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Adaptive Data Envelopment Analysis Models of Ecosystems of Megalopolises
Abstract
Data envelopment analysis is an effective method for assessing the relative sustainability of ecosystems in megalopolises, which are characterized by a variety of environmental and socio-economic indicators. The existing models do not allow adapting the parameters of data envelopment analysis models to the preferences of the decision-maker and do not provide a consistent assessment of the effectiveness of complex socio-economic systems. The most important characteristics of complex socio-economic systems have to be calculated by indirect methods by solving a number of optimization problems. Adaptive data envelopment analysis models are developed to determine the sustainability of ecosystems in megalopolises on the basis of ecological and socio-economic indicators of anthropogenic load. In the proposed adaptive models, intermediate results at the previous stage of the functioning of the megalopolis ecosystem are only partially consumed at the next stage. A part of the input parameters of the functioning of the ecosystems of the megalopolis can be freely distributed. Additional input parameters are directly consumed at the next stage of the functioning of the megalopolis ecosystem. The optimal values of the parameters of the models are determined on the basis of the dialogue procedure of sequential cutting of multidimensional sets using affine subspaces. Indicators of sustainability of ecosystems of megalopolises, which characterize a low level of anthropogenic load, are calculated.
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Possibilistic Data Envelopment Analysis (PDEA) is one of the most applicable and popular approaches in the literature to deal with imprecise and ambiguous data in DEA models. In this approach, with respect to tendency of decision maker (DM) in taking optimistic, pessimistic and compromise attitude, three measures including possibility, necessity and credibility measures are used to form the Fuzzy DEA (FDEA) models, respectively. However, decision makers may have different preference and so it is necessary to customize fuzzy DEA models according to properties of DMUs. This paper proposes a novel fuzzy DEA model based on general fuzzy measure in which the attitude of DMUs could be determined by the optimistic-pessimistic parameters. As a result, the proposed FDEA model is general, applicable, flexible, and adjustable based on each DMUs. A numerical example is used to explain the proposed approach while usefulness and applicability of this approach have been illustrated using a real data set to measure efficiency of 38 hospital in United States.
We define a fuzzy multi-objective multi-period network DEA model customized to evaluate the dynamic performance of oil refineries in the presence of undesirable outputs. In particular, we use a standard fuzzy operator to define the efficiency levels so as to integrate multiple objectives and periods of time within a unique maximization framework. Managers and decision makers are provided with a model characterized by its operational simplicity that allows for the straightforward implementation of standard spreadsheet software. The model is applied to a real-life case study, where the capacity of refineries to optimize their performance through the refining process is analyzed together with the introduction of value-added products that preserve and enhance the environmental dimensions of the refining process. The inclusion of a real-life case study aims at illustrating the efficacy and applicability of the proposed method relative to those of more conventional models. Moreover, the range of the time period covered allows us to analyze the evolution of efficiency beyond the standard two-period Malmquist framework generally considered in the literature dealing with the behavior of refineries.
In practice, the concept of incentives is extensively applied in the allocation process for guiding the behaviours of an organization's units to satisfy the goals of the organization. However, this concept is rarely considered in data envelopment analysis (DEA)-based allocation research. This paper proposes a two-step incentive approach for allocating common revenues or fixed costs. The first step is performance evaluation. Considering the noncooperative game relationship of decision-making units (DMUs), a DEA game cross-efficiency method is selected to measure the efficiency scores of DMUs in this paper. The second step is incentive allocation. Based on the performance evaluation, we propose our incentive method for allocating revenues or fixed costs. We further provide simple equations to calculate the global optimal solution for our nonlinear programme allocation models. Several properties are explored, and we i) obtain the allocation interval rule of DMUs with the incentives, ii) investigate the quantitative relationship between the allocation gap and the optimal allocation plan, and iii) prove that the optimal allocation plan obtained by our allocation model is unique. The results of an empirical application highlight the applicability of our allocation method and solution approach. In this study, we obtain several important practical insights, including that i) our method has positive effects on performance improvement and ii) our method can work well even in an information asymmetric decision-making environment.
With the building of sustainable cities being listed as one of the Sustainable Development Goals in the 2030 Agenda, cities in developing countries are facing more severe challenges. Therefore, it has become very urgent to evaluate and compare sustainability under different policy intervention scenarios. Based on the principle of system dynamics, this study constructed an urban sustainability evaluation model covering six subsystems: economy, livelihood, risk, environment, pollution governance, and resource. Using 13 cities in the Beijing-Tianjin-Hebei region as study cases, 5 future policy scenarios were designed under the framework of the Shared Socioeconomic Pathways to simulate the variation of the urban sustainability index in each city by 2035. The results reveal that: (1) Medium and small-sized cities around Beijing are facing more challenges to achieve sustainable urban development; (2) the urban sustainability index in each city varies under different policy scenarios. (3) the gap of urban sustainability in the Beijing-Tianjin-Hebei region does not show a significant narrowing trend and is likely to widen in the future. The approach can also be applied to other regions to provide decision support for choosing urban development pathways after comparing possible future trajectories of sustainable urban development.
Data Envelopment Analysis (DEA) is a linear programming based model which evaluates the relative efficiency of Decision Making Units (DMUs), with multiple inputs and outputs. Conventional DEA evaluates DMUs with their own weights and separates them into efficient and inefficient. To provide a full ranking of DMUs or select one of them (as the most preferred one), more discrimination is necessary. This paper presents a method that ranks extreme efficient units by comparing the volumes of their optimal weight sets, approximately, through generating some random weight vectors. To illustrate the proposed method, some numerical examples are provided.
Robust optimization has become the state-of-the-art approach for solving linear optimization problems with uncertain data. Though relatively young, the robust approach has proven to be essential in many real-world applications. Under this approach, robust counterparts to prescribed uncertainty sets are constructed for general solutions to corresponding uncertain linear programming problems. It is remarkable that in most practical problems, the variables represent physical quantities and must be nonnegative. In this paper, we propose alternative robust counterparts with nonnegative decision variables – a reduced robust approach which attempts to minimize model complexity. The new framework is extended to the robust Data Envelopment Analysis (DEA) with the aim of reducing the computational burden. In the DEA methodology, first we deal with the equality in the normalization constraint and then a robust DEA based on the reduced robust counterpart is proposed. The proposed model is examined with numerical data from 250 European banks operating across the globe. The results indicate that the proposed approach (i) reduces almost 50% of the computational burden required to solve DEA problems with nonnegative decision variables; (ii) retains only essential (non-redundant) constraints and decision variables without alerting the optimal value.
Performance measurement is one of the most essential real life decision making problems faces several criteria and different types of uncertainty and vagueness. Human expertise is mandatory for such situation although it is not enough to overcome such complicated cases. Expert systems which can sense, analyze and incorporate all details of real life decision making problems are required. In this paper an expert system is proposed in form of an uncertain Data Envelopment Analysis (DEA) approach. More formally a mixed fuzzy-robust uncertainty is addressed in the proposed DEA. Two scenario-based robust DEA models under Constant Return to Scale (CRS) and Variable Return to Scale (VRS) conditions have been proposed. Since the observed values for the inputs and outputs of Decision Making Units (DMUs) in each scenario may be ambiguous or vague, fuzzy DEA models corresponding to each of the robust scenarios are developed. So, this paper proposes four fuzzy-robust DEA models, which simultaneously maintain the advantage of each of the fuzzy and robust approaches, and at same time calculate the upper and lower bounds of the efficiency scores of DMUs under CRS and VRS conditions. Finally, to evaluate the validity and applicability of the proposed models, two numerical examples and a real case study in Small and Medium-sized Enterprises (SMEs) are presented and discussed.
Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries.
In this paper we present an integrated Data Envelopment Analysis-Multiple Criteria Decision Aid (DEA-MCDA) model which can be applied to increase the discrimination power of DEA. The aim is to restrict weight values of a DEA model by using tools from MCDA. This model leads to more reasonable inputs/outputs weights while in classic DEA models, some inputs/outputs may be characterized by very low or high weight values. To achieve this goal we use the stability intervals based on PROMETHEE II (Preference Ranking Organization METHod for Enrichment of Evaluations) as weight constraints in DEA. Furthermore, the unicriterion net flow scores matrix is used instead of the initial evaluation matrix. By doing so, we already integrate preferential information in the DEA process. By construction, the best results are compatible with the PROMETHEE II ranking. Additional comparisons with the outputs of other decision making techniques are provided based on two examples.
Based on literatures in recent years on DEA models with interval data, this paper aims at enhancing the interval efficiencies for inefficient DMUs. Ideal points are used to determine the extent of inefficient DMUs that can be improved. Numbers of specific programs are established to obtain the target point as a benchmarking on the efficient frontier, and bring the adjusted inputs and outputs as respectively close to their target ones as possible. The interval efficiencies can be improved by increasing only outputs, decreasing only inputs or adjusting both simultaneously, so that the lower bound of the interval efficiency can be increased as much as possible while the upper bound can attains one. The research is based on the interval data setting, so the approach is proposed to make sure the final adjusted data are still interval data. Finally, a numerical example is shown to illustrate the idea of the method.
We present in this paper a general network DEA approach to deal with efficiency assessments in multi-stage processes. Our approach complies with the composition paradigm, where the efficiencies of the stages are estimated first and the overall efficiency of the system is obtained ex post. We use multi-objective programming as modeling framework. This provides us the means to assess unique and unbiased efficiency scores and, if required, to drive the efficiency assessments effectively in line with specific priorities given to the stages. A direct comparison with the multiplicative decomposition approach on data drawn from the literature brings into light the advantages of our method and some critical points that one should be concerned about when using the multiplicative efficiency decomposition
Efficient solutions in Multi-Objective Integer Linear Programming (MOILP) problems are categorized into two distinct types, supported and non-supported. Many researchers try to gain some conditions to determine whether a feasible solution is efficient, nevertheless there is no attempt to identify the efficiency status of a given efficient solution, i.e. supported and non-supported. In this paper, we first verify the relationships between Data Envelopment Analysis (DEA) and MOILP and then design two distinct practical procedures: the first one specifies whether or not an arbitrary feasible solution is efficient, meanwhile the second one, as the main aim of this study, determines the efficiency status of an efficient solution. Finally, as a contribution of the suggested approach, we illustrate the drawback of Chen and Lu’s methodology (Chen and Lu, 2007) which is developed for solving an extended assignment problem.
Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. Two-stage DEA models do not require a priori specification of input and output weights (or multipliers) and by letting these weights run freely, estimates of system and process efficiencies are obtained. This paper proposes a methodology for a fuzzy two-stage DEA model, where the weights are restricted in ranges and input-output data are treated as fuzzy numbers. The assurance region approach is utilized to restrict weight flexibility in the model. Based on Zadeh’s extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the fuzzy efficiency score. We then transform this pair of two-level mathematical programs into a pair of conventional one-level mathematical programs to calculate the bounds of the fuzzy efficiency scores. The examples of non-life insurance companies in Taiwan and IT impact on firm performance are illustrated to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy.
The mixed integer linear programming (MILP) models are proposed to estimate the performance of decision making units (DMUs) including both integer and real values in data envelopment analysis (DEA). There are several studies to propose MILPs in the literature of DEA; however, they have some major shortcomings unfortunately. This study firstly mentioned the shortcomings in the previous researches and secondly suggests a robust MILP based on the Kourosh and Arash Method (KAM). The proposed linear model, integer-KAM (IKAM), has almost all capabilities of the linear KAM and significantly removes the shortcomings in the current MILPs. For instance, IKAM benchmarks and ranks all technically efficient and inefficient DMUs at the same time. It detects outliers, and estimates the production frontier significantly. A numerical example of 39 Spanish airports with four integer inputs and three outputs including two integer values and a real value also represents the validity of the statements.