Jesús T. Pastor

• Doctor of Mathematics
• Miguel Hernández University of Elche

In platform engineering, every second is precious and every resource is important. As infrastructure becomes more complex, managing environments as code is the next step in the maturation of modern DevOps organizations.

Helm encapsulates all K8s objects into a package, reducing interaction with individual yaml files. In addition to this, most third-party vendors also provide pre-built Helm charts to simplify the process of deploying their products into K8s. Therefore, Helm is often the first choice for installing ready-made solutions such as monitoring, database a...

Considering any graph technical inefficiency measure, we show that the so-called standard or traditional approach for decomposing profit inefficiency relying on Fenchel-Mahler inequalities obtained from duality theory, establishes that profit inefficiency is greater than or equal to the product of technical inefficiency times a positive factor expr...

The traditional approach decomposing profit inefficiency into the sum of its technical and its allocative components identifies first the frontier projection of each firm based on the exogenous choice of a specific technical measure, e.g., based on slacks, directional, etc. However, in real life situations, firms and organizations are interested in...

We introduce two desirable properties concerning the allocative efficiency term in the decomposition of economic efficiency. Since Farrell, economic efficiency, defined in terms of the cost, revenue, profitability, or profit functions, is decomposed into a technical efficiency measure and allocative efficiency. Resorting to duality theory, allocati...

The reverse directional distance function, shortly RDDF, is a relatively recent concept introduced by Pastor et al. (2016). It is an apparently simple idea and, at the same time, a fruitful one. Let us start considering an efficiency measure (EM) and a finite sample of firms to be analyzed, FJ. As we have shown throughout most of the previous chapt...

The usual and well-established methods, explained and used in most of the previous chapters, for deriving a specific overall economic inefficiency decomposition associated with a given technical efficiency measure (multiplicative or additive), which we refer to as the traditional approaches, rely on the same “modus operandi”; i.e., they are based o...

The canonical model of perfect competition, resulting in social welfare maximization, assumes all kinds of technical and allocative inefficiencies away. In equilibrium, economic theory establishes that in contestable markets, competition forces draw firms towards profit maximization (Vickers, 1995). This in turn requires that, on one hand, firms ex...

The enhanced Russell graph measure, ERG, (Pastor et al., 1999) was designed as a new global efficiency measure to overcome the computational difficulties of the Russell graph measure of technical efficiency, RG (Färe et al., 1985). Historically, Farrell (1957) implemented the first measure of technical efficiency, while Färe and Lovell (1978), afte...

Over past decades, one of the aspects related to the measurement of technical efficiency that has attracted the attention of Data Envelopment Analysis (DEA) researchers for the last decades has been the development of the generalized efficiency measures (GEMs), also called graph measures. The initial motivation for these measures was the design of...

From the beginning of DEA as a well-defined multi-output-multi-input tool for measuring efficiency, a huge number of technical efficiency measures have been introduced in the literature. Each of them implements a different way of gauging the “distance” from a firm in the interior of the technology to its efficient frontier (radially, hyperbolically...

This chapter is concerned with the measurement of profitability efficiency, defined as the ratio of revenue to cost, and its multiplicative decomposition into a productive efficiency measure—including technical and scale efficiencies, corresponding to the generalized distance function introduced by Chavas and Cox (1999), and allocative efficiency....

Data Envelopment Analysis can determine both a technical efficiency score and benchmarking information on how to change inputs and outputs to reach the efficient frontier if the firm under evaluation is technically inefficient. All measures studied in this book resort to the determination of benchmarking information through the calculation of the f...

After the introduction in the Data Envelopment Analysis literature of the radial measures, other approaches and ways of measuring the distance from a firm to the efficient frontier were defined, with the aim of solving certain drawbacks of the radial ones. On the one hand, radial measures are too restrictive in the sense that each assessed unit is...

The birth of the directional distance function as an inefficiency measure was linked to the consumer theory work developed by Luenberger in the early 1900s. Luenberger (1992a) introduced the concept of the benefit function in consumer theory in order to develop group welfare relations and, particularly, considered the Shephard’s input distance func...

In this chapter, we summarize the analytical framework found in the book by presenting the main concepts in an intuitive and accessible way while relying on supporting graphical illustrations to ease comprehension. Arguably, the measurement of economic efficiency dates back to the seminal paper by Farrell (1957), who introduced the definition, deco...

As we showed in Chap. 8, by duality, the directional distance function (DDF) is related to a measure of profit inefficiency that is calculated as the normalized deviation between optimal and actual profit at market prices. However, in the most usual case where the selected directional vector corresponds to the observed values in inputs and outputs...

In this chapter, we present the classic approach to calculate and decompose cost and revenue efficiency based on Shephard’s radial input and output distance functions. These decompositions follow closely the presentation done in Chap. 2 where both economic efficiency measures can be separated into technical and allocative components, i.e., expressi...

In this paper, we characterize local circularity for the Laspeyres, Paasche, and Fisher price indexes. In the first two cases, we begin by deriving a sufficient condition for achieving circularity that establishes that at least one of two proposed equalities must hold. We end up showing that the sufficient condition is also necessary. We continue w...

There is variation in how long it takes a golfer to win for the first time on the PGA tour. There are also golfers who never win. We investigate the time to first win using a survival function methodology, including shots gained measures of golfing ability, number of events played, experience prior to joining the tour, the competition, as explanato...

This paper proposes a new method to measure economic inefficiency of decision making units based on the calculation of the least distance to the Pareto-efficient frontier in Data Envelopment Analysis (DEA). While all previously published approaches that have dealt with the problem of determining least distances to the efficient frontier are focus o...

We begin by providing contextual background for this book, the second in a series. We continue by proclaiming the importance of efficiency and productivity, for businesses, industries and nations. We then summarise the chapters in the book, which consist of an equal number of advances in the analytical foundations of efficiency and productivity mea...

This book surveys the state-of-the-art in efficiency and productivity analysis, examining advances in the analytical foundations and empirical applications. The analytical techniques developed in this book for efficiency provide alternative ways of defining optimum outcome sets, typically as a (technical) production frontier or as an (economic) cos...

Cross-efficiency has been developed for the evaluation of cross-sectional data in Data Envelopment Analysis. This paper extends cross-efficiency evaluation introducing the concept of cross-productivity. The extension proposed here is aimed at providing a dynamic peer-evaluation of decision making units, based on the standard Luenberger indicator, w...

The national golf organizations support the development of golf in their country and one of the signs of their success is the generation of elite professional golfers. In this paper, we analyze the emergence of elite professional golfers in eighteen European nations. The efficiency of these nations is measured through output-oriented Data Envelopme...

A natural multiplicative efficiency measure for the Constant Returns to Scale Proportional Directional Distance Function (pDDF) is derived, relating its associated linear program to that of the well-known output-oriented radial efficiency measurement model. Based on this relationship, a traditional CCD (Caves, Christensen and Diewert) Malmquist ind...

This paper proposes two new Luenberger-type indicators, one for measuring productivity change of decision making units in the full input-output space, and the other for determining profit inefficiency change over time when information on market prices is also available. Both approaches are based upon the recently introduced Weighted Additive Distan...

Classification is a defining feature of Para-sport, and sports-specific classification systems determined through multidisciplinary scientific research are required, i.e., evidence-based and focused on the relationship between the impairment and the key performance determinants. Data envelopment analysis (DEA) was applied as a classification tool u...

Bounded additive models in Data Envelopment Analysis (DEA) under the assumption of Constant Returns to Scale (CRS) were recently introduced in the literature (Cooper et al., 2011, Pastor et al., 2013 and 2015). In this paper, we propose to extend the so far generated knowledge about bounded additive models to the family of Directional Distance Func...

Previous work suggests that the charter value hypothesis is theoretically grounded and empirically supported, but not universally. Accordingly, this paper aims to perform an analysis of the relations among charter value, risk taking, and supervision that take into account the relations’ complexity. Specifically, using the CAMELS rating system as a...

In this paper we describe a Shiny interactive Web application (RStudio, 2013) by RStudio (RStudio, 2012) which is used to estimate technical efficiency through Data Envelopment Analysis (DEA), a technique widely used by engineers and operation research practitioners. The Shiny interactive Web application is based on a unified method for computing t...

Life is mostly surrounded by uncertainties. Mathematics, as part of life, deals also with them. As an applied mathematician I have decided to relate my own research experiences, a relevant part of my life, so that people from younger generations can appreciate how research topics may appear just by chance. The second message I would like to transmi...

This article examines the impact of the reforms introduced in the structure of the Portuguese local administration after the bailout agreement in 2011 on the efficiency and productivity of municipalities. In order to determine a measure of productivity change, we apply the global Malmquist productivity index to assess the performance of the 278 Por...

The Slacks-Based Measure was introduced by Tone (2001) in order to estimate technical efficiency in the input-output space by taking into account all sources of technical inefficiency and satisfying, at the same time, many interesting properties. Since then, the Slacks-Based Measure has attracted the interest of numerous researchers and practitione...

Over the last twenty years an increasing number of studies have relied on the standard definition of the Malmquist-Luenberger index proposed by Chung et al. (1997) [J. Environ. Manage., 51, 229-240], to assess environmental sensitive productivity change. While recent contributions have shown that it suffers from relevant drawbacks related to incons...

We begin by providing some historical background behind this book. We continue by discussing the significance of the three operative words in the title of the book—advances, efficiency and productivity. We then briefly summarize the chapters in the book, which divide into advances in the analytical foundations of efficiency and productivity, and ad...

The concept of loss distance functions is introduced and compared with other functional representations of the technology including the Hölder metric distance functions (Briec and Lesourd in J Optim Theory Appl 101(1):15–33, 1999), the directional distance functions due to Chambers et al. (J Econ Theory 70(2):407– 419 1996; J Optim Theory Appl 98(2...

The aim of any Data Envelopment Analysis (DEA) inefficiency model is to calculate the efficient projection of each unit belonging to a certain finite sample. The reverse directional distance function (RDDF) is a new tool developed in this chapter that allows us to express any known DEA inefficiency model as a directional distance function (DDF). He...

Data Envelopment Analysis (DEA) is a well-known methodology for estimating technical efficiency from a set of inputs and outputs of Decision Making Units (DMUs). This paper is devoted to computational aspects of DEA models when the determination of the least distance to the Pareto-efficient frontier is the goal. Commonly, these models have been add...

In the European Union there are two figures of quality protection for agri-food products, according to EC Regulation 1151/2012, which are: Protected Designations of Origin (PDOs) and Protected Geographical Indications. In addition, in the case of wine, traditional nomenclatures coexist in each country. Thus, in the Spanish case we could find within...

Since it was introduced, Data Envelopment Analysis (DEA) has been applied to many different areas and has also been extended to numerous production contexts. In this paper, we focus our attention on the production framework under output quotas. Many types of markets throughout the world are subject to intervention by government policies, with the p...

This paper proposes a new method to measure productivity change of decision making units in the full input-output space. The new approach is based on the calculation of the least distance to the Pareto-efficient frontier and hence provides the closest targets for evaluated decision making units to reach the strongly efficient frontier with least ef...

Cost or revenue efficiency measurement based on the approach initiated by Farrell has received great attention from academics and practitioners since the fifties. Farrell's approach decomposes cost efficiency into two different sources, viz. technical efficiency and allocative efficiency. Technical efficiency is estimated by means of the Shephard i...

Determining the least distance to the efficient frontier for estimating technical inefficiency, with the consequent determination of closest targets, has been one of the relevant issues in recent Data Envelopment Analysis literature. This new paradigm contrasts with traditional approaches, which yield furthest targets. In this respect, some techniq...

Virgin olive oil is a key ingredient of the renowned Mediterranean diet. In this context, the main objective of this study was to estimate and decompose productivity change for Protected Designations of Origin (PDOs) in the Spanish virgin olive oil sector for the period 2008-2013. To this end, we introduced a Luenberger-type indicator based on a sp...

Distance functions in production theory are mathematical structures that characterize the belonging to the reference technology through a numerical value, behave as technical efficiency measures when the focus is analyzing an observed input-output vector within its production possibility set and present a dual relationship with some support functio...

We propose a new approach to estimate technical coefficients from a set of Decision Making Units (DMUs) under the assumption that their production plans are set by process engineers through Linear Programming (LP) techniques. The idea behind this approach is that most manufacturing and agricultural firms routinely resort to LP-based modeling in the...

Data Envelopment Analysis (DEA) is a non-parametric technique for estimating the technical efficiency of a set of Decision Making Units (DMUs) from a database consisting of inputs and outputs. This paper studies DEA models based on maximizing technical efficiency, which aim to determine the least distance from the evaluated DMU to the production fr...

Recently, in a Data Envelopment Analysis (DEA) framework, Färe and Grosskopf [15] argued that the input directional distance function is invariant to affine data transformations under variable returns to scale (VRS), which includes, as a particular case, the property of translation invariance. In this paper we show that, depending on the directiona...

In this survey, we present, for the first time, a classification scheme for distance functions, considering two broad groups: the multiplicative and the additive distance functions. Guiding empirical work is one of the objectives of this paper; for this reason, we consider only linear distance functions within a data envelopment analysis (DEA) fram...

Overall inefficiency measurement and decomposition are important for firms facing a world of changing prices since the resultant loss has implications on managers' decision making. In this paper, we draw attention to some problems within existing approaches to decompose overall inefficiency into its sources and propose new revenue and cost ineffici...

In this chapter we present an overview of the different approaches that have considered translation invariant Data Envelopment Analysis (DEA) models. Translation invariance is a relevant property for dealing with non-positive input and/or non-positive output values. We start by considering the classical approach and continue revising recent contrib...

The Bounded Adjusted Measure (BAM), initially defined for the additive model, which is a variable returns to scale (VRS) model, was extended to the constant returns to scale (CRS) case [7]. The added range-bounds, which maintain unaltered the production possibility set (PPS) under VRS, showed an influential effect under CRS, reducing the correspond...

We discuss how to properly decompose economic efficiency when the underlying technology is nonhomothetic using alternative allocative and technical efficiency criteria. We first show that only under the production of one output and assuming the particular case of constant returns to scale homotheticity, we may claim that the standard radial models...

Data Envelopment Analysis (DEA) is a non-parametric technique for estimating technical efficiency of a set of units. DEA also provides information on benchmarking. In this paper, we study DEA models based on closest efficient targets, which are associated with the least distance and allow inefficient units to find the easiest way to achieve the eff...

This chapter examines the process of benchmarking in healthcare. In particular, we focus on hospital performance. We are especially interested in showing that the determination of closest targets as a benchmarking technique has significant advantages over traditional Data Envelopment Analysis (DEA) methods for signaling keys for the inefficient hos...

In for-profit organizations, profit efficiency decomposition is considered important since estimates on profit drivers are of practical use to managers in their decision making. Profit efficiency is traditionally due to two sources - technical efficiency and allocative efficiency. The contribution of this paper is a novel decomposition of technical...

Spain is the world’s leading olive oil producer and exporter; representing more than half of the EU’s production and around the 40% of the worldwide production. In markets where increasingly become more important the aspects related to the geographical origin of the products, the Protected Designations of Origin (PDO) are an essential tool for impr...

Spain is the world's leading olive oil producer and exporter; representing more than half of the EU's production and around the 40% of the worldwide production. In markets where increasingly become more important the aspects related to the geographical origin of the products, the Protected Designations of Origin (PDO) are an essential tool for impr...

Espana es el principal productor y exportador mundial de aceite de oliva, con mas de la mitad de la produccion de la Union Europea y entorno al 40% de la mundial. En unos mercados en los que cada vez cobran mas importancia los aspectos relacionados con el origen geografico del producto, las Denominaciones de Origen son una herramienta esencial para...

The determination of closest efficient targets has attracted increasing interest of researchers in recent Data Envelopment Analysis (DEA) literature. Several methods have been introduced in this respect. However, only a few attempts exist that analyze the implications of using closest targets on the technical inefficiency measurement. In particular...

A key element of competitiveness in the tourism industry is the use of new information and communications technology (ICT). To analyse the efficiency in attracting tourists via the Web for a set of 16 Mediterranean countries, the authors use non-parametric bounded adjusted measure (BAM) models. Two models are proposed: the first analyses the influe...

Data Envelopment Analysis (DEA) is a nonparametric technique to estimate the current level of efficiency of a set of entities. DEA also provides information on how to remove inefficiency through the determination of benchmarking information. This paper is devoted to study DEA models based on closest efficient targets, which are related to the short...

A key element of competitiveness in the tourism industry is the use of new information and communications technology (ICT). To analyse the efficiency in attracting tourists via the Web for a set of 16 Mediterranean countries, the authors use non-parametric bounded adjusted measure (BAM) models. Two models are proposed: the first analyses the influe...

This article aims to establish a methodology for comparing golf-tourism efficiency of a set of 14 Mediterranean countries easily using three Data Envelopment Analysis (DEA) models. We have compared three DEA models. The first model resorts only to physical variables, while the latter two also consider cybermetric variables. Approximately one-third...

The directional distance function has been introduced in the efficiency literature with the intention of relaxing the fixed orientations represented by its classical input and output counterparts. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit ma...

Dealing with weighted additive models in Data Envelopment Analysis guarantees that any projection of an inefficient unit belongs to the strong efficient frontier, among other interesting properties. Recently, constant returns to scale (CRS) range-bounded models have been introduced for defining a new additive-type efficiency measure (see Cooper et...

This is a special issue in JPA in honour of Prof. Knox Lovell, an expert in efficiency and productivity measurement.

In this paper, we show how Data Envelopment Analysis (DEA) may be used to measure and decompose revenue inefficiency, taking into account all sources of technical waste in the context of an application to assess the Spanish quality wine sector, in particular Designation of Origin (DO) wines. We try to go beyond the standard approaches, which use Sh...

Apart from the well-known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist–Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity meas...

The problem of deriving the closest projection to the efficient frontier has been one of the relevant issues in recent Data Envelopment Analysis (DEA) literature. One of the challenges related to this issue is to find a ‘well-defined’ efficiency measure. Overall, this means that the measure should satisfy a set of interesting properties from an eco...

The wine Common Market Organisation has established two concepts for recognizing the quality of wines in the European Union (EU). The first corresponds to the so-called Protected Designation of Origin (PDO), and the second to the Protected Geographical Indication (PGI). The set of Spanish PDOs includes the subset of Spanish DOs (Designation of Orig...

As a measure of overall technical inefficiency, the Directional Distance Function (DDF) introduced by Chambers, Chung, and Färe ties the potential output expansion and input contraction together through a single parameter. By duality, the DDF is related to a measure of profit inefficiency, which is calculated as the normalized deviation between opt...

This paper studies the application of a genetic algorithm (GA) for determining closest efficient targets in Data Envelopment Analysis. Traditionally , this problem has been solved in the literature through unsatisfactory methods since all of them are related in some sense to a combinatorial NP-hard problem. This paper presents and studies some algo...

Gerard Debreu introduced a well known radial efficiency measure which he called a “coefficient of resource utilization.” He derived this scalar from a much less well known “dead loss” function that characterizes the monetary value sacrificed to inefficiency, and which is to be minimized subject to a normalization condition. We use Debreu’s loss fun...

This paper is concerned with formulating directional distance functions assuming that firms operate subject to rate-of-return regulation. To this end, we consider two different contexts. First, we assume that input prices are known, which allows us to extend the rate of return regulated version of Farrell efficiency. Secondly, we assume that input...

In this paper we show that given a utility threshold Luenberger's benefit function correctly represents individual preferences as long as specific reference commodity bundles are considered. We further show a condition which is sufficient for reaching Pareto optimality that generalizes the zero-maximum principle proposed by Luenberger. Under our hy...

Recently, in a data envelopment analysis framework, Amirteimoori and Kordrostami [A Euclidean distance-based measure of efficiency in data envelopment analysis, Optimization 59 (2010), pp. 985–996] introduced a Euclidean distance-based measure of efficiency in order to obtain the shortest path to the strongly efficient frontier from an assessed uni...

In a large number of organizations the figure of a centralized decision maker exists who supervises all of the operating units. In this environment the operating units have semi- autonomous operations but central direction. It then seems necessary to develop approaches that permit both the central and local managers to receive appropriate considera...

A difficult aspect of improving the efficiency of service organisations in the developed world is the need to lay-off experienced people, whose training had significant costs and where later replacements are both costly and time consuming. This paper shows a novel way to reallocate personnel resources between tasks within a specific unit as well as...

An issue that has received little attention in the Data Envelopment Analysis literature is the decomposition of profit inefficiency by means of measures that account all sources of technical inefficiency. In this paper we introduce a new way to measure and decompose profit inefficiency through weighted additive models. All our results are derived f...

The authors assess the performance of professional tennis players from the perspective of the efficiency of their game using data envelopment analysis (DEA). This research can complement the information provided by the Association of Tennis Professionals (ATP) ranking, which is concerned with their competitive performance. The DEA provides an index...

A decade ago the Range Adjusted Measure (RAM) was introduced for use with Additive Models. The empirical experience gained since then recommends developing a new measure with similar characteristics but with more discriminatory power. This task is accomplished in this paper by introducing the Bounded Adjusted Measure (BAM) in connection with a new...

In this paper we introduce a new Malmquist productivity index that has three attractive features: it avoids linear programming infeasibilities under variable returns to scale, it allows for technical regress, and it does not need to be recomputed when a new time period is added to the data set. The proposed index is compared to both the adjacent Ma...

There are several distance function definitions in a general production framework, including Data Envelopment Analysis, which can be used to describe the production technology and to define corresponding measures of technical efficiency (notably the Shephard and the directional distance functions). This paper introduces a generalisation of the dist...

This paper extends two directional distance function models, the Multi-directional Efficiency Analysis (MEA) Model and the Range Directional Model (RDM), in order to account for any type of technical inefficiency, i.e. both directional and non-directional inefficiencies. We first focus on the variable returns to scale (VRS) case, because both VRS-M...

This paper attempts to analyse whether banking technology and environmental conditions act as barriers for the entry of foreign banks in each European banking industry. We evaluate how the efficiency score of a representative commercial bank of a given European country changes if it decides to move abroad. To carry out this analysis, we use a sampl...

In this note we show, by means of several examples, that a directional distance function model cannot be matched with an additive model. Specifically, we show the difference between the directional slacks-based measure and the corresponding directional distance function.

Recently, in a Data Envelopment Analysis (DEA) framework, Baek and Lee (2009) [1]introduced a weighted Least-Distance Efficiency Measure to obtain the “shortest” projection from a considered unit to the strongly efficient production frontier. The mentioned authors tried to show that the proposed measure is well defined. Unfortunately, they did not...