.     

Hierarchical network systems: An application to high-technology industry in China

In real world situations, there is a hierarchical structure exists in a specific organization and each component has its network process. However, such hierarchical network system has not been well studied in previous literature, and misleading results often are produced. The current paper discusses a data envelopment analysis (DEA) modelling technique for a network structure where a hierarchical system consists of components having two-stage series processes. An additive network DEA is proposed to evaluate the performance of this type of network structure. The overall and divisional efficiencies of the system and each component can be derived, and the relationship between system efficiency, divisional efficiency and the ones of components is discussed. The newly developed additive network DEA is nonlinear and cannot be converted into a linear program. A semidefinite programming (SDP) approach is developed for effectively solving this model and the global solution can be guaranteed. Another linear multiplicative network DEA also developed for this hierarchical system. The two newly developed models are illustrated with a case of the performance evaluation of high-technology industry in China.     

On network two stages variable returns to scale Dea models

Multiplicative decomposition of stages indices is shown to be consistent with Vrs network technologies. It is also shown why the primal dual correspondence breaks for serial network Vrs models. Different Vrs models can be associated with alternative transfer pricing systems, within the network. Multiplicative decomposition implies marginal cost pricing across stages. While other pricing systems (full cost) correspond to some of the known non-multiplicatively decomposable Vrs models, proposed in the literature. Stages indices, therefore, respond not only to efficiency, but also to the network’s distributive criteria across stages. The distributive contents of stage indices provide the key element for a solution to the problem of measuring scale efficiency in network systems. Multiplicative decomposable Vrs models can be extended to more general network systems, containing both parallel and in series structures. The cost of this generalisation is that efficiency indices are referred to modified stages, that is to stages that include dummy processes. In perspective, these results contribute to show how organisational aspects, such as transfer pricing systems, could be modelled once network technologies are approached from the multiplier (ratio) side.     

基于信息度量的企业组织系统协同性评价

提出组织协同性一些新的概念和理论;建立了评价组织协同性指标体系;定义了企业组织系统固有协同性、应变协同性、管理层次、管理跨度、关系集合结构、关系水平、协同跨度、协同轨迹、协同机制、协同方式、协同职能幅度、职能凝聚度、协同效率等协同性参量.同时应用管理熵理论的基本原理,拓展了复杂性理论结构学派的研究方法应用于组织系统协同性运行度量尺度建模、量化评价、理论方法研究,从协同结构、协同方式和协同功能等多维度建立协同性熵信息评价数学模型,给出适应于非同维度协同问题求解的降维方法,并结合企业协同管理活动进行了应用与实证研究.     

A modified DEA cross efficiency method with negative data and its application in supplier selection

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

     

非独立并联生产系统的DEA效率评价研究

对复杂生产系统进行效率评价,是改善其生产效率的基础.针对非独立并联结构生产系统的效率评价问题开展研究.首先,将两阶段非独立并联生产系统等价为先并联后串联结构的混联生产系统;其次,将混联生产系统的整体效率定义为各串联子系统效率的乘积,而各个串联子系统的效率则定义为内部各并联子系统效率的加权和,并给出了对应的DEA效率评价模型;最后,有关定理和算例分析证实了该模型能更合理地评价此类生产系统的技术效率,能够更大程度地挖掘系统整体性能改善的潜力.     

Intra-Organizational and inter-organizational resource allocation in two-stage network systems

There are organizational systems, such as bank branches and two-stage supply chains, which are composed of multiple parallel two-stage structures. Resource allocation in these systems is to maximize the benefit of the overall organization from a global viewpoint. In this study, we consider two types of systems at an organizational level: a centralized organizational system treating the whole two-stage production process as a basic unit, and a decentralized organizational system including two sub-organizations (groups) treating one of the two-stage production processes as a basic unit. We propose intra-organizational and inter-organizational resource allocation plans for two different organizational systems, respectively. Specially, two modes of free intermediate resource allocation (Free IRA) and fixed intermediate resource allocation (Fixed IRA) are discussed for the decentralized organizational system. The proposed allocation plans are based on two-stage data envelopment analysis models with bi-level formulations, in which the upper-level model is to maximize the entire organizational effectiveness (total outputs minus total inputs) by determining the optimized input resources and output targets while the lower-level model is concerned with efficiency constraints of all decision-making units simultaneously. The developed methods are illustrated by an application to a real-world problem with 17 city bank branches.     

Neighborhood-based uncertainty generation in social networks

Imprecision, incompleteness and dynamic exist in a wide range of network applications. It is difficult to decide the uncertainty relationship among nodes since traditional models are not meaningful in uncertain networks, and the inherent computational complexity of the problems with uncertainty is always intractable. In this paper, we study how to capture uncertainty in networks by transforming a series of snapshots of a network to an uncertain graph. A novel sampling scheme is also proposed which enables the development of efficient algorithms to measure uncertainty in networks. Considering the practical aspects of neighborhood relationship in real networks, a framework is introduced to transform an uncertain network into a deterministic weighted network where the weights on edges can be measured by Jaccard-like index. The comprehensive experimental evaluation results on real data demonstrate the effectiveness and efficiency of our algorithms.     

基于效率的企业资源配置部门剥离条件研究

研究企业中资源配置部门的剥离条件问题.首先,建立了企业资源配置部门的控制模型,并定义了效率概念;然后,分别对企业中的单一资源配置部门和多资源配置部门的剥离条件进行分析,给出判断这2种资源配置部门的剥离分界点公式.由此得到结论:完全竞争市场中,企业根据剥离分界点,把要配置的资源分为稀缺程度较高和稀缺程度较低2类,前者应由企业资源配置部门来配置,后者应由市场来配置;如果市场配置某种资源的效率低于企业部门的配置效率,则企业部门是市场的替代,反之,市场则替代企业部门.     

Ensemble ranking: Aggregation of rankings produced by different multi-criteria decision-making methods

One of the essential problems in multi-criteria decision-making (MCDM) is ranking a set of alternatives based on a set of criteria. In this regard, there exist several MCDM methods which rank the alternatives in different ways. As such, it would be worthwhile to try and arrive at a consensus on this important subject. In this paper, a new approach is proposed based on the half-quadratic (HQ) theory. The proposed approach determines an optimal weight for each of the MCDM ranking methods, which are used to compute the aggregated final ranking. The weight of each ranking method is obtained via a minimizer function that is inspired by the HQ theory, which automatically fulfills the basic constraints of weights in MCDM. The proposed framework also provides a consensus index and a trust level for the aggregated ranking. To illustrate the proposed approach, the evaluation and comparison of ontology alignment systems are modeled as an MCDM problem and the proposed framework is applied to the ontology alignment evaluation initiative (OAEI) 2018, for which the ranking of participating systems is of the utmost importance.     

中立型两阶段交叉效率评价方法

在数据包络分析中，已有的两阶段交叉效率评价方法，不仅只能用于基本两阶段网络结构，而且没有中立地分解子阶段效率。文章提出了一个既适用于基本两阶段网络结构，又适用于具有共享输入的两阶段网络结构的，中立型交叉效率评价方法。该方法定义自评时整体效率等于子阶段效率的加权和，在自评整体效率最大的前提下，从使各子阶段效率都尽可能大的角度为每个决策单元分别确定一组最优权重，进而通过互评计算决策单元整体和子阶段的最终效率得分。最后，通过两个实例验证了方法的实用、合理、有效。     

基于修剪平均的神经网络集成时序预测方法

由于复杂时序存在结构性断点和异常值等问题，往往导致预测模型训练效果不佳，并可能出现极端预测值的情况。为此，本文提出了基于修剪平均的神经网络集成预测方法。该方法首先从训练数据中生成多组训练集，然后分别训练多个神经网络预测模型，最后将多个神经网络的预测结果使用修剪平均策略进行集成。相较于简单平均策略而言，修剪平均策略不容易受到极值的影响，能够使集成模型获得鲁棒性强的预测效果。在实证研究中，本文构造了两种神经网络集成预测模型，分别为基于修剪平均的自举神经网络集成模型(Trimmed Average based Bootstrap Neural Network Ensemble, TA-BNNE)和基于修剪平均的蒙特卡洛神经网络集成模型(Trimmed Average based Monte Carlo Neural Network Ensemble, TA-MCNNE)，并采用这两种模型对NN3竞赛数据集进行预测，结果表明在常规和复杂数据集上，修剪平均策略比简单平均策略具有更好的预测精度。此外，本文将所提出的集成模型与NN3的前十名模型进行比较，发现两种模型在全部数据集上均超过了第6名，在复杂数据集上的表现均超过了第1名，进一步验证本文所提方法的有效性。     

基于项目网络支配和扩散关系的研发项目组合选择

项目组合包含多项目且项目间存在相互作用和依赖关系，针对传统项目组合评价方法忽略了各项目间依赖关系的不足，本文采用复杂网络理论和PageRank算法，提出一种新的项目优先级排序方法（PPRM）。首先，本文建立研发项目多属性评价准则，分析了项目间的支配关系以及技术和经验在项目间的扩散关系。然后，以项目为节点、以支配和扩散关系为边，分别构建了项目支配和扩散网络，进一步，采用设计结构矩阵（DSM）和K-shell方法建立了基于支配网络的项目影响力模型，并建立了考虑项目之间多次扩散传播的综合扩散概率模型。综合项目节点影响力和扩散关系，本文构建了基于PageRank算法的研发项目优先级排序模型。最后，以某研发项目组合选择为例，验证了本文所建立的模型和算法可有效分析项目组合中的排序问题。     

基于地心天际球面坐标的低轨卫星通信网络簇结构协同工作机制设计

低轨LEO（Low earth orbit）卫星通信网络系统星间链路结构与链接关系十分复杂，如何实现该系统的高度可靠、高效工作是一件十分复杂和困难的工作。传统路由算法多选择分布式路由，忽略了卫星内部的分簇管理，在一定程度上，大大增加了算法的时间复杂度和空间复杂度。针对此问题，本文从LEO卫星通信网络的特征出发，运用空间通信技术，分簇规划技术与排队图示评审技术Q-GERT（Queuing graphic evaluation review technique），首先构建LEO卫星通信网络的地心天际球面坐标体系，搭建具有分簇架构的多层次通信网络；其次基于网络综合效能最优化，设计能够实现高度分布式协同通信业务管理的路由模型与算法；最后通过案例研究，表明本文所提工作机制的实用性与有效性。     

基于主从博弈的两部门并行系统的效率评价

本文研究了一类典型并行系统的效率评价问题：（1）决策单元由两个并行的子单元组成;（2）在整个系统中,某一子单元居于主导地位,另一子单元居于从属地位;（3）两个子单元之间存在部分共享的投入资源,且无法明显区别该资源在不同子单元之间的分配比例。在分析决策单元整体效率及内部子单元效率的基础上,基于主从博弈思想,提出一种能同时确定系统整体效率及内部子单元效率的评价方法,该方法能够在评价系统效率的同时,实现共享资源的有效分配。最后,采用一个实例分析说明了所提方法的合理性和有效性。     

Target intermediate products setting in a two-stage system with fairness concern

In a two-stage system with two divisions connected in series, fairly setting the target outputs for the first stage or equivalently the target inputs for the second stage is critical, in order to ensure that the two stages have incentives to collaborate with each other to achieve the best performance of the whole system. Data envelopment analysis (DEA) as a non-parametric approach for efficiency evaluation of multi-input, multi-output systems has drawn a lot of attention. Recently, many two-stage DEA models were developed for studying the internal structures of two-stage systems. However, there was no work studying fair setting of the target intermediate products (or intermediate measures) although unreasonable setting will result in unfairness to the two stages because setting higher (fewer) intermediate measures means that the first (second) stage must make more efforts to achieve the overall production plan. In this paper, a new DEA model taking account of fairness in the setting of the intermediate products is proposed, where the fairness is interpreted based on Nash bargaining game model, in which the two stages negotiate their target efficiencies in the two-stage system based on their individual efficiencies. This approach is illustrated by an empirical application to insurance companies.