Free Disposal Hull Technology Research Articles

Centralized allocations in free disposal hull technologies

Centralized allocations in free disposal hull technologies

Benchmarking with nonconvex production possibility set through data envelopment analysis: An application to China’s transportation system

Convex production possibility set (PPS) is an implicit assumption in previous benchmarking studies. Some scholars point out that the implicit assumption is inconsistent with the classical economic theory although it facilitates operational analysis. Hence, the present study develops a new benchmarking approach on the basis of technology that assumes convexity on consumption correspondence instead of imposing convexity on PPS, in which the closest benchmark with the least effort is identified. First, the correlation between two classical technologies in benchmarking (convex PPS and free disposal hull technology), and two nonconvex PPS (production correspondence and consumption correspondence), are identified. Next, the extreme efficient DMUs are identified to describe Pareto-efficient points on the frontier of the consumption correspondence. Then, the closest benchmark is determined by selecting a Pareto-efficient point that minimizes the distance between the evaluated unit and the efficient frontier of consumption correspondence. In addition, this study employs the Manhattan distance for benchmarking, and the proposed approach is flexible to accommodate other distances to derive different economic interpretations. Besides, the proposed approach introduces a new non-radial efficiency measure and conceptualizes a benchmark index by relaxing the convexity assumption on PPS. Finally, the proposed approach is applied to select benchmarks and measure performance for China’s transportation system. The proposed approach contributes to relaxing convexity assumption on PPS in benchmarking using DEA and provides a powerful managerial instrument to improve the performance of China’s transportation system.

The closest strong efficient targets in the FDH technology: an enumeration method

This paper is concerned with the identification of the closest strong efficient target of a Decision Making Unit (DMU) in the Free Disposal Hull (FDH) technology in Data Envelopment Analysis (DEA). The paper uses the geometrical properties of the FDH Production Possibility Set (PPS) to design and test an enumeration algorithm to obtain the minimum distance from a DMU to the strong efficient frontier of the PPS, corresponding to each of the various returns to scale assumptions. The proposed method solves some simple optimization problems whose optimal solutions are obtained by calculating a limited number of ratios. Then, an attempt will be made to mitigate the problem of the lack of unit and translation invariance of the selected distances by considering weighted norms. Finally, the applicability of the presented method is illustrated by a numerical example using real data.

Global sub-increasing and global sub-decreasing returns to scale in free disposal hull technologies: Definition, characterization and calculation

Global Returns to Scale (GRS) is an important notion in performance analysis under Free Disposal Hull (FDH) technologies. Ray Average Productivity (RAP) function has a crucial role in interpreting the GRS. We define two new notions, called Global Sub-Increasing RTS (G-SIRS) and Global Sub-Decreasing RTS (G-SDRS), invoking the behaviour of the RAP function at its maximizers. These notions are useful from a managerial standpoint, because they help the decision maker to decide about contracting or expanding the operation of the units under consideration. After presenting a motivating example and defining G-SIRS and G-SDRS, some theorems are proved to characterize these new notions. A polynomial-time algorithm is sketched which is able to determine the GRS of the Decision Making Units (DMUs) under evaluation. The second part of the paper is devoted to calculating a stability interval for GRS. It is done through some theorems and a polynomial-time algorithm. The results of the paper are illustrated by numerical examples as well as empirical studies with real-world data. Computational experiments are reported as well.

Frontier Visualization and Estimation of Returns to Scale in Free Disposal Hull Models

The free disposal hull (FDH) model of production technology assumes free disposability of all inputs and outputs, but does not make any convexity assumptions. In this paper, we develop an algorithm for the reconstruction of the frontier of the FDH technology that corresponds to its sections by different two-dimensional planes. From a practical perspective, the suggested algorithm is useful for the visualization and exploration of the efficient frontier of the FDH technology. Furthermore, based on the suggested algorithm, we develop a new procedure for the evaluation of returns to scale in the FDH technology. Compared to the existing methods, our approach does not require assessing the efficiency of productive units in the reference technologies, which is known to be a computationally intensive task. Our theoretical results are confirmed by computational experiments in applications with real-life data sets from different industries.

Efficiency measurement with a non-convex free disposal hull technology

We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier. Taking this result into account, we develop a new class of FDH least-distance measures that satisfy strong monotonicity and show that the developed (in)efficiency measurement framework has a natural profit interpretation.

Estimation of congestion in free disposal hull models using data envelopment analysis.

This paper deals with evaluating congestion in free disposal hull (FDH) models. There are several approaches in data envelopment analysis (DEA) literatures which discuss the theory and application of congestion. However, almost all of these approaches considered convex DEA technologies. So, in the case of nonconvex technologies, including FDH technology, this field is almost nil. This paper makes an attempt to fill in this void. To do so, this study provides a pairwise comparisons-based algorithm to evaluate congestion in FDH model. This algorithm identifies the sources of congestion and estimates its amounts. It is also capable of detecting the losses amounts of output due to congestion. The validity of the proposed model is demonstrated using some numerical and empirical examples.

Axiomatic foundations of efficiency measurement on data-generated technologies

We assess the ability of three well-known technical efficiency indexes, the Debreu-Farrell index, the Fare–Lovell index, and the Zieschang index, to satisfy the Fare–Lovell axioms and continuity axioms (for technologies as well as input quantities) on the class of technologies generated by standard mathematical-programming methods of measuring efficiency: data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Fare–Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu–Farrell index), but (b) none of the indexes satisfies all Fare–Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.

A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models

The free disposal hull (FDH) model, introduced by Deprins et al. [The Performance of Public Enterprises Concepts and Measurements, Elsevier, 1984], is based on a representation of the production technology given by observed production plans, imposing strong disposability of inputs and outputs but without the convexity assumption. In its traditional form, the FDH model assumes implicitly variable returns to scale (VRS) and the model was solved by a mixed integer linear program (MILP). The MILP structure is often used to compare the FDH model to data envelopment analysis (DEA) models although an equivalent FDH LP model exists (see Agrell and Tind [Journal of Productivity Analysis 16 (2) (2001) 129]). More recently, specific returns to scale (RTS) assumptions have been introduced in FDH models by Kerstens and Vanden Eeckaut [European Journal of Operational Research 113 (1999) 206], including non-increasing, non-decreasing, or constant returns to scale (NIRS, NDRS, and CRS, respectively). Podinovski [European Journal of Operational Research 152 (2004) 800] showed that the related technical efficiency measures can be computed by mixed integer linear programs. In this paper, the modeling proposed here goes one step further by introducing a complete LP framework to deal with all previous FDH models.

Using dominance in forming bounds on DEA models: The case of experimental agricultural data

Dominance techniques are used to create optimistic and pessimistic convex free-disposal hull technologies for data sets. These optimistic and pessimistic technologies create bounds within which can reasonably expect the true technology to lie. The potential differences between these optimistic and pessimistic reference technologies are examined by comparing the reference technologies for data drawn from agricultural field trials. Empirical analysis suggests that there are significant differences between the reference technologies.