A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system

Shih-Heng Yu () and Chia-Wei Hsu ()
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Shih-Heng Yu: National United University
Chia-Wei Hsu: Tungnan University

Annals of Operations Research, 2020, vol. 287, issue 1, No 21, 515-535

Abstract: Abstract Conventional data envelopment analysis (DEA) may generate the non-integer targets for integer-valued inputs and outputs of decision-making units (DMUs). To derive the convincing projections, integer-valued DEA has attracted much attention. Given the integrality restriction, Du et al. (Eur J Oper Res 218(1):186–192, 2012) proposed the super-efficiency approach consisting of additive integer-valued and additive super-efficiency integer-valued models for the differentiation of efficient DMUs, thereby raising the discriminatory power. This paper extends their approach to develop a simpler but stricter version, which we refer to as the unified additive super-efficiency model. The newly-developed model has three advantages. First, the slacks of input excess, input saving, output shortage and output surplus can be directly computed in a single program to obtain the efficiencies of inefficient DMUs and super-efficiencies of efficient DMUs. Secondly, it suggests the strongly Pareto-efficient projections for efficient DMUs. Finally, the identified super-efficiencies allow for the property of continuity. A comparison of the proposed model, with Du et al.’s (2012) and standard additive super-efficiency approaches is discussed using a numerical example. In addition, the applicability of the proposed model is illustrated by a data set covering 13 bus companies operating in the municipal bus system of Taichung. Our work not only provides managerial insights into the primary sources of inefficiency and super-efficiency but also contributes to the current understanding of how super-efficiency would be effectively and accurately measured in the presence of integer-valued data.

Keywords: Data envelopment analysis; Integer-valued data; Super-efficiency; Slacks; Strongly Pareto-efficient (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-019-03448-z

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