Marginal Values and Returns to Scale for Nonparametric Production Frontiers

European Journal of Operational Research

2017

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The notion of returns to scale (RTS) is well-established in data envelopment analysis (DEA). In the variable returns-to-scale production technology, the RTS characterization is closely related to other scale characteristics, such as the scale elasticity, most productive scale size (MPSS), and global RTS types indicative of the direction to MPSS. In recent years, a number of alternative production technologies have been developed in the DEA literature. Most of these technologies are polyhedral, and hence are closed and convex sets. Examples include technologies with weakly disposable undesirable outputs, models with weight restrictions and production trade-offs, technologies that include several component production processes, and network DEA models. For most of these technologies, the relationship between RTS and other scale characteristics has remained unexplored. The theoretical results obtained in this paper establish such relationships for a very large class of closed convex technologies, of which polyhedral technologies are an important example.

Section: Introductionmentioning

confidence: 99%

Returns to scale in convex production technologies

European Journal of Operational Research

2017

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“…The dual program (9) can be used for the returns-to-scale (RTS) characterization of efficient DMUs in technology T MHRS . As follows from a more general result established by Podinovski et al (2016) 11 , the one-sided (left-hand and right-hand) scale elasticities and the type of RTS in the MHRS technology are defined by the extreme optimal values ω min and ω max of the variable ω in program (9). A similar relationship is well known for the standard VRS model (Banker Remark 7.…”

Section: Theorem 3 the Dual To The Output-oriented Program (8) Is Eqmentioning

confidence: 97%

“…For example, the incorporation of an upper bound on the proportion p 11. The results of Podinovski et al (2016) apply to any polyhedral technology. They extend and operationalize earlier results of Chambers and Färe (2008).…”

Section: Tablementioning

confidence: 98%

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Nonparametric Production Technologies with Multiple Component Processes

Olesen

Sarrico

2018

Operations Research

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We develop a nonparametric methodology for assessing the efficiency of decision making units operating in a production technology with several component processes. The latter is modeled by the new multiple hybrid returns-to-scale (MHRS) technology, formally derived from an explicitly stated set of production axioms.In contrast with the existing models of data envelopment analysis (DEA), the MHRS technology allows the incorporation of component-specific and shared inputs and outputs that represent several proportional (scalable) component production processes, as well as nonproportional inputs and outputs. Our approach does not require information about the allocation of shared inputs and outputs to component processes or any assumptions about this allocation. We demonstrate the usefulness of the suggested approach in an application in the context of secondary education, and also in a Monte Carlo study based on a simulated data generating process.

“…The CRS multiplier model can be shown to maximize the ratio of the total weighted output to the total weighted input (efficiency ratio) of DMU o , provided no such ratio across all observed DMUs can exceed the value of 1. The VRS multiplier model has an additional dual variable interpretable in terms of returns to scale and scale elasticity (Banker et al 1984, Podinovski et al 2009, Podinovski and Førsund 2010, Sahoo and Tone 2015, Podinovski et al 2016. As pointed by Charnes et al (1978), the optimal input and output weights are the most favorable to DMU o and show it in the best light in comparison to all observed DMUs.…”

Section: Introductionmentioning

confidence: 99%

Optimal weights in DEA models with weight restrictions

European Journal of Operational Research

2016

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According to a conventional interpretation of a multiplier DEA model, its optimal weights show the decision making unit under the assessment, denoted DMU o , in the best light in comparison to all observed DMUs. For multiplier models with additional weight restrictions such an interpretation is known to be generally incorrect (specifically, if weight restrictions are linked or nonhomogeneous), and the meaning of optimal weights in such models has remained unclear. In this paper we prove that, for any weight restrictions, the optimal weights of the multiplier model show DMU o in the best light in comparison to the entire technology expanded by the weight restrictions. This result is consistent with the fact that the dual envelopment DEA model benchmarks DMU o against all DMUs in the technology, and not only against the observed DMUs. Our development overcomes previous concerns about the use of weight restrictions of certain types in DEA models and provides their rigorous and meaningful interpretation.