DEA Models for Parallel Systems: Game-Theoretic Approaches

Juan Du (), Joe Zhu (), Wade D. Cook () and Jiazhen Huo ()
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Juan Du: School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
Joe Zhu: International Center for Auditing and Evaluation, Nanjing Audit University, Nanjing 211815, P. R. China;
Wade D. Cook: Schulich School of Business, York University, Toronto, Ontario, Canada M3J 1P3, Canada
Jiazhen Huo: School of Economics and Management, Tongji University, Shanghai 200092, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 02, 1-22

Abstract: In many settings, systems are composed of a group of independent sub-units. Each sub-unit produces the same set of outputs by consuming the same set of inputs. Conventional data envelopment analysis (DEA) views such a system as a "black-box", and uses the sum of the respective inputs and outputs of all relevant component units to calculate the system efficiency. Various DEA-based models have been developed for decomposing the overall efficiency. This paper further investigates this kind of structure by using the cooperative (or centralized) and non-cooperative (Stackelberg or leader–follower) game theory concepts. We show that the existing DEA approaches can be viewed as a centralized model that optimizes the efficiency scores of all sub-units jointly. The proposed leader–follower model will be useful when the priority sequence is available for sub-units. Consider, for example, the evaluation of relative efficiencies of a set of manufacturing facilities where multiple work shifts are operating. Management may wish to determine not only the overall plant efficiency, but as well, the performance of each shift in some priority sequence. The relationship between the system efficiency and component efficiencies is also explored. Our approaches are demonstrated with an example whose data set involves the national forests of Taiwan.

Keywords: Data envelopment analysis (DEA); parallel systems; efficiency; centralized model; leader–follower model (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915500086

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