A cautionary note on methods of comparing programmatic efficiency between two or more groups of DMUs in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann-Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal-Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann-Whitney and Kruskal-Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework. © 2007 Springer Science+Business Media, LLC

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal

Estimating Effectiveness of the Control of Violence and Socioeconomic Development in Colombia: An Application of Dynamic Data Envelopment Analysis and Data Panel Approach

This paper develops an index to evaluate the level of effectiveness of the control of violence based on the data envelopment analysis approach. The index is used to examine the grade of effectiveness of the control of violence at the level of Colombian departments between 1993 and 2007. Comparing the results across Colombian departments, we find that the majority of departments show improvement in their scores of effectiveness. A second stage of the regression model reveals that departments with a higher gross domestic product and higher education and employment are more effective in the control of violence, whereas departments with higher political violence, unemployment rates, unsatisfied basic needs, a displaced population, and hectares cultivated with coca show lower effectiveness in the control of violence. All these findings are of particular interest in the formulation and development of policies against violence, taking into account that organised forms of violence, such as drug trafficking, impede the adequate effectiveness of its control. Moreover, violence decreases social investments, generating alterations in social services that produce long-run deterioration in faith in the government’s ability to govern, which should become an incentive to further violence

Eco-efficiency measurement and material balance principle:an application in power plants Malmquist Luenberger Index

Incorporating Material Balance Principle (MBP) in industrial and agricultural performance measurement systems with pollutant factors has been on the rise in recent years. Many conventional methods of performance measurement have proven incompatible with the material flow conditions. This study will address the issue of eco-efficiency measurement adjusted for pollution, taking into account materials flow conditions and the MBP requirements, in order to provide ‘real’ measures of performance that can serve as guides when making policies. We develop a new approach by integrating slacks-based measure to enhance the Malmquist Luenberger Index by a material balance condition that reflects the conservation of matter. This model is compared with a similar model, which incorporates MBP using the trade-off approach to measure productivity and eco-efficiency trends of power plants. Results reveal similar findings for both models substantiating robustness and applicability of the proposed model in this paper

A classification of DEA models when the internal structure of the Decision Making Units is considered

We classify the contributions of DEA literature assessing Decision Making Units (DMUs) whose internal structure is known. Starting from an elementary framework, we define the main research areas as shared flow, multilevel and network models, depending on the assumptions they are subject to. For each model category, the principal mathematical formulations are introduced along with their main variants, extensions and applications. We also discuss the results of aggregating efficiency measures and of considering DMUs as submitted to a central authority that imposes constraints or targets on them. A common feature among the several models is that the efficiency evaluation of the DMU depends on the efficiency values of its subunits thereby increasing the discrimination power of DEA methodology with respect to the black box approach

Resource Allocation in an Asymmetric Technology Race with Temporary Advantages

Naval Research Logistics, V. 59, No. 2, pp 128-145.http://dx.doi.org/10.1002/nav.21477We consider two opponents that compete in developing aeymmetric technologies where each party's technology is aimed at damaging (or neutralizing) the other's technology. The situation we consider is different than the classical problem of commercial R&D races in two ways: First, while in sommercial R&D races the competitors compete over the control of market share, in our case the comprtition is about the effectiveness of technologies with respect to certain capabilities. Second, in contrast with the "winner-takes-all" assumption that characterizes much of the literature on this field in the commercial world, we assume that the party that wins gains a temporary advantage that expires when the other party develops a superior technology. We formulate a variety of models that apply to a one-sided situation, where one of the two parties has to determine how much to invest in developing a technology to counter another technology employed by the other party. The decision problems are expressed as (convex) nonlinear optimization problems. We present an application that provides some operational insights regarding optimal resource allocation. We also consider a two-sided situation and develop a Nash equilibrium solution that sets investment values, so that both parties have no incentive to change their investments

Network Optimization Models for Resource Allocations in Developing Military Countermeasures

Operations Research, V. 60, No. 1, pp 48-63.http://dx.doi.org/10.1287/opre.1110.1002A military arms race is characterized by an iterative development of measures and countermeasures. An attacker attempts to introduce new weapons in order to gain some advantage. whereas a defender attempts to develop countermeasures that can mitigate or even eliminate the effects of the weapons. This paper addresses the defender's decision problem: given limited resources, which countermeasures should be developed and how much should be invested in their development to minimize the damge caused by the attacker's weapos over a certain time horizon. We formulate several optimization models, corresponding to different operational settings, as sonstrained shortest-path problems and variants thereof. We then demonstrate the potential applicability and robusteness of this apporach with respect to various scenarios