Two-Stage DEA: An Application to Major League Baseball
01 Apr 2003-Journal of Productivity Analysis (Kluwer Academic Publishers)-Vol. 19, Iss: 2, pp 227-249
TL;DR: In this article, the authors use DEA to model DMUs that produce in two stages, with output from the first stage becoming input to the second stage, and apply the model to Major League Baseball, demonstrating its advantages over a standard DEA model.
Abstract: We show how to use DEA to model DMUs that produce in two stages, with output from the first stage becoming input to the second stage. Our model allows for any orientation or scale assumption. We apply the model to Major League Baseball, demonstrating its advantages over a standard DEA model. Our model detects inefficiencies that standard DEA models miss, and it can allow for resource consumption that the standard DEA model counts towards inefficiency. Additionally, our model distinguishes inefficiency in the first stage from that in the second stage, allowing managers to target inefficient stages of the production process.
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TL;DR: Li et al. as mentioned in this paper extended the centralized model to measure the DEA efficiency of the two-stage process with non splittable shared inputs and outputs, and a weighted additive approach was used to combine the two individual stages.
Abstract: Data envelopment analysis (DEA) is an effective non-parametric method for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and outputs. In many real situations, the internal structure of DMUs is a two-stage network process with shared inputs used in both stages and common outputs produced by the both stages. For example, hospitals have a two-stage network structure. Stage 1 consumes resources such as information technology system, plant, equipment and admin personnel to generate outputs such as medical records, laundry and housekeeping. Stage 2 consumes the same set of resources used by stage 1 (named shared inputs) and the outputs generated by stage 1 (named intermediate measures) to provide patient services. Besides, some of outputs, for instance, patient satisfaction degrees, are generated by the two individual stages together (named shared outputs). Since some of shared inputs and outputs are hard split up and allocated to each individual stage, it needs to develop two-stage DEA methods for evaluating the performance of two-stage network processes in such problems. This paper extends the centralized model to measure the DEA efficiency of the two-stage process with non splittable shared inputs and outputs. A weighted additive approach is used to combine the two individual stages. Moreover, additive efficiency decomposition models are developed to simultaneously evaluate the maximal and the minimal achievable efficiencies for the individual stages. Finally, an example of 17 city branches of China Construction Bank in Anhui Province is employed to illustrate the proposed approach.
14 citations
01 Jan 2021
TL;DR: This paper attempts to extend the traditional two-stage network DEA models to the uncertain two- Stage DEA models with the application of uncertainty theory, where inputs, intermediates and outputs are considered to be uncertain variables to deal with the problem of inaccurate data.
Abstract: The two-stage network DEA models based on the framework that the efficiency of the whole stage is equal to the product of the efficiencies of two sub-stages can not only turn the ‘black box’ into the ‘glass box’ to identify the root causes of the inefficiency of the network system, but also consider the relationship between the two sub-stages within the whole stage. Nowadays, the two-stage network DEA models have been widely applied in the field of economy and management, such as green supply chain and reverse supply chain. Due to the novelty of evaluation indexes, these emerging research objects with network structure, such as green supply chain, involve not only traditional evaluation indexes such as cost and time, but also some novel evaluation indexes such as customer satisfaction and flexibility. However, these new evaluation indexes are difficult to quantify accurately, which will lead to the failure of the traditional two-stage network DEA models. Therefore, this paper attempts to extend the traditional two-stage network DEA models to the uncertain two-stage network DEA models with the application of uncertainty theory. In the new models, inputs, intermediates and outputs are considered to be uncertain variables to deal with the problem of inaccurate data. Finally, a numerical example of the uncertain two-stage network DEA models will be presented for illustration.
14 citations
TL;DR: In this paper, the authors proposed an efficiency-based mechanism for state funding of public colleges and universities using data envelopment analysis, which provides incentives to institution administrators to eliminate wasteful spending and increase positive outcomes while maintaining educational quality and research productivity.
Abstract: We propose an efficiency-based mechanism for state funding of public colleges and universities using data envelopment analysis. We describe the philosophy and the mathematics that underlie the approach and apply\break the proposed model to data from 362 U.S. public four-year colleges and universities. The model provides incentives to institution administrators to eliminate wasteful spending and increase positive outcomes while maintaining educational quality and research productivity. The institutions in our study spent $96.74 billion, and states would reimburse $88.02 billion. Thus efficiency-based funding would reduce state government expenditures on these institutions by $8.72 billion, or approximately 9.0 percent. Efficiency-based funding is politically viable, as demonstrated by North Carolina’s successful use of this approach in pupil transportation operations since 1994. The model will be of interest to state legislators, state education officials, and others who are concerned with funding...
14 citations
TL;DR: The DEA model is extended to considering the decision-making unit (DMU) with the network structure and it is shown that a network DMU is network-efficient if and only if it is efficient at all stages, which follows the Bellman Optimal Principle.
Abstract: This paper extends the DEA model to considering the decision-making unit (DMU) with the network structure. We define the network DMU and its network DEA efficiency based on the postulate system. On the series structure of the DMU, we further discuss a sequential optimization model originally proposed by Sexton and Lewis.1,2 Based on their work, we extend to the DMU with general network of k stages and propose a composite network DEA model which evaluate the network DEA efficiency by solving only one linear programming. We show that the network efficiency obtained from the composite model is equivalent to that obtained by the sequential optimization model. We show that a network DMU is network-efficient if and only if it is efficient at all stages. That is, the network-efficient DMU follows the "Bellman Optimal Principle." Our model shows that if a network DMU is not DEA-efficient, then it is not efficient at one stage at least. We also define the projection of the network DMU on the corresponding production possibility set of network DMUs. Finally, we discuss other basic structures of the network DMU and show that the overall network DEA model can be extended to the general network DMU.
13 citations
01 Jan 2019
TL;DR: The underlying notions of network DEA methods and their advantages over the classical DEA ones are described, which are capable of reflecting accurately the DMUs’ internal operations as well as to incorporate their relationships and interdependences.
Abstract: Performance measurement deals with ongoing monitoring and evaluation of the operations of the organizations so as to be able to improve their productivity and performance. Thus, the adoption of performance evaluation methods is necessary, which are capable of taking into account all the environmental factors of the organization, identifying the inefficient production processes and suggesting adequate ways to improve them. Such a method is Data Envelopment Analysis (DEA), which is the most popular non-parametric and data driven technique for assessing the efficiency of homogeneous decision making units (DMUs) that use multiple inputs to produce multiple outputs. The DMUs may consist of several sub-processes that interact and perform various operations. DEA has a wide application domain, such as public sector, banks, education, energy systems, transportation, supply chains, countries and so forth. However, the classical DEA models treat the DMU as a “black box”, i.e. a single stage production process that transforms some external inputs to final outputs. In such a setting, the internal structure of the DMU is not taken into consideration. Thus, the conventional DEA models fail to mathematically represent the internal characteristics of the DMUs, as well as they fall short to provide precise results and useful information regarding the sources that cause inefficiency. To consider for the internal structure of the DMUs, recent methodological advancements are developed, which extend the standard DEA and constitute a new field, namely the network DEA. The network DEA methods are capable of reflecting accurately the DMUs’ internal operations as well as to incorporate their relationships and interdependences. In network DEA, the DMU is considered as a network of interconnected sub-units, with the connections indicating the flow of intermediate products. In this chapter, we describe the underlying notions of network DEA methods and their advantages over the classical DEA ones. We also conduct a critical review of the state-of-the art methods in the field and we provide a thorough categorization of a great volume of network DEA literature in a unified manner. We unveil the relations and the differences of the existing network DEA methods. In addition, we report their limitations concerning the returns to scale, the inconsistency between the multiplier and the envelopment models as well as the inadequate information that provide for the calculation of efficient projections. The most important network DEA methods do not secure the uniqueness of the efficiency scores, i.e. the same level of overall efficiency is obtained from different combinations of the efficiencies of the sub-processes. Also, the additive efficiency decomposition method provides biased efficiency assessments. Finally, we discuss about the inability of the existing approaches to be universally applied on every type of network structure.
13 citations
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TL;DR: In this paper, a non-parametric productivity measure that explicitly incorporates intermediate products is proposed, which is based on the Productivity Index (PII) and employs a nonparametric approach to measure productivity.
462 citations
TL;DR: A nonparametric, linear programming, frontier procedure for obtaining a measure of managerial efficiency that controls for exogenous features of the operating environment is introduced.
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441 citations
"Two-Stage DEA: An Application to Ma..." refers methods in this paper
...Sexton and Silkman (2000) and Fried et al. (1999) present similar but distinct approaches to dealing with site characteristics in standard DEA models....
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TL;DR: In this article, the authors introduce a frontier model for productivity measurement that explicitly recognizes that some inputs are produced and consumed within the production technology, where intermediate inputs may also be final output.
Abstract: The purpose of this paper is to introduce a frontier model for productivity measurement that explicitly recognizes that some inputs are produced and consumed within the production technology. Here we differ from Koopmans (1951) by assuming that the intermediate inputs may also be final output. This assumption is in line with current international trade theory, where intermediate inputs are tradable. Our model consists of two production units that are interconnected in a network to form a production technology. The productivity measure employed here is the so-called Malmquist productivity index. This index consists of ratios of distance functions. Here these distance functions are defined on the network technology and they are computed using linear programming techniques.
439 citations
TL;DR: It is found that the decomposition of production into subproduction processes reduces the dimensions of problem specification, with the effect that a larger number of variables may be usefully included in the model.
Abstract: Agricultural production is often characterised by multiple inputs and multiple outputs to multiple production processes. Where an output from one process is used as an input to another, this output is called an intermediate product. This is a common situation when a farm produces both crops and livestock. The analysis of production efficiency is important for the evaluation of agricultural policy, but until recently, no methods have explicitly included intermediate products. This study applies a non-parametric technique of efficiency measurement which includes intermediate products. The data set is a sample of dairy farms drawn using a complex survey design. The use of non-parametric efficiency measurement and the subsequent application of bootstrapping and kernel density estimation to the results allow inferences to be drawn concerning the whole population from which the sample was drawn. We find that the decomposition of production into subproduction processes reduces the dimensions of problem specification, with the effect that a larger number of variables may be usefully included in the model.
145 citations