Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services

Simulation is a powerful tool for modeling complex systems with intricate relationships between various entities and resources. Simulation optimization refers to methods that search the design space (i.e., the set of all feasible system configurations) to find a system configuration (also called a design point) that gives the best performance. Since simulation is often time consuming, sampling as few design points from the design space as possible is desired. However, in the case of multiple objectives, traditional simulation optimization methods are ineffective to uncover the efficient frontier. We propose a framework for multi-objective simulation optimization that combines the power of genetic algorithm (GA), which can effectively search very large design spaces, with data envelopment analysis (DEA) used to evaluate the simulation results and guide the search process. In our framework, we use a design point's relative efficiency score from DEA as its fitness value in the selection operation of GA. We apply our algorithm to determine optimal resource levels in surgical services. Our numerical experiments show that our algorithm effectively furthers the frontier and identifies efficient design points.     

Data envelopment analysis: Prior to choosing a model

In this paper, we address several issues related to the use of data envelopment analysis (DEA). These issues include model orientation, input and output selection/definition, the use of mixed and raw data, and the number of inputs and outputs to use versus the number of decision making units (DMUs). We believe that within the DEA community, researchers, practitioners, and reviewers may have concerns and, in many cases, incorrect views about these issues. Some of the concerns stem from what is perceived as being the purpose of the DEA exercise. While the DEA frontier can rightly be viewed as a production frontier, it must be remembered that ultimately DEA is a method for performance evaluation and benchmarking against best-practice. DEA can be viewed as a tool for multiple-criteria evaluation problems where DMUs are alternatives and each DMU is represented by its performance in multiple criteria which are coined/classified as DEA inputs and outputs. The purpose of this paper is to offer some clarification and direction on these matters.     

基于偏好DEA模型的中国纺织业效率评价

基于具有输入输出指标偏好信息的数据包络分析模型评价中国纺织工业的效率,给出了描述规模报酬不变和规模报酬可变假设的DEA模型及其对偶规划的一种形式。模型克服传统DEA模型应用中常见的决策单元权重为零进而高估决策单元效率的不合理现象,有效地测算了中国31个地区纺织工业的经济运行效率,并分析了地区间效率水平差异的原因。利用各决策单元在经验生产前沿面上的投影点,估计了中国纺织工业的随机生产前沿函数,最后用效率弹性线性递减模型分析了销售收入、人均资产、台港澳和外商投资对各地区效率的微观影响关系。     

Goal directed benchmarking for organizational efficiency

In this paper, we extend the standard data envelopment analysis (DEA) model to include longer term top management goals. This extension is in recognition of the fact that benchmarking for decision making units (DMUs) is more than a purely monitoring process, and includes a component of future planning. The new model uses a goal programming structure to find points on the efficient frontier which are realistically achievable by DMUs, but at the same time achieving a closer approach to long term organizational goals (as distinct from the local performance of individual DMUs). Consideration is given to the possibility of adjusting constraints on the DMU by investment in extended inputs or new technologies, in which case minimization of associated investment costs becomes an additional management objective.     

随机环境下的多投入多产出生产前沿面估计

传统的DEA模型假设观测样本的投入产出都是确定型数据, 这使得DEA在实际应用中受到限制, 本文提出的基于拟似然估计的多投入多产出随机非参数包络数据 (PLE-StoNED) 方法拓展了这个假设, 能够估计随机环境下的生产前沿面.本文证明, 生产可能集假设条件下的前沿面可以用一个有凹凸性和单调性限制的函数来表示.相较之前的StoNED方法, 本文提出的方法可以估计随机环境下多投入多产出决策单元 (DMU) 的前沿面.通过Monte Carlo实验, 多投入多产出PLE-StoNED方法的有效性得到验证, 它可纠正DEA等传统方法产生的偏误.最后, 实证研究部分运用这一新提出的方法估计了中国大陆商业银行的生产前沿面和效率.本文提出的方法弥补了DEA缺乏统计性的不足, 可为决策者在随机环境下对多投入多产出决策单元进行生产力和效率评估提供决策参考.     

LASSO variable selection in data envelopment analysis with small datasets

The curse of dimensionality problem arises when a limited number of observations are used to estimate a high-dimensional frontier, in particular, by data envelopment analysis (DEA). The study conducts a data generating process (DGP) to argue the typical “rule of thumb” used in DEA, e.g. the required number of observations should be at least larger than twice of the number of inputs and outputs, is ambiguous and will produce large deviations in estimating the technical efficiency. To address this issue, we propose a Least Absolute Shrinkage and Selection Operator (LASSO) variable selection technique, which is usually used in data science for extracting significant factors, and combine it in a sign-constrained convex nonparametric least squares (SCNLS), which can be regarded as DEA estimator. Simulation results demonstrate that the proposed LASSO-SCNLS method and its variants provide useful guidelines for the DEA with small datasets.     

A use of a nonparametric statistic for DEA frontier shift: the Kruskal and Wallis rank test

A new use of the nonparametric statistic, referred to as the “Kruskal and Wallis rank test”, is proposed in this study. The nonparametric statistic examines whether or not any frontier shift occurs among observed periods. To document its practicality, the proposed statistic is incorporated into the framework of Window Malmquist Analysis (WMA) that is structured by combining Data Envelopment Analysis (DEA) window analysis with the Malmquist index approach. As an important case study, this research applies the new technique to examine the performance of Japanese postal services from 1983 to 1997. Two policy implications are derived from the empirical study.     

How to better identify the true managerial performance: State of the art using DEA

Our motivation is to detail a potential improvement on the three-stage analysis published by Fried et al. [Accounting for environmental effects and statistical noise in data envelopment analysis. Journal of Productivity Analysis 2002;17:157–74] that can distinguish true performers from those that may be advantaged by favourable environments or measurement errors. The method starts with data envelopment analysis (DEA), and continues with stochastic frontier analysis to explain the variation in organisational performance in terms of the operating environment, statistical noise and managerial efficiency. It concludes with DEA again using adjusted data to reveal a measure of performance based on management efficiency only. Our proposed contributions include (i) a comprehensive approach where total input and output slacks are identified simultaneously for non-radial inefficiencies before levelling the playing field, (ii) identifying percent adjustments attributable to the environment and statistical noise, and (iii) using a fully units-invariant DEA model.     

基于DEA的作业分析与评价模型

论文将数据包络分析(DEA)引入了作业成本管理(ABM),用定量化分析模型从不同角度分析了作业消耗资源和提供价值的效率,并进行了实证分析。基于DEA的作业分析与评价模型可以得到以下信息:(1)确定作业消耗资源的DEA有效性;(2)确定各DMU在有效生产前沿面上的投影,并为下一期间的作业改进提供信息;(3)确定资源输入的总体利用率和各项输入可变资源的利用率;(4)采用复合DEA模型评价非财务指标对作业有效性的影响。     

两阶段DEA前沿面投影问题研究——兼对我国上市银行运营绩效进行评价

DEA方法,即数据包络分析方法,是一种用于评价决策单元(Decision Making Units,DMUs)相对有效性的实证方法。近年来DEA方法已经广泛的应用于各行各业的绩效评价中,并发展出两阶段DEA方法。两阶段DEA方法相对于传统DEA方法的优势在于,它不但可以提供被评价对象的总体效率值,还可以分别生成每一阶段的效率值。但正是由于中间要素的存在,按照传统的DEA方法来调整两阶段DEA投入、产出要素的优化过程已不能成功投影在有效前沿面上。本文基于两阶段DEA方法,通过加入"虚拟中间要素"在两阶段DEA中嵌入一个"虚拟阶段",这样不但完善了两阶段DEA的逻辑结构,而且成功的将被评价单元投影到有效前沿面。最后本文应用以上方法对我国上市银行的运营绩效进行了实证分析。实证结果令我们意外的是,国有商业银行运营绩效优于股份制银行。     

基于最近距离投影的DEA两阶段效率评价方法研究

数据包络分析是进行效率评价最重要的方法之一。传统的数据包络分析理论主要寻找有效前沿面上的最远距离投影，在极大化无效性指数的同时也面临着效率改进的巨大难度和高额成本。对于具有两阶段内部生产结构的决策单元，本文从考虑最小改进难度的视角出发，提出了最近距离投影的两阶段效率评价方法。该方法首先得到所有强有效决策单元的线性组合，且这些组合均占优于被评价的两阶段决策单元。然后建立了两阶段范围调整效率评价模型，在确定具有最近投影距离的占优组合的同时，得到了两阶段评价效率。最后，本文运用我国32家上市银行的年度数据对所提出方法进行了应用验证。     

Association of DEA super-efficiency estimates with financial ratios: Investigating the case for Chinese banks

The great majority of applications of the popular frontier technique data envelopment analysis (DEA) do not test for the association of efficiency estimates with key performance indicators used by industry observers. Nevertheless, identifying efficiency estimates’ associations with commonly accepted financial measures of performance could guide benchmarking activities, pricing decisions, and regulatory monitoring. Thus, the current paper investigates to what extent bank DEA super-efficiency estimates are associated with key financial ratios. A low correlation may present an opportunity to address inefficiencies that were not obvious in financial ratio analysis, thus enabling an update of inferences drawn from ratios. Regressing ratios on efficiency estimates may also help predict financial ratios. Where an input–output specification is comprised of key financial ratios, DEA can also be used to objectively identify benchmarks for ratio analysis based on actual observed data collected from peers. Nine super-efficiency DEA formulations across two profitability models are systematically tested. The slacks-based measure of DEA with a parsimonious profitability efficiency model emerges as the most significant combination explaining the variation in the two industry ratios, post-tax profit/average total assets and return on average equity.     

Economic efficiency when prices are not fixed: disentangling quantity and price efficiency

This paper proposes an approach to compute cost efficiency in contexts where units can adjust input quantities and to some degree prices so that through their joint determination they can minimise the aggregate cost of the outputs they secure. The model developed is based on the data envelopment analysis (DEA) framework and can accommodate situations where the degree of influence over prices ranges from minimal to considerable. When units cannot influence prices at all the model proposed reduces to the standard cost efficiency DEA model for the case where prices are taken as exogenous. In addition to the cost efficiency model, we introduce an additive decomposition of potential cost savings into a quantity and a price component, based on Bennet indicators.     

Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA

In benchmarking, organizations look outward to examine others’ performance in their industry or sector. Often, they can learn from the best practices of some of them and improve. In order to develop this idea within the framework of Data Envelopment Analysis (DEA), this paper extends the common benchmarking framework proposed in Ruiz and Sirvent (2016) to an approach based on the benchmarking of decision making units (DMUs) against several reference sets. We refer to this approach as cross-benchmarking. First, we design a procedure aimed at making a selection of reference sets (as defined in DEA), which establish the common framework for the benchmarking. Next, benchmarking models are formulated which allow us to set the closest targets relative to the reference sets selected. The availability of a wider spectrum of targets may offer managers the possibility of choosing among alternative ways for improvements, taking into account what can be learned from the best practices of different peer groups. Thus, cross-benchmarking is a flexible tool that can support a process of future planning while considering different managerial implications.     

Egoist's dilemma: a DEA game

This paper deals with problems of consensus-making among individuals or organizations with multiple criteria for evaluating their performance when the players are supposed to be egoistic; in the sense that each player sticks to his superiority regarding the criteria. We analyze this situation within the framework or concept developed in data envelopment analysis (DEA). This leads to a dilemma called the `egoist's dilemma'. We examine this dilemma using cooperative game theory and propose a solution. The scheme developed in this paper can also be applied to attaining fair cost allocations as well as benefit–cost distributions.     

分税制以来中国地方财政支农绩效评价：基于分级支出视角

本文运用DEA-TOBIT法对分税制以来中国地方政府财政支农分级支出绩效及其外部影响因素进行了实证分析。总体来看,1993-2007年分级视角下的中国各省份及东中西的财政支农资金的配置效率呈持续降低态势;浙江、江苏、河南始终处于前沿面,而内蒙古、云南、陕西、宁夏、新疆、山西、黑龙江处于低效状态;西部地区均低于东部、中部和全国的平均水平。TOBIT回归显示,城镇化率因子对于全国和西东中地区均显著,且对于中部地区贡献度最大,而农户固定资产投资、农业机械装机总动力以及劳动力文化程度因子仅对于特定区域显著。     

Theoretical perspectives of trade-off analysis using DEA

Because of the piecewise linear nature of the frontier in data envelopment analysis (DEA), estimated marginal rates of substitution are only valid for infinitesimal, or small finite, changes in one or more variables. Analysing the impacts of very small changes is not adequate for many situations, where the consequences of substantial changes in variables are of interest to for instance managers. This paper develops methods for evaluating larger, i.e. non-marginal, tradeoffs between variables in DEA. The methods are capable of handling both scalar and additive changes. Finally, the approaches for evaluating basic pairwise tradeoffs are generalised in order to enable assessment of the impact on one or more throughputs of the change in one or more of the other throughputs.     

基于DEA的作业消耗资源效率分析

将数据包络分析(DEA)引入了作业成本管理(ABM),给出了适用的定量化分析方法,从不同角度分析了作业消耗资源的效率.确定作业消耗资源的DEA有效性;确定各DMU在有效生产前沿面上的"投影",并为下一期间的作业改进提供信息;确定资源投入的总体利用率和各项输入可变资源的利用率.最后,用该模型对某企业的作业进行了实证分析.     

Common benchmarking and ranking of units with DEA

This paper develops a common framework for benchmarking and ranking units with DEA. In many DEA applications, decision making units (DMUs) experience similar circumstances, so benchmarking analyses in those situations should identify common best practices in their management plans. We propose a DEA-based approach for the benchmarking to be used when there is no need (nor wish) to allow for individual circumstances of the DMUs. This approach identifies a common best practice frontier as the facet of the DEA efficient frontier spanned by the technically efficient DMUs in a common reference group. The common reference group is selected as that which provides the closest targets. A model is developed which allows us to deal not only with the setting of targets but also with the measurement of efficiency, because we can define efficiency scores of the DMUs by using the common set of weights (CSW) it provides. Since these weights are common to all the DMUs, the resulting efficiency scores can be used to derive a ranking of units. We discuss the existence of alternative optimal solutions for the CSW and find the range of possible rankings for each DMU which would result from considering all these alternate optima. These ranking ranges allow us to gain insight into the robustness of the rankings.     

Opening the black box of efficiency analysis: An illustration with UAE banks

Standard data envelopment analysis (DEA) does not provide adequate detail to identify the specific sources of inefficiency embedded in interacting divisions of an organization. On the other hand, network DEA gives access to this underlying diagnostic information that would otherwise remain undiscovered. As a first study of its kind, the paper illustrates an application of non-oriented network slacks-based measure using simulated profit center data that, in turn, rely on actual aggregate data on domestic commercial banks in the United Arab Emirates (UAE). The study also contributes to a perennial research problem, namely, inability of the outside researcher to access internal data for developing or testing new methods. In addition to these contributions to the Operations Research literature, focusing on UAE contributes to banking literature because this rapidly expanding part of the Middle East seldom appears in frontier efficiency literature.