A decision support framework for internal audit prioritization in a rental car company: A combined use between DEA and AHP

Corporate scandals such as those at Tyco, Enron, and WorldCom have caused the decline of public trust in accounting and reporting practices. In response, US passed the Sarbanes Oxley Law (Sarbanes) in 2002, the most important corporate governance law since securities laws in 1930s. Section 302 of Sarbanes mandates corporations to ensure accurate financial disclosure and to take greater financial reporting and control responsibilities. Management is required to make an annual assertion regarding the design and effectiveness of company’s internal controls. Consequently, many internal auditing resources are stretched. The objective of this case study is to develop a multi-criteria decision making aid that can identify the most critical businesses units within a corporation. Using the aid, we can use efficiently and effectively the internal auditing resources. Internal audits determine if the accounting processes and systems are working as intended. It focuses on the reliability of the accounting data and evaluates business through financial, operational, and compliance review. It assesses the risk of asset loss, studies business processes, and identifies opportunities to improve efficiency and effectiveness. This study explores the potential of applying data envelopment analysis (DEA) and analytic hierarchy process (AHP) to determine the business units that need audit. Compared with conventional methods, the proposed combined model incorporates a much wider range of quantitative and qualitative criteria, and provides a more detailed and thorough study. The proposed evaluation framework is comprehensive and flexible and it shows great potential for internal audit prioritization and resource allocation.     

A new DEA ranking system based on changing the reference set

This research proposes a new ranking system for extreme efficient DMUs (Decision Making Units) based upon the omission of these efficient DMUs from reference set of the inefficient DMUs. We state and prove some facts related to our model. A numerical example where the proposed method is compared with traditional ranking approaches is shown.     

A modified complete ranking of DMUs using restrictions in DEA models

Alirezaee and Afsharian [1] have proposed a new index, namely, Balance Index, to rank DMUs. In this paper, we will use their examples to illustrate that the proposed index is not stable. As a result, the corresponding rankings are also unstable. Then we analyze where an error occurs in the new method for complete ranking of decision making units and amend it by introducing the Maximal Balance Index. The numeral example reports the reasonability of our methods.     

Computation of efficient targets in DEA models with production trade-offs and weight restrictions

Recently new models of data envelopment analysis (DEA) were introduced that incorporate production trade-offs between inputs and outputs or based on them weight restrictions. In this paper, we develop a computational procedure suitable for the practical application of such models. We show that the standard two-stage optimisation procedure used in DEA to test the full efficiency of units and identify their efficient targets may work incorrectly in the new models. The modified procedure consists of three stages: the first evaluates the radial efficiency of the unit, the second identifies its efficient target, and the third its reference set of efficient peers. Each stage requires solving one linear program for each unit.     

On the boundedness of the SORM DEA models with negative data

Emrouznejad et al. (2010) proposed a Semi-Oriented Radial Measure (SORM) model for assessing the efficiency of Decision Making Units (DMUs) by Data Envelopment Analysis (DEA) with negative data. This paper provides a necessary and sufficient condition for boundedness of the input and output oriented SORM models.     

A one-model approach based on relaxed combinations of inputs for evaluating input congestion in DEA

This paper provides a one-model approach of input congestion based on input relaxation model developed in data envelopment analysis (e.g. [G.R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion — Considering textile industry of China, Applied Mathematics and Computation (1) (2004) 263–273; G.R. Jahanshahloo, M. Khodabakhshi, Determining assurance interval for non-Archimedean ele improving outputs model in DEA, Applied Mathematics and Computation 151 (2) (2004) 501–506; M. Khodabakhshi, A super-efficiency model based on improved outputs in data envelopment analysis, Applied Mathematics and Computation 184 (2) (2007) 695–703; M. Khodabakhshi, M. Asgharian, An input relaxation measure of efficiency in stochastic data analysis, Applied Mathematical Modelling 33 (2009) 2010–2023]. This approach reduces solving three problems with the two-model approach introduced in the first of the above-mentioned reference to two problems which is certainly important from computational point of view. The model is applied to a set of data extracted from ISI database to estimate input congestion of 12 Canadian business schools.     

Fixed cost and resource allocation based on DEA cross-efficiency

In many managerial applications, situations frequently occur when a fixed cost is used in constructing the common platform of an organization, and needs to be shared by all related entities, or decision making units (DMUs). It is of vital importance to allocate such a cost across DMUs where there is competition for resources. Data envelopment analysis (DEA) has been successfully used in cost and resource allocation problems. Whether it is a cost or resource allocation issue, one needs to consider both the competitive and cooperative situation existing among DMUs in addition to maintaining or improving efficiency. The current paper uses the cross-efficiency concept in DEA to approach cost and resource allocation problems. Because DEA cross-efficiency uses the concept of peer appraisal, it is a very reasonable and appropriate mechanism for allocating a shared resource/cost. It is shown that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency DEA-based iterative method is further extended into a resource-allocation setting to achieve maximization in the aggregated output change by distributing available resources. Such allocations for fixed costs and resources are more acceptable to the players involved, because the allocation results are jointly determined by all DMUs rather than a specific one. The proposed approaches are demonstrated using an existing data set that has been applied in similar studies.     

A note on a variant of radial measure capable of dealing with negative inputs and outputs in DEA

The recent contribution by Cheng et al. (2013) presents a variant of the traditional radial input- and output-oriented efficiency measures whereby original values are replaced with absolute values. This comment spells out that this article contains some imprecisions and therefore presents some further results.     

One-stage and two-stage DEA estimation of the effects of contextual variables

Two-stage data envelopment analysis (2-DEA) is commonly used in productive efficiency analysis to estimate the effects of operational conditions and practices on performance. In this method the DEA efficiency estimates are regressed on contextual variables representing the operational conditions. We re-examine the statistical properties of the 2-DEA estimator, and find that it is statistically consistent under more general conditions than earlier studies assume. We further show that the finite sample bias of DEA in the first stage carries over to the second stage regression, causing bias in the estimated coefficients of the contextual variables. This bias is particularly severe when the contextual variables are correlated with inputs. To address this shortcoming, we apply the result that DEA can be formulated as a constrained special case of the convex nonparametric least squares (CNLS) regression. Applying the CNLS formulation, we develop a new semi-nonparametric one-stage estimator for the coefficients of the contextual variables that directly incorporates contextual variables to the standard DEA problem. The proposed method is hence referred to as one-stage DEA (1-DEA). Evidence from Monte Carlo simulations suggests that the new 1-DEA estimator performs systematically better than the conventional 2-DEA estimator both in deterministic and noisy scenarios.     

Preference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates

There are different ways to allow the voters to express their preferences on a set of candidates. In ranked voting systems, each voter selects a subset of the candidates and ranks them in order of preference. A well-known class of these voting systems are scoring rules, where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners. One of the most important issues in this context is the choice of the scoring vector, since the winning candidate can vary according to the scores used. To avoid this problem, Cook and Kress [W.D. Cook, M. Kress, A data envelopment model for aggregating preference rankings, Management Science 36 (11) (1990) 1302–1310], using a DEA/AR model, proposed to assess each candidate with the most favorable scoring vector for him/her. However, the use of this procedure often causes several candidates to be efficient, i.e., they achieve the maximum score. For this reason, several methods to discriminate among efficient candidates have been proposed. The aim of this paper is to analyze and show some drawbacks of these methods.     

Allocating the fixed cost as a complement of other cost inputs: A DEA approach

In cost allocation problem, traditional DEA approaches allocate the fixed cost among a group of decision making units (DMUs), and treat the allocated cost as an extra input of each DMU. If costs except for the fixed cost are regarded as inputs in the cost allocation problem, then it is obvious that the fixed cost is a complement of other inputs rather than an extra independent input. Therefore it is necessary to combine the allocated cost with other cost measures in cost allocation problem. Based on this observation, this paper investigates the relationship between the allocated cost and the DEA efficiency score and develops a DEA-based approach to allocate the fixed cost among various DMUs. An example of allocating advertising expenditure between a car manufacturer and its dealers is presented to illustrate the method proposed in this paper.     

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.     

基于DEA与Malmquist指数法的区域科技创新效率评价——以重庆市为例

本文以重庆市为例,运用DEA方法结合Malmquist指数分析了一个区域内不同性质的企事业单位的科技创新效率,从而得出整个区域的科技创新效率情况。研究发现,重庆市技术进步和全要素生产率较高,而技术效率、纯技术效率、规模效率有所下降,全要素生产率的提高主要是技术进步引起的。因此重庆市科技创新的首要任务是进行重庆创新领域的制度与管理调整。     

Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms

In a recent article, Briec, Kerstens and Vanden Eeckaut (2004) develop a series of nonparametric, deterministic non-convex technologies integrating traditional returns to scale assumptions into the non-convex FDH model. They show, among other things, how the traditional technical input efficiency measure can be analytically derived for these technology specifications. In this paper, we develop a similar approach to calculate output and graph measures of technical efficiency and indicate the general advantage of such solution strategy via enumeration. Furthermore, several analytical formulas are established and some algorithms are proposed relating the three measurement orientations to one another.     

A comment on “solving the puzzles of structural efficiency”

In a recent paper by Li and Cheng [Li,S.K., Cheng, Y.S., 2007. Solving the puzzles of structural efficiency. European Journal of Operational Research 180(2), 713–722], they developed the shadow price model to solve the existing puzzles of structural efficiency theoretically. However, we observe that the optimal shadow price vector in the shadow price model by Li and Cheng (2007) is not always unique. As a result, the decomposition of the structural efficiency is arbitrarily generated, depending on the shadow price vector we choose. Finally, an example with multiple inputs and outputs is used to illustrate the phenomenon.     

Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools

Public sector output provision is influenced not only by discretionary inputs but also by exogenous environmental factors. In this paper, we extended the literature by developing a conditional DEA estimator of allocative efficiency that allows a decomposition of overall cost efficiency into allocative and technical components while simultaneously controlling for the environment. We apply the model to analyze technical and allocative efficiency of Dutch secondary schools. The results reveal that allocative efficiency represents a significant 37 percent of overall cost efficiency on average, although technical inefficiency is still the dominant part. Furthermore, the results show that the impact of environment largely differs between schools and that having a more unfavorable environment is very expensive to schools. These results highlight the importance of including environmental variables in both technical and allocative efficiency analysis.     

A distance friction minimization approach in data envelopment analysis: A comparative study on airport efficiency

This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving projection model, for both input reduction and output increase. In this approach, a generalized distance function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional projection function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner.     

A study on the persistence of Farrell’s efficiency measure under a dynamic framework

This article introduces a sequence of four systematic methods to examine the extent to which the economic efficiency of Taiwan’s commercial banks persists and to uncover the potential dynamic link between bank performance and various financial indicators. Quasi-fixed inputs are explicitly incorporated in the DEA model to account for possible adjustment costs, regulation, or indivisibilities. Among the four methods, the dynamic panel data model and the Markov model appear to be exploited for the first time in the area of the DEA approach. Evidence is found that bank efficiency exhibits moderate persistence over the sample period, implying that the given sample banks fail to adjust their production techniques in a timely manner. Regulatory authorities and bank managers are suggested to be aware of the level of undesirable non-performing loans due to their close relationship with bank performance.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

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.