Frontier Visualization and Estimation of Returns to Scale in Free Disposal Hull Models (original) (raw)
Related papers
1994
Affiliations of the other authors: K.U. Leuven and UFSIA; and UFSIA and KULAK respectively. The authors thank J. COUDER for his superb programming assistance and I. JANSSENS, D. DE GRAEVE, the editor of this journal and two referees for their comments on an earlier version. The authors are responsible for any remaining errors. 2. See FARE, GROSSKOPF, and LOVELL (1985) and SEIFORD and THRALL (1990) for a review. A complete characterization of types of efficiency is found in FARE, GROSSKOPF and LOVELL ( 1985). 4. Recently TULKENS and VANDEN EECKAUT (1993) relaxed the need for the representation of the boundary of the production possibility set by defining technical efficiency solely in terms of pairwise dominance relations.
DEStech Transactions on Computer Science and Engineering, 2019
A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation of production units. Kerstens and Vanden Eeckaut were the first who considered the notion and evaluation of RTS for nonconvex Free Disposal Hull (FDH) models. Their methods are based on the comparison of the radial efficiency scores of a production unit in the FDH model and the corresponding non-increasing and non-decreasing RTS reference models. At the same time Cesaroni, Kerstens and Van de Woestyne noted the absence of papers in the world literature devoted to methods of frontier visualization in nonconvex models. In this paper, we developed methods for visualization of production function of nonconvex models and of the corresponding non-increasing and non-decreasing models. Our approach of frontier visualization can be used for decision making based on nonconvex models, it allows us to evaluate RTS for FDH models. Our results are confirmed by computational experiments in applications with real-life data sets.
An Improved Non-Convex Model for Discriminating Efficient Units in Free Disposal Hull
Measurement, 2015
A number of methods, including data envelopment analysis (DEA), have been proposed for evaluating the performance of decision making units (DMUs) converting multiple inputs into multiple outputs. The free disposal hull (FDH) is an alternative non-parametric, deterministic production method useful to evaluate the technical efficiency of DMUs. Unlike DEA, the FDH imposes minimal assumptions on the production technology and it does not require convexity. The conventional FDH model assigns an efficiency score less than one to inefficient DMUs, from which a ranking can be derived. However, all efficient DMUs have an efficiency score of 1 and, hence, equal ranking. Several ranking methods have been proposed to discriminate among the efficient DMUs. These ranking methods are sometimes either break down or produce infeasible solution(s). The Mehrabian, Alirezae, Jahanshahloo (MAJ) (1999) method is usually used to discriminate among the efficient DMUs in convex DEA problems, while the MAJ-FDH method proposed by Sun and Hu (2009) has been used to discriminate among the efficient DMUs in non-convex DEA problems. In this paper: (1) we show that the MAJ-FDH model is not always feasible; (2) we propose a modified MAJ-FDH model, both input and output oriented, and mathematically prove that this model is always feasible; (3) we show that the proposed method can produce an optimal solution without the need to solve the integer programming problem; (4) we prove the validity of the proposed method through theorems; and (5) we provide two numerical examples to demonstrate the applicability and show the efficacy of the proposed method.
European Journal of Operational Research, 1998
This paper evaluates a variety of technical efficiency measures based on a given nonparametric reference technology, the free disposal hull (FDH). Specifically, we consider the radial measure of and the nonradial measures of F'fire (1975), F'~e and and . Furthermore, input-based, output-based, and graph efficiency versions of these four measures are computed. Theoretical consideration as to the best choice among these alternative measures is inconclusive; therefore, we examine this problem from an empirical viewpoint. Calculating thirteen different measures of technical efficiency for a sample of US banks, we compare the measures' efficiency distributions and rankings, paying particular attention to how well the radial measure approximates its nonradial alternatives. 9 1998 Elsevier Science B.V.
2016
Traditional cost-efficiency analysis methods require exact and precise values for inputs, outputs and input prices. However, this is not the case in many real-life applications. This study proposes a rough costefficiency approach to the problem of ranking efficient decision making units (DMUs). Based on rough set theory, a nonparametric methodology for cost-efficiency analysis is developed. The merits of this methodology include computational ease and the capacity to incorporate data uncertainty. Furthermore, it applies to both convex data envelopment analysis (DEA) and non-convex free disposal hull (FDH) technologies under different returns-to-scale assumptions. A numerical example and a real-life case study in the Japanese banking industry demonstrate the applicability of the proposed framework. In particular, the rankings of the DMUs resulting from the proposed models are compared with those obtained using the maximum technical efficiency loss index. © 2016 Elsevier B.V. All righ...
Frontier visualization for nonconvex models with the use of purposeful enumeration methods
Doklady Mathematics, 2017
Free Disposal Hull (FDH) model was proposed in the end of 20-th century for performance measurement and management of complex units. Production possibility set of FDH model is a nonconvex set. For this reason, nonlinear integer programming methods and enumeration methods have been used for computations of various characteristics of units' performance. However, as Cesaroni, Kerstens and Van de Woestyne noted, there are no methods in the world scientific literature for frontier visualization in nonconvex FDH models. In this paper, an approach is proposed for frontier visualization with the use of methods of purposeful enumeration. Computational experiments, conducted with the use of real-life data sets, confirm reliability and effectiveness of proposed algorithms.
ALGORITHM MODELING FOR CONSTRUCTING A CONCAVE EFFICIENT FRONTIER
Pesquisa Operacional, 2020
When analyzed from the perspective of one input and one output, the classic Data Envelop- ment Analysis (DEA) model (known as BCC after its developers Banker, Charnes, and Cooper) presents an efficient frontier with “downward” concavity (convex), therefore delivering variable returns to scale. However, these returns show a decrease in marginal productivity as the number of inputs increases, that is, the frontier presents decreasing global returns to scale. Both the convex frontier (DEA BCC) and the concave frontier (“upward” concavity) present average productivities that vary along the curve; thus, the local returns to scale are variable. It is claimed that the two formats are complementary, and therefore both should be verified in the literature. Thus, this article proposes an algorithm capable of modeling an efficient frontier, for one input or one output, with increasing global returns to scale, whereby an increase in input causes an increase in marginal productivity.
Frontier production functions: Improved procedures for estimation and application
2006
Scope and purpose-There is a great deal of current interest in the topic of industrial productivity. Traditional productivity measures which focus on output per man-hour of labor are considered inadequate because they ignore the contributions of energy, capital and raw materials to the production process. A superior tool for measuring industrial productivity is the frontier production function. It is the locus of the maximum output attainable from given amounts of inputs under existing technology. Deviations of observations from this locus can be used to measure the technical efficiency of the observations relative to the technically efficient observations which form the locus. This paper develops improved procedures for estimating the parameters of frontier functions and for identifying technically efficient observations. It also introduces a method for clustering observations on the basis of qualitative considerations prior to the estimation procedure. The goal of this research is to widen the applicability of these methods of measuring productivity and to reduce the computational burden associated with using them.
DEA efficiency analysis with identifying efficient and full-inefficient frontier
International Mathematical Forum, 2007
Data envelopment analysis (DEA) is a mathematical programming technique for identifying relative efficiency scores of decision making units (DMUs). Recently, Amirteimoori (2007) Introduced an alternative efficiency measure based on efficient and anti-efficient frontiers. In this paper we introduce a new computational framework for identifying full-efficient and inefficient frontier of production possibility set (PPS) in DEA models with variable return to scale. This facets apply in finding full-efficient and inefficient DMUs, sensitivity and stability analysis, ranking, and etc.
Using Free Disposal Hull Models in Supply Chain Management
International Journal of Mathematical Modelling & Computations, 2013
To help improve customer relationship management (CRM), greater emphasis is given to the aspect of quality in the supply chain management and improve supply chain performance through is integrated business management and strategic partnerships. On the other hand, strategic supply chain management decisions are made at a company level that determine benets and eciencies of the supply chain and eective management of supply chains assists to product and delivery of a variety of products at low cost, high quality products, short lead times and services at the least cost. Hence, performance evaluation is of most importance for eective supply chain management. This paper gives a new application of DEA model, and FDH model to evaluate the supply chain. The basic motivation is to ensure that eciency evaluations are eected from only observed performances.