Integrated data envelopment analysis: Global vs. local optimum

Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European Journal of Operational Research 201, 477–489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.’s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm.     

Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification

The full dimensional efficient facets (FDEFs) of a production possibility set (PPS) play a key role in data envelopment analysis (DEA). Finding the FDEFs has been the subject of intensive research over the past decade. The available algorithms for finding the FDEFs in the current DEA literature either require information about the position of all the extreme efficient decision-making units on the facets of the PPS or knowledge of all extreme optimal solutions of the multiplier form of the BCC model. In this article, we develop an algorithm that does not require such crucial information that may not be easily available. To this purpose, we first carefully analyse the structure of the FDEFs of PPS with BCC technology, using basic concepts of polyhedral set theory. We then utilize this information to devise an algorithm for finding the FDEFs, using mixed integer linear programming. We illustrate our algorithm using a set of real data.     

Anchor points in DEA

Anchor points play an important role in DEA theory and application. They define the transition from the efficient frontier to the “free-disposability” portion of the boundary. Our objective is to use the geometrical properties of anchor points to design and test an algorithm for their identification. We focus on the variable returns to scale production possibility set; our results do not depend on any particular DEA LP formulation, primal/dual form or orientation. Tests on real and artificial data lead to unexpected insights into their role in the geometry of the DEA production possibility set.     

An integrated fuzzy simulation-fuzzy data envelopment analysis algorithm for job-shop layout optimization: The case of injection process with ambiguous data

This paper puts forward an integrated fuzzy simulation-fuzzy data envelopment analysis (FSFDEA) algorithm to cope with a special case of single-row facility layout problem (SRFLP). Discrete-event-simulation, a powerful tool for analyzing complex and stochastic systems, is employed for modeling different layout formations. Afterwards, a range-adjusted measure (RAM) is used as a data envelopment analysis (DEA) model for ranking the simulation results and finding the optimal layout design. Due to ambiguousness associated with the processing times, fuzzy sets theory is incorporated into the simulation model. Since the results of simulation are in the form of possibility distributions, the DEA model is treated on a fuzzy basis; therefore, a recent possibilistic programming approach is used to convert the fuzzy DEA model to an equivalent crisp one. The proposed FSFDEA algorithm is capable of modeling and optimizing small-sized SRFLP’s in stochastic, uncertain, and non-linear environments. The solution quality is inspected through a real case study in a refrigerator manufacturing company.     

Measuring Technical,Allocative and Overall Efficiencies Using a DEA Algorithm

This study presents an effectively-designed algorithm for measuring technical, allocative and overall efficiencies, using data envelopment analysis (DEA). The specially designed DEA code takes advantage of unique features related to the DEA algorithm. Computational efficiency of the proposed DEA algorithm is confirmed by a Monte Carlo simulation study.     

Ratio-based RTS determination in weight-restricted DEA models

This paper provides computationally efficient approaches for determining to which returns to scale (RTS) class a unit belongs in weight-restricted Data Envelopment Analysis (DEA) models. A non-traditional computational algorithm is introduced. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. Some theorems and algorithms are given. Computational advantages of the provided results are discussed and one of the algorithms is illustrated using real world data.     

二阶段加法DEA模型的生产可能集与生产前沿面

针对二阶段加法DEA模型的中间要素的特殊性,构造生产可能集及其公理体系,由此定义生产前沿面,并建立DEA有效和生产前沿面之间的等价关系.通过构造一个多目标规划模型,建立该问题的Pareto有效解与DEA有效之间的等价关系.     

Allocating fixed costs or resources and setting targets via data envelopment analysis

In many applications of data envelopment analysis (DEA), there is often a fixed cost or input resource which should be imposed on all decision making units (DMUs). Cook and Zhu [W.D. Cook, J. Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers and Operations Research 32 (2005) 2171-2178] propose a practical DEA approach for such allocation problems. In this paper, we prove that when some special constraints are added, Cook and Zhu’s approach probably has no feasible solution. The research of this paper focuses on two main aspects: to obtain a new fixed costs or resources allocation approach by improving Cook and Zhu’s approach, and to set fixed targets according to the amount of fixed resources shared by individual DMUs. When such special constraints are attached, our model is proved to be able to achieve a feasible costs or resources allocation. Numerical results for an example from the literature are presented to illustrate our approach.     

A robust data envelopment analysis model with different scenarios

Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company.     

Quantile–DEA classifiers with interval data

This research intends to develop the classifiers for dealing with binary classification problems with interval data whose difficulty to be tackled has been well recognized, regardless of the field. The proposed classifiers involve using the ideas and techniques of both quantiles and data envelopment analysis (DEA), and are thus referred to as quantile–DEA classifiers. That is, the classifiers first use the concept of quantiles to generate a desired number of exact-data sets from a training-data set comprising interval data. Then, the classifiers adopt the concept and technique of an intersection-form production possibility set in the DEA framework to construct acceptance domains with each corresponding to an exact-data set and thus a quantile. Here, an intersection-form acceptance domain is actually represented by a linear inequality system, which enables the quantile–DEA classifiers to efficiently discover the groups to which large volumes of data belong. In addition, the quantile feature enables the proposed classifiers not only to help reveal patterns, but also to tell the user the value or significance of these patterns.     

Computational learning of the conditional phase-type (C-Ph) distribution

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a data set as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output. The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.     

Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs

This paper develops a DEA (data envelopment analysis) model to accommodate competition over outputs. In the proposed model, the total output of all decision making units (DMUs) is fixed, and DMUs compete with each other to maximize their self-rated DEA efficiency score. In the presence of competition over outputs, the best-practice frontier deviates from the classical DEA frontier. We also compute the efficiency scores using the proposed fixed sum output DEA (FSODEA) models, and discuss the competition strategy selection rule. The model is illustrated using a hypothetical data set under the constant returns to scale assumption and medal data from the 2000 Sydney Olympics under the variable returns to scale assumption.     

A new chance-constrained DEA model with birandom input and output data

The purpose of conventional Data Envelopment Analysis (DEA) is to evaluate the performance of a set of firms or Decision-Making Units using deterministic input and output data. However, the input and output data in the real-life performance evaluation problems are often stochastic. The stochastic input and output data in DEA can be represented with random variables. Several methods have been proposed to deal with the random input and output data in DEA. In this paper, we propose a new chance-constrained DEA model with birandom input and output data. A super-efficiency model with birandom constraints is formulated and a non-linear deterministic equivalent model is obtained to solve the super-efficiency model. The non-linear model is converted into a model with quadratic constraints to solve the non-linear deterministic model. Furthermore, a sensitivity analysis is performed to assess the robustness of the proposed super-efficiency model. Finally, two numerical examples are presented to demonstrate the applicability of the proposed chance-constrained DEA model and sensitivity analysis.     

Fuzzy data envelopment analysis (DEA): Model and ranking method

Data Envelopment Analysis (DEA) is a very effective method to evaluate the relative efficiency of decision-making units (DMUs). Since the data of production processes cannot be precisely measured in some cases, the uncertain theory has played an important role in DEA. This paper attempts to extend the traditional DEA models to a fuzzy framework, thus producing a fuzzy DEA model based on credibility measure. Following is a method of ranking all the DMUs. In order to solve the fuzzy model, we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm. When the inputs and outputs are all trapezoidal or triangular fuzzy variables, the model can be transformed to linear programming. Finally, a numerical example is presented to illustrate the fuzzy DEA model and the method of ranking all the DMUs.     

Rank order data in DEA: A general framework

In data envelopment analysis (DEA), performance evaluation is generally assumed to be based upon a set of quantitative data. In many real world settings, however, it is essential to take into account the presence of qualitative factors when evaluating the performance of decision making units (DMUs). Very often rankings are provided from best to worst relative to particular attributes. Such rank positions might better be presented in an ordinal, rather than numerical sense. The paper develops a general frame work for modeling and treating qualitative data in DEA and provides a unified structure for embedding rank order data into the DEA framework. The existing techniques are discussed and their equivalence is demonstrated. Both continuous and discrete projection models are provided. It is shown that qualitative data can be treated in conventional DEA methodology.     

Negative data in DEA: a directional distance approach applied to bank branches

This paper is drawn from the use of data envelopment analysis (DEA) in helping a Portuguese bank to manage the performance of its branches. The bank wanted to set targets for the branches on such variables as growth in number of clients, growth in funds deposited and so on. Such variables can take positive and negative values but apart from some exceptions, traditional DEA models have hitherto been restricted to non-negative data. We report on the development of a model to handle unrestricted data in a DEA framework and illustrate the use of this model on data from the bank concerned.     

生产可能集为凸包时的相对有效性评价模型

给出了一个评价决策单元相对有效性的新的DEA模型,它所对应的生产可能集被称为凸包形生产可能集,同时讨论了该模型解的存在性,定义了决策单元技术DEA有效和"上投影"的概念,断定一个决策单元的"上投影"相对于原来的决策单元是技术DEA有效的。最后给出一个应用新模型进行设施农业效率评价的例子。     

An application of DEA for comparative analysis and ranking of regions in Serbia with regards to social-economic development

In this paper, we use data envelopment analysis (DEA) to estimate how well regions in Serbia utilize their resources. Based on data for four inputs and four outputs we applied an output-oriented CCR DEA model and it appears that 17 out of 30 regions are efficient. For each inefficient unit, DEA identifies the sources and level of inefficiency for each input and output. An output-oriented set of targets is determined for 13 inefficient regions. In addition, the possibilities of combining DEA and linear discriminant analysis (LDA) in evaluating performance are explored. The efficient regions are ranked using a cross efficiency matrix and an output-oriented version of Andersen–Petersen’s DEA model and the results are analyzed and compared.     

Including principal component weights to improve discrimination in data envelopment analysis

This research further develops the combined use of principal component analysis (PCA) and data envelopment analysis (DEA). The aim is to reduce the curse of dimensionality that occurs in DEA when there is an excessive number of inputs and outputs in relation to the number of decision-making units. Three separate PCA–DEA formulations are developed in the paper utilising the results of PCA to develop objective, assurance region type constraints on the DEA weights. The first model applies PCA to grouped data representing similar themes, such as quality or environmental measures. The second model, if needed, applies PCA to all inputs and separately to all outputs, thus further strengthening the discrimination power of DEA. The third formulation searches for a single set of global weights with which to fully rank all observations. In summary, it is clear that the use of principal components can noticeably improve the strength of DEA models.