Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

Measuring Eco-efficiency of Production: A Frontier Approach

Eco-efficiency of production is an important concept both from the viewpoint of society and business community; but as yet, there is no unambiguous way to its measurement. The purpose of this paper is to present a general measurement framework based on production theory and the activity analysis approach. Although we exploit the existing methods and techniques, our approach diverges essentially from the usual treatments of the environmental performance of firms in the productive efficiency analysis. The main difference between our approach and the earlier studies is that we build on the definition of eco-efficiency as the ratio of economic value added to the environmental damage index. Related to this orientation, we also approach eco-efficiency from a more aggregate perspective. Our general framework is illustrated by an empirical application to the evaluation of eco-efficiency of road transportation in Finland.Eco-efficiency, Environmental Pressures, Aggregation, Benefit of the Doubt Weighting, Distance Function, Activity Analysis, Data Envelopment Analysis, Road transportation

Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix

Cross-efficiency evaluation method is an effective and widespread adopted data envelopment analysis (DEA) method with self-assessment and peer-assessment to evaluate and rank decision making units (DMUs). Extant aggressive, benevolent, and neutral cross-efficiency methods are used to evaluate DMUs with competitive, cooperative, and nontendentious relationships, respectively. In this paper, a symmetric (nonsymmetric) compete-cooperate matrix is introduced into aggressive and benevolent cross-efficiency methods and compete-cooperate cross-efficiency method is proposed to evaluate DMUs with diverse (relative) relationships. Deviation maximization method is applied to determine the final weights of cross-evaluation to enhance the differentiation ability of cross-efficiency evaluation method. Numerical demonstration is provided to illustrate the reasonability and practicability of the proposed method

Disentangling Within- and Between-Country Efficiency Differences of Bank Branches

In this paper we propose a framework to assess the efficiency of bank branch networks operating in different financial environments. The framework can be used to disentangle within- from between-country performance differences. The framework is constructive in that it identifies operational aspects responsible for superior performance and suggests guidelines for branch improvement. We report results from three bank branch networks in the U.K., Greece and Cyprus, and demonstrate how branch networks can benefit from such international comparisons.Bank Branch Efficiency, International Benchmarks, Data Envelopment Analysis.

Benchmarking Sustainable Development: A Synthetic Meta-index Approach

The need for monitoring countries’ overall performance in Sustainable Development (SD) is widely recognized, but the methods for aggregating vast amounts of empirical data remain rather crude. This paper examines the so-called ‘benefit-of-the-doubt’ weighting method as a tool for identifying benchmarks without imposing strong normative judgement about SD priorities. The weighting method involves linear optimization techniques, and allows countries to emphasize and prioritize those SD aspects for which they perform relatively well. Using this method, we construct a meta-index of SD (MISD), which combines 14 existing aggregate SD indices (developed by well-established organizations and/or expert teams) into a single synthesizing overall SD index. Within a sample of 154 countries, our index identifies 6 benchmark countries (3 high-income countries and 3 upper-middle-income countries), but also a number of seriously under-performing countries. We view this approach as a first step towards more systematic international comparisons, aimed at facilitating diffusion of the best practices and policies from the benchmark countries to the less developed world.Sustainable Development, Integrated Assessment, Benchmarking, benefit of the doubt weighting, Data Envelopment Analysis

Allocating the fixed cost:an approach based on data envelopment analysis and cooperative game

Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res 235(1): 206–214, 2014) proposed a novel approach for allocating the fixed cost based on the game cross-efficiency method by taking the game relations among users in efficiency evaluation. This paper proves that the novel approach of Du et al. (Eur J Oper Res 235(1): 206–214, 2014) is equivalent to the efficiency maximization approach of Li et al. (Omega 41(1): 55–60, 2013), and may exist multiple optimal cost allocation plans. Taking into account the game relations in the allocation process, this paper proposes a cooperative game approach, and uses the nucleolus as a solution to the proposed cooperative game. The proposed approach in this paper is illustrated with a dataset from the prior literature and a real dataset of a steel and iron enterprise in China

Improvement Of Discrimination Power And Weight Dispersion In Multi-Criteria Data Envelopment Analysis

Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. Kekurangan keupayaan mendiskriminasi dan kelemahan pengagihan pemberat kekal sebagai isu utama dalam Analisis Penyampulan Data (DEA). Semenjak model DEA berbilang kriteria (MCDEA) pertama yang dibentuk pada akhir tahun 1990an, hanya pendekatan pengaturcaraangol; yakni, GPDEA-CCR dan GPDEA-BCC telah diperkenalkan bagi menyelesaikan masalah berkenaan dalam konteks berbilang kriteria

An evaluation of cross-efficiency methods: With an application to warehouse performance

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a cross-efficiency method based on a rank-order DEA model to accommodate the ordinal nature of some key variables characterizing warehouse performance. This is one of the first comparisons of methods on a real-life dataset and the first time that a model allowing for qualitative variables is included in such a comparison. Our results show that the choice of model matters, as one obtains statistically different rankings from each one of them. This holds in particular for the multiplicative and game-theoretic methods whose results diverge from the classic method. From a managerial perspective, focused on the applicability of the methods, we evaluate them through a multidimensional metric which considers their capability to rank DMUs, their ease of implementation, and their robustness to sensitivity analyses. We conclude that standard weight-restriction methods, as initiated by Sexton et al. [48], perform as well as recently introduced, more sophisticated alternativesSpanish Ministry of Science and Innovation (Ministerio de Ciencia e Innovación), the State Research Agency (Agencia Estatal de Investigación) and the European Regional Development Fund (Fondo Europeo de Desarrollo Regional) under grants EIN2020-11226

Housing Ranking: a model of equilibrium between buyers and sellers expectations

The equilibrium set of housing units (alternatives) can be characterized from the standpoint of both the demander and the supplier. The current work describes an application of the multicriteria single price model to the ranking of alternatives. By a generalization of the single price model and from both viewpoints an efficiency index can be calculated. We demonstrate how, in equilibrium, the two viewpoints result inevitably in inverse orders of ranking. The model is illustrated by a sample of housing units in the city of Valencia, Spain.

Calculating Super Efficiency of DMUs for Ranking Units in Data Envelopment Analysis Based on SBM Model

There are a number of methods for ranking decision making units (DMUs), among which calculating super efficiency and then ranking the units based on the obtained amount of super efficiency are both valid and efficient. Since most of the proposed models do not provide the projection of Pareto efficiency, a model is developed and presented through this paper based on which in the projection of Pareto-efficient is obtained, in addition to calculating the amount of super efficiency. Moreover, the model is unit invariant, and is always feasible and makes the amount of inefficiency effective in ranking