Measurement of Returns-to-Scale using Interval Data Envelopment Analysis Models

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkThe economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterized by intervals. For instance, the heat losses of the combined production of heat and power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input – output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Measuring the Efficiency of Pesantren Cooperatives: Evidence in Indonesia

The Cooperative (Koperasi) as a non-Bank financial institution has the purpose of improving the welfare of its members as Koperasi Hidmat and the staffs of Latifah Mubarokiyah Koperasi Ponses Suryalaya that have been since decades ago. Over time, the ideal cooperative can show a significant development and increase the welfare of its members. This study aims to determine the efficiency of cooperative as a benchmark, because by known the performance value of a cooperation, it will known the weeknesses and advantages so that it can be improved the weaknesses and maintain the advantages.The method used is apply Data Envelopment Analysis (DEA). Inputs used from principal savings, mandatory savings, and fixed assets while the output used from savings in the cooperative, savings in other cooperative and SHU. As for result of this research indicates there are 9 perfect efficient DMUs (100 %) and inefficient DMU is 11 DMUs, consisting of 7 (IRS conditions) and 4 (DRS condition). The most inefficient cooperative is Koperasi Hidmat (2014) of 30.66% efficiency level.Kopkar IAILM is able to maintain its grade efficiency level from 2009 to 2015 when compared to other DMUs cooperatives in the observation, except in 2014. The calculation of efficiency level in this research is relative and it is not absolute, so that it is possible when the cooperative sample is added or the observation year is expanded, so it will get different result. The necessity of any cooperative or BMT based on Pondok Pesantren to make annual financial statements in order to increase accountability and transparency of fund management

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

EVALUATION OF IRANIAN SMALL AND MEDIUM-SIZED INDUSTRIES USING THE DEA BASED ON ADDITIVE RATIO MODEL – A REVIEW

Data Envelopment Analysis (DEA) is a prominent procedure in the decision-making process with a pivotal role in the sustainable development assay. Project identification is the first step of sustainability assessment in the Environmental Impact Assessment (EIA) program for the industrial projects prior to complete establishment. The present review research comprised 405 Iranian industries assessment regarding both input and output criteria via DEA integrated with the ratio model of Additive Ratio ASsessment (ARAS) and weighing systems of Kendall and Friedman's tests supported by SPSS software. The findings deployed a classification for Iranian industries pertaining to industries' nominal capacity in certain clusters. Also, the current review paved the pathway towards executing both energy and materials streams in industries

Methodological Developments in Human Development Literature

The present paper is a review of methodological advancements in human development literature starting from 1990 till date. While highlighting the contribution of UNDP to the concept of human development and construction of HDI it mentions that the introduced concept and method of measurement is a huge qualitative improvement over the earlier concept of growth and per capita GDP measurement. Although the human development report started with a poor methodology, thanks to the galaxy of scholars for their untiring efforts and invaluable contributions in the successive years that enabled UNDP in refining its methodology to a large extent. There is no denying fact that there is no end to refinements, the purpose for which Mahbub ul Haq struggled in his entire life has been served

Hospital Efficiency: An Empirical Analysis of District and Grant-in-Aid Hospitals in Gujarat

This study focuses on analysing the hospital efficiency of district level government hospitals and grant-in-aid hospitals in Gujarat. The study makes an attempt to provide an overview of the general status of the health care services provided by hospitals in the state of Gujarat in terms of their technical and allocative efficiency. One of the two thrusts behind addressing the issue of efficiency was to take stock of the state of healthcare services (in terms of efficiency) provided by grant-in-aid hospitals and district hospitals in Gujarat. The motivation behind addressing the efficiency issue is to provide empirical analysis of governments policy to provide grants to not-for-profit making institutions which in turn provide hospital care in the state. The study addresses the issue whether grant-in-aid hospitals are relatively more efficient than public hospitals. This comparison between grant-in-aid hospitals and district hospitals in terms of their efficiency has been of interest to many researchers in countries other than India, and no consensus has been reached so far as to which category is more efficient. The relative efficiency of government and not-for-profit sector has been reviewed in this paper. It is expected that the findings of the study would be useful to evaluate this policy and help policy makers to develop benchmarks in providing the grants to such institutions.