DEA-like models for the efficiency evaluation of hierarchically structured units

Castelli, Lorenzo; Pesenti, Raffaele; Ukovich, Walter

doi:10.1016/s0377-2217(03)00182-6

Cited by 140 publications

(55 citation statements)

References 6 publications

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“…As shown in Yang et al (2000), Castelli et al (2004), and Kao (2008) e * 0 is equal to the maximum relative efficiency of its subunits, and DMU 0 is: -weakly efficient if and only if there exists at least one of its subunits which is weakly efficient relative to the corresponding subunits of other DMUs; -CCR-efficient if and only if each of its subunits is CCR-efficient relative to the corresponding subunits of other DMUs.…”

Section: Elementary Modelmentioning

confidence: 97%

“…It is worth noting that Model (2) can also be directly derived from the formulation of the relative efficiency maximization of e 0 as a comparison of DMU 0 with all the existing DMUs (Castelli et al 2004), as it is customary in the classical DEA framework. Also Färe and Primont (1984) proposed a multiple input and single output elementary configuration.…”

Section: Elementary Modelmentioning

confidence: 99%

“…Conversely, Castelli et al (2004) linked the DMU and subunit efficiencies of a two-stage process under constant returns to scale (see Fig. 3).…”

Section: Multi-stage Dmusmentioning

confidence: 99%

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A classification of DEA models when the internal structure of the Decision Making Units is considered

2008

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We classify the contributions of DEA literature assessing Decision Making Units (DMUs) whose internal structure is known. Starting from an elementary framework, we define the main research areas as shared flow, multilevel and network models, depending on the assumptions they are subject to. For each model category, the principal mathematical formulations are introduced along with their main variants, extensions and applications. We also discuss the results of aggregating efficiency measures and of considering DMUs as submitted to a central authority that imposes constraints or targets on them. A common feature among the several models is that the efficiency evaluation of the DMU depends on the efficiency values of its subunits thereby increasing the discrimination power of DEA methodology with respect to the black box approach.Keywords Efficiency evaluation · Data envelopment analysis · Networks · Hierarchy · Multi-stage production processes Data Envelopment Analysis (DEA) has been a standard tool for evaluating the relative efficiencies of Decision Making Units (DMUs) since the paper of Charnes et al. (1978) based on the seminal work of Farrell (1957). Some underlying assumptions are common to classical DEA models. The efficiency of a DMU is defined as the weighted ratio of the outputs (products or outcomes) yielded by the DMU over the inputs (resources used or consumed). All DMUs considered are homogeneous, i.e., they all have the same types of inputs and outputs, and are independent, i.e., no constraint binds input and output levels of a DMU with the inputs and outputs of other DMUs. Furthermore, DMUs are seen as black boxes, i.e., their internal structures are not considered. As a consequence, generally, there is no clear L. Castelli ( ) · W. Ukovich

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Section: Elementary Modelmentioning

confidence: 97%

Section: Elementary Modelmentioning

confidence: 99%

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A classification of DEA models when the internal structure of the Decision Making Units is considered

2008

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“…Kao (1998) applied the Färe and Primont's methodology for measuring the efficiency of forest districts with multiple working circles in Taiwan. Castelli et al (2004) discussed a hierarchical structure in which if there is only one layer, it becomes a parallel system. The works of Färe et al (1997), Tsai and Molinero (2002) and Yu (2008) extend of the independent parallel system where certain resources are shared by some units.…”

Section: Introductionmentioning

confidence: 99%

The Efficiency Measurement of Parallel Production Systems: A Non-radial Data Envelopment Analysis Model

Ашрафи¹,

Jaafar²,

Bakar³

et al. 2011

Journal of Computer Science

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Problem statement: Data Envelopment Analysis (DEA) is a non-parametric technique for measuring the relative efficiency of a set of production systems or Decision Making Units (DMU) that have multiple inputs and outputs. Sometimes, DMUs have a parallel structure, in which systems composed of parallel units work individually; the sum of their own inputs/outputs is the input/output of the system. For this type of system, conventional DEA models treat each DMU as a black box and ignore the performance of its units. Approach: This study introduces a DEA model in Slacks-Based Measure (SBM) formulation which considers the parallel relationship of the units within the system in measuring the efficiency of the system. Under this framework, the overall efficiency of the system is expressed as a weighted sum of the efficiencies of its units. Results: As an SBM model, the proposed model is non-radial and is suitable for measuring the efficiency when inputs and outputs may change non-proportionally. A theoretical result shows that if any unit of a parallel system is inefficient then the system is inefficient. Conclusion: This study introduces a non-radial DEA model, takes into account the operation of individual components within the parallel production system, to measure the overall efficiency as well as the efficiencies of sub-processes. This helps the decision makers recognize inefficient units and make later improvements.

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“…Assuming that the first scenario be feasible using the clustering method, the second one requires more complex mathematical methods to be used, such as non-parametric optimization [19,20] and its various modification [21,22]. Note.…”

mentioning

confidence: 99%

Developing Regional Environmental Management Models in Compliance with the Innovative Format of ISO 14001:2015

Ratner¹

2017

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DEA-like models for the efficiency evaluation of hierarchically structured units

Cited by 140 publications

References 6 publications

A classification of DEA models when the internal structure of the Decision Making Units is considered

A classification of DEA models when the internal structure of the Decision Making Units is considered

The Efficiency Measurement of Parallel Production Systems: A Non-radial Data Envelopment Analysis Model

Developing Regional Environmental Management Models in Compliance with the Innovative Format of ISO 14001:2015

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