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

Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we find the optimal scale to be situated around 7 to 10 million m3.Free Disposal Hull, economies of scale, optimal size, water sector

Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies.

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a .rst step, the presence of scale (and scope) economies is veri.ed. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we .nd the optimal scale to be situated around 7 to 10 million m3.

Assessing the Efficiency of Mass Transit Systems in the United States

Frustrated with increased parking problems, unstable gasoline prices, and stifling traffic congestion, a growing number of metropolitan city dwellers consider utilizing the mass transit system. Reflecting this sentiment, a ridership of the mass transit system across the United States has been on the rise for the past several years. A growing demand for the mass transit system, however, necessitates the expansion of service offerings, the improvement of basic infrastructure/routes, and the additional employment of mass transit workers, including drivers and maintenance crews. Such a need requires the optimal allocation of financial and human resources to the mass transit system in times of shrinking budgets and government downsizing. Thus, the public transit authority is faced with the dilemma of “doing more with less.” That is to say, the public transit authority needs to develop a “lean” strategy which can maximize transit services with the minimum expenses. To help the public transit authority develop such a lean strategy, this report identifies the best-in-class practices in the U.S. transit service sector and proposes transit policy guidelines that can best exploit lean principles built upon best-in-class practices

Using DEA to estimate the importance of objectives for decision makers

In this paper we establish further connections between DEA and Multi-criteria Decision Analysis by suggesting a particular way to estimate preference weights for different objectives using DEA. We claim that the virtual multipliers obtained from a standard DEA model are not suitable to measure the preferences of a decision maker. Our suggestion takes advantage of the parallelism between DEA and the methodology proposed by Sumpsi et al. (1997) by projecting each unit on a linear combination of the elements of the pay-off matrix. Finally, we make an application of the proposed methodology to agricultural economics in a case study with Spanish data.Data Envelopment Analysis, Multicriteria Decision Analysis, preferences, weights, virtual multipliers.

Sensitivity analysis of network DEA illustrated in branch banking

Users of data envelopment analysis (DEA) often presume efficiency estimates to be robust. While traditional DEA has been exposed to various sensitivity studies, network DEA (NDEA) has so far escaped similar scrutiny. Thus, there is a need to investigate the sensitivity of NDEA, further compounded by the recent attention it has been receiving in literature. NDEA captures the underlying performance information found in a firm?s interacting divisions or sub-processes that would otherwise remain unknown. Furthermore, network efficiency estimates that account for divisional interactions are more representative of a dynamic business. Following various data perturbations overall findings indicate positive and significant rank correlations when new results are compared against baseline results - suggesting resilience. Key findings show that, (a) as in traditional DEA, greater sample size brings greater discrimination, (b) removing a relevant input improves discrimination, (c) introducing an extraneous input leads to a moderate loss of discrimination, (d) simultaneously adjusting data in opposite directions for inefficient versus efficient branches shows a mostly stable NDEA, (e) swapping divisional weights produces a substantial drop in discrimination, (f) stacking perturbations has the greatest impact on efficiency estimates with substantial loss of discrimination, and (g) layering suggests that the core inefficient cohort is resilient against omission of benchmark branches. Various managerial implications that follow from empirical findings are discussed in conclusions.

Resampling in Data Envelopment Analysis illustrated by a hospital example

Workshop 2015 -Advances in DEA Theory and Applications (December 1-2, 2015)In this paper, we propose new resampling models in data envelopment analysis (DEA). Input/output values are subject to change for several reasons, e.g., measurement errors, hysteretic factors, arbitrariness and so on. Furthermore, these variations differ in their input/output items and their decision-making units (DMU). Hence, DEA efficiency scores need to be examined by considering these factors. Resampling based on these variations is necessary for gauging the confidence interval of DEA scores. We propose two resampling models. The first model utilizes historical data, e.g., past-present, for estimating data variations, imposing chronological order weights which are supplied by Lucas series (a variant of Fibonacci series). The second one deals with future prospects. This model aims at forecasting the future efficiency score and its confidence interval for each DMU. We applied our models to dataset composed of Japanese municipal hospitals.The workshop is supported by JSPS (Japan Society for the Promotion of Science), Grant-in-Aid for Scientific Research (B), #25282090, titled “Studies in Theory and Applications of DEA for Forecasting Purpose.本研究はJSPS科研費 基盤研究(B) 25282090の助成を受けたものです

Using a modified DEA model to estimate the importance of objectives. An application to agricultural economics.

This paper shows a connection between Data Envelopment Analysis (DEA) and the methodology proposed by Sumpsi et al. (1997) to estimate the weights of objectives for decision makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of Multiple Attribute Decision Analysis the basic contribution of this paper is a new interpretation of the methodology by Sumpsi et al. (1997) in terms of efficiency. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures which does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.Multicriteria Decision Making, Goal Programming, Weights, Preferences, Data Envelopment Analysis.

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented

A Data Envelopment Analysis Toolbox for MATLAB

The Data Envelopment Analysis Toolbox is a new package for MATLAB that includes functions to calculate the main data envelopment analysis models. The package includes code for the standard radial input, output and additive measures, allowing for constant and variable returns to scale, as well as recent developments related to the directional distance function, and including both desirable and undesirable outputs when measuring efficiency and productivity; i.e., Malmquist and Malmquist-Luenberger indices. Bootstrapping to perform statistical analysis is also included. This paper describes the methodology and implementation of the functions, and reports numerical results using a reliable productivity database on US agriculture to illustrate their use