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

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.

A reasonable benchmarking frontier using DEA : an incentive scheme to improve efficiency in public hospitals

There exists research relating management concepts with productivity measurement methods that offers useful solutions for improving management control in the public sector. Within this sphere, we connect agency theory with efficiency analysis and describe how to define an incentives scheme that can be applied in the public sector to monitor the efficiency and productivity of managers. To fulfill the main objective of this research, we propose an iterative process for determining what we define as a ‘reasonable frontier’, a concept that provides the foundation required to establish the incentive scheme for the managers. Our ‘reasonable frontier’ has the following properties: i) it detects the presence of outliers, ii) it proposes a procedure to establish the influence introduced by extreme observations, and iii) it sorts out the problem of data masking. The proposed method is applied to a sample of hospitals taken from the public network of the Spanish health service. The results obtained confirm the applicability of the proposal made. Summing up, we define and apply a useful method, combining aspects of agency theory and efficiency analysis, which is of interest to those public authorities trying to design effective incentive schemes which influence the decision making of the public managers

Multicriteria ranking using weights which minimize the score range

Various schemes have been proposed for generating a set of non-subjective weights when aggregating multiple criteria for the purposes of ranking or selecting alternatives. The maximin approach chooses the weights which maximise the lowest score (assuming there is an upper bound to scores). This is equivalent to finding the weights which minimize the maximum deviation, or range, between the worst and best scores (minimax). At first glance this seems to be an equitable way of apportioning weight, and the Rawlsian theory of justice has been cited in its support.We draw a distinction between using the maximin rule for the purpose of assessing performance, and using it for allocating resources amongst the alternatives. We demonstrate that it has a number of drawbacks which make it inappropriate for the assessment of performance. Specifically, it is tantamount to allowing the worst performers to decide the worth of the criteria so as to maximise their overall score. Furthermore, when making a selection from a list of alternatives, the final choice is highly sensitive to the removal or inclusion of alternatives whose performance is so poor that they are clearly irrelevant to the choice at hand

Microfinance institutions and efficiency

Microfinance Institutions (MFIs) are special financial institutions. They have both a social nature and a for-profit nature. Their performance has been traditionally measured by means of financial ratios. The paper uses a Data Envelopment Analysis (DEA) approach to efficiency to show that ratio analysis does not capture DEA efficiency.Special care is taken in the specification of the DEA model. We take a methodological approach based on multivariate analysis. We rank DEA efficiencies under different models and specifications; e.g., particular sets of inputs and outputs. This serves to explore what is behind a DEA score. The results show that we can explain MFIs efficiency by means of four principal components of efficiency, and this way we are able to understand differences between DEA scores. It is shown that there are country effects on efficiency; and effects that depend on Non-governmental Organization (NGO)/non-NGO status of the MFI