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

Ranking Efficient DMUs Using the Variation Coefficient of Weights in DEA

Abstract One of the difficulties of Data Envelopment Analysis(DEA) is the problem of de_ciency discrimination among efficient Decision Making Units (DMUs) and hence, yielding large number of DMUs as efficient ones. The main purpose of this paper is to overcome this inability. One of the methods for ranking efficient DMUs is minimizing the Coefficient of Variation (CV) for inputs-outputs weights. In this paper, it is introduced a nonlinear model for ranking efficient DMUs based on the minimizing the mean absolute deviation of weights and then we convert the nonlinear model proposed into a linear programming form

Multi-objective Optimization and its Engineering Applications

Many practical optimization problems usually have several conflicting objectives. In those multi-objective optimization, no solution optimizing all objective functions simultaneously exists in general. Instead, Pareto optimal solutions, which are ``efficient" in terms of all objective functions, are introduced. In general we have many Pareto optimal solutions. Therefore, we need to decide a final solution among Pareto optimal solutions taking into account the balance among objective functions, which is called ``trade-off analysis". It is no exaggeration to say that the most important task in multi-objective optimization is trade-off analysis. Consequently, the methodology should be discussed in view of how it is easy and understandable for trade-off analysis. In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively easily. Seeing Pareto frontiers, we can grasp the trade-off relation among objectives totally. Therefore, it would be the best way to depict Pareto frontiers in cases with two or three objectives. (It might be difficult to read the trade-off relation among objectives with three dimension, though). In cases with more than three objectives, however, it is impossible to depict Pareto forntier. Under this circumstance, interactive methods can help us to make local trade-off analysis showing a ``certain" Pareto optimal solution. A number of methods differing in which Pareto optimal solution is to be shown, have been developed. This paper discusses critical issues among those methods for multi-objective optimization, in particular applied to engineering design problems

Robustness analysis based on weight restrictions in data envelopment analysis

Includes bibliographical references.Evaluating the performance of organisations is essential to good planning and control. Part of this process is monitoring the performance of organisations against their goals. The comparative efficiency of organizations using common inputs and outputs makes it possible for organizations to improve their performance so that can operate as the most efficient organizations. Resources and outputs can be very diversified in nature and it is complex to assess organizations using such resources and outputs. Data Envelopment Analysis models are designed to facilitate this of assessment and aim to evaluate the relative efficiency of organisations. Chapter 2 is dedicated to the basic Data Envelopment Analysis. We present the following: * A review of the Data Envelopment Analysis models; * The properties and particularities of each model. In chapter 3, we present our literature survey on restrictions. Data Envelopment Analysis is a value-free frontier which has the of yielding more objective efficiency measures. However, the complete freedom in the determination of weights for the factors and products) relevant to the assessment of organisations has led to some problems such as: zero-weights and lack of discrimination between efficient organizations. Weight restriction methods were introduced in order to tackle these problems. The first part of chapter 3 in detail the motivations for weight restrictions while the second part presents the actual weight restriction rnethods

The Generalized DEA Model of Fundamental Analysis of Public Firms, with Application to Portfolio Selection

Fundamental analysis is an approach for evaluating a public firm for its investmentworthiness by looking at its business at the basic or fundamental financial level. The focus of this thesis is on utilizing financial statement data and a new generalization of the Data Envelopment Analysis, termed the GDEA model, to determine a relative financial strength (RFS) indicator that represents the underlying business strength of a firm. This approach is based on maximizing a correlation metric between GDEA-based score of financial strength and stock price performance. The correlation maximization problem is a difficult binary nonlinear optimization that requires iterative re-configuration of parameters of financial statements as inputs and outputs. A two-step heuristic algorithm that combines random sampling and local search optimization is developed. Theoretical optimality conditions are also derived for checking solutions of the GDEA model. Statistical tests are developed for validating the utility of the RFS indicator for portfolio selection, and the approach is computationally tested and compared with competing approaches. The GDEA model is also further extended by incorporating Expert Information on input/output selection. In addition to deriving theoretical properties of the model, a new methodology is developed for testing if such exogenous expert knowledge can be significant in obtaining stronger RFS indicators. Finally, the RFS approach under expert information is applied in a Case Study, involving more than 800 firms covering all sectors of the U.S. stock market, to determine optimized RFS indicators for stock selection. Those selected stocks are then used within portfolio optimization models to demonstrate the superiority of the techniques developed in this thesis

Comparative evaluation of public universities in Malaysia using data envelopment analysis

Applications of Data Envelopment Analysis (DEA) for the assessment of performance of universities have been widely reported in the literature. Often the number of universities under the assessment is relatively small compared to the number of performance measures (inputs and outputs) used in the analysis, which leads to a low discriminating power of DEA models on efficiency scores. The main objective of this thesis is the development of improved DEA models that overcome the above difficulty, using a sample of public universities in Malaysia as an illustrative application. The proposed new approach combines the recently introduced Hybrid returns to scale (HRS) model with the use of additional information about the functioning of universities stated in the form of production trade-offs. The new model developed in this thesis, called Hybrid returns to scale model with trade-offs (HRSTO), is applied to a sample of eighteen universities, which is considered to be a very small sample for the DEA methodology. Our results show that, in contrast with standard DEA models, the new model is perfectly suitable for such samples and discriminates well between good and bad performers. The proposed combined use of HRS model with production trade-offs is a novel methodology that can be used in other applications of DEA. Overall, the thesis makes several contributions of the theory and practice of DEA. First, for the first time, it is shown that the higher education sector satisfies the assumptions and can be modelled using the proposed HRSTO model. Second, also for the first time, it is shown that production trade-offs can be assessed for such applications and the methodology of their assessment has been developed and used in the thesis. Third, it is demonstrated that the HRSTO model significantly improves the discriminating power of analysis compared to standard DEA models, which is particularly important for small data sets. Fourth, it is concluded that the HRS model is further improved if production trade-offs are used. Fifth, by experimenting with different specific values of production trade-offs, it is shown that even the most conservative estimates of trade-offs notably improve the model. Finally, our results contribute to the more general discussion of the performance of universities in Malaysia and identification of the best performers among them

Sustainability Analysis Of Intelligent Transportation Systems

Commuters in urban areas suffer from traffic congestion on a daily basis. The increasing number of vehicles and vehicle miles traveled (VMT) are exacerbating this congested roadway problem for society. Although literature contains numerous studies that strive to propose solutions to this congestion problem, the problem is still prevalent today. Traffic congestion problem affects society’s quality of life socially, economically, and environmentally. In order to alleviate the unsustainable impacts of the congested roadway problem, Intelligent Transportation Systems (ITS) has been utilized to improve sustainable transportation systems in the world. The purpose of this thesis is to analyze the sustainable impacts and performance of the utilization of ITS in the United States. This thesis advances the body of knowledge of sustainability impacts of ITS related congestion relief through a triple bottom line (TBL) evaluation in the United States. TBL impacts analyze from a holistic perspective, rather than considering only the direct economic benefits. A critical approach to this research was to include both the direct and the indirect environmental and socio-economic impacts associated with the chain of supply paths of traffic congestion relief. To accomplish this aim, net benefits of ITS implementations are analyzed in 101 cities in the United States. In addition to the state level results, seven metropolitan cities in Florida are investigated in detail among these 101 cities. For instance, the results of this study indicated that Florida saved 1.38 E+05 tons of greenhouse gas emissions (tons of carbon dioxide equivalent), $420 million of annual delay reduction costs, and$17.2 million of net fuel-based costs. Furthermore, to quantify the relative impact and sustainability performance of different ITS technologies, several ITS solutions are analyzed in terms of total costs (initial and operation & maintenance costs) and benefits (value of time, emissions, and safety). To account for the uncertainty in benefit and cost ii analyses, a fuzzy-data envelopment analysis (DEA) methodology is utilized instead of the traditional DEA approach for sustainability performance analysis. The results using the fuzzy-DEA approach indicate that some of the ITS investments are not efficient compared to other investments where as all of them are highly effective investments in terms of the cost/benefit ratios approach. The TBL results of this study provide more comprehensive picture of socio-economic benefits which include the negative and indirect indicators and environmental benefits for ITS related congestion relief. In addition, sustainability performance comparisons and TBL analysis of ITS investments contained encouraging results to support decision makers to pursue ITS projects in the future