Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?

Single-stage DEA models aim to assess the input or output radial efficiency of a decision making unit and potential mix inefficiency in a single optimization stage. This is achieved by incorporating the sum of input and output slacks, multiplied by a small (theoretically non-Archimedean infinitesimal) value epsilon in the envelopment model or, equivalently, by using this value as the lower bound on the input and output weights in the dual multiplier model. When this approach is used, it is common practice to select a very small value for epsilon. This is based on the expectation that, for a sufficiently small epsilon, the radial efficiency and optimal slacks obtained by solving the single-stage model should be approximately equal to their true values obtained by the two separate optimization stages. However, as well-known, selecting a small epsilon may lead to significant computational inaccuracies. In this paper we prove that there exists a threshold value, referred to as the effective bound, such that, if epsilon is smaller than this bound, the solution to the single-stage program is not approximate but precise (exactly the same as in the two-stage approach), provided there are no computational errors

Uncertain Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a nonparametric, data driven method to conduct relative performance measurements among a set of decision making units (DMUs). Efficiency scores are computed based on assessing input and output data for each DMU by means of linear programming. Traditionally, these data are assumed to be known precisely. We instead consider the situation in which data is uncertain, and in this case, we demonstrate that efficiency scores increase monotonically with uncertainty. This enables inefficient DMUs to leverage uncertainty to counter their assessment of being inefficient. Using the framework of robust optimization, we propose an uncertain DEA (uDEA) model for which an optimal solution determines 1) the maximum possible efficiency score of a DMU over all permissible uncertainties, and 2) the minimal amount of uncertainty that is required to achieve this efficiency score. We show that the uDEA model is a proper generalization of traditional DEA and provide a first-order algorithm to solve the uDEA model with ellipsoidal uncertainty sets. Finally, we present a case study applying uDEA to the problem of deciding efficiency of radiotherapy treatments

Parametric programming: An illustrative mini encyclopedia

Parametric programming is one of the broadest areas of applied mathematics. Practical problems, that can be described by parametric programming, were recorded in the rock art about thirty millennia ago. As a scientific discipline, parametric programming began emerging only in the 1950\u27s. In this tutorial we introduce, briefly study, and illustrate some of the elementary notions of parametric programming. This is done using a limited theory (mainly for linear and convex models) and by means of examples, figures, and solved real-life case studies. Among the topics discussed are stable and unstable models, such as a projectile motion model (maximizing the range of a projectile), bilevel decision making models and von Stackelberg games of market economy, law of refraction and Snell\u27s law for the ray of light, duality, Zermelo\u27s navigation problems under the water, restructuring in a textile mill, ranking of efficient DMU (university libraries) in DEA, minimal resistance to a gas flow, and semi-abstract parametric programming models. Some numerical methods of input optimization are mentioned and several open problems are posed

Post-crisis cost efficiency of Jamaican banks

Deregulation, re-regulation and continuing globalisation embody an imperative that banks increase efficiency in order to survive. We employ the Simar-Wilson (2007) two-step double bootstrap Data Envelopment Analysis method to measure whether cost efficiency among Jamaican banks has improved between 1999 and 2009 following a number of post-crisis responses aimed at strengthening and improving the sector. Efficiency is extracted from a meta-frontier construction for the full sample period. In addition we conduct tests for unconditional beta- and sigma-convergence and overall, the results suggest that there has been a tendency towards improvement in bank efficiency levels for the industry as a whole but there is also evidence that foreign banks show a higher trend improvement in efficiency

Measuring hotel performance:Toward more rigorous evidence in both scope and methods

This paper extends the literature on hotel performance in both scope and methods. We introduce a model that accounts for heterogeneity in a flexible way and allows for the measurement of both efficiency and productivity. The model also accounts for the endogeneity problem in inputs and the issue of unobserved prices. We use a large sample of hotel companies that spreads across multiple geographical regions and locations, and accounts for some interesting and key determinants of hotel performance. We provide more validation to some contradictory findings in the literature. We show that large hotels do not necessarily outperform small hotels, and that hotel efficiency differs based on location, geographical region and type of service. The results further indicate that productivity growth is not a driving force in the industry

MULTIPLE COMPARISONS WITH THE BEST: BAYESIAN PRECISION MEASURES OF EFFICIENCY RANKINGS

A large literature exists on measuring the allocative and technical efficiency of a set of firms. A segment of this literature uses data envelopment analysis (DEA), creating relative efficiency rankings that are nonstochastic and thus cannot be evaluated according to the precision of the rankings. A parallel literature uses econometric techniques to estimate stochastic production frontiers or distance functions, providing at least the possibility of computing the precision of the resulting efficiency rankings. Recently, Horrace and Schmidt (2000) have applied sampling theoretic statistical techniques known as multiple comparisons with control (MCC) and multiple comparisons with the best (MCB) to the issue of measuring the precision of efficiency rankings. This paper offers a Bayesian multiple comparison alternative that we argue is simpler to implement, gives the researcher increased exibility over the type of comparison made, and provides greater, and more in-tuitive, information content. We demonstrate this method on technical efficiency rankings of a set of U.S. electric generating firms derived within a distance function framework.Research Methods/ Statistical Methods,

EFFICIENCY ANALYSIS IN SPARE PART RETAIL USING DATA ENVELOPMENT ANALYSIS

The retail business sector contributes a large per capita to Indonesia so this sector has a vital role in the Indonesian economy. The retail business in Indonesia is growing day by day, and business competition is showing quite rapid development, especially on spare part retail businesses in Padang. The sales of spare parts from year to year do not increase significantly. The number of players entering this market makes competition is building up. One of them is the spare parts retailer who has established business since 1974 and already has five branch stores in Padang. In the current conditions, the potential of spare parts retail business has not realized and has not organized optimally. It is necessary to measure efficiency to determine the performance of spare parts retail business processes, so players in this business can improve their business and can compete with other competitors. Based on the problems that have been explained, it is needed an efficiency analysis on the spare parts retail business to measure the efficiency level of the company, so the company can implement improvement to improve the efficiency level and can through market competition. Efficiency analysis was conducted on one spare part retailer that already has five spare part retail branches in Padang using Data Envelopment Analysis method, which uses an input-oriented BCC model. This model was chosen because the retail business is a dynamic sector, so changing in input or output does not affect the other linearly. In other words, changing the values of input does not cause a change in outputs in the same amount. The inputs used in this study are the size of the land, number of employees, number of deliveries, total costs. The output used in this study is a number of customers and number of sales. The results of relative efficiency analysis represent that four retails have been operating relatively efficiently in period one and period two, namely retail 1, 2, 3, and 4, while retail 5 is relatively inefficient. Then, in period three, the number of retailers relatively efficiently is decreased to two retailers, namely retail 2 and 4, while retail 1, 3, and 5, were relatively inefficient. Input factor that dominant contributes to the level of efficiency spare part retail, namely the size of land, number of deliveries, and total costs

Microfinance Institutions’ Efficiency in the MENA Region: a Bootstrap-DEA approach

The purpose of this study is to evaluate the performance of microfinance institutions in The MENA region over the period 2006-2009. Following Simar and Wilson (1998, 2000) we use a DEA-Bootstrapping methodology to drift appropriate measures of DEA efficiency scores. The estimated results show that average efficiency of the most countries in the region has decreased over the period under study. Results also reveal that efficiency significantly differs by legal status of the microfinance institutions. Keywords: Microfinance, DEA, Bootstrap, MENA

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