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Measuring efficiency with products,by-products and parent-offspring relations: A conditional two-stage DEA model
Affiliation:1. School of Management, University of Science and Technology of China, Hefei, Anhui Province 230026, PR China;2. Hefei University of Technology, Hefei, Anhui Province 230026, PR China;3. Schulich School of Business, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3;1. School of Science, Sichuan University of Science and Engineering, Zigong 643000, China;2. Department of Mathematics, Nanchang University, Nanchang 330031, China;3. Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China;1. Faculty of Science, Ningbo University, Ningbo 315211, PR China;2. School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, PR China;1. Dipartimento di Scienze/Ingegneria dell׳Informazione e Matematica, Università degli Studi dell׳Aquila, Via Vetoio, Coppito, I-67010 L׳Aquila, Italy;2. Dipartimento di Ingegneria dell׳Informazione, Università Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy;1. Department of Production Network Planning, Daimler Trucks, DE-70546 Stuttgart, Germany;2. TUM School of Management, Technische Universität München, Arcisstrasse 21, DE-80333 Munich, Germany;1. Department of Industrial Management, University of Seville, Spain;2. Agro-ecosystems History Laboratory, University Pablo de Olavide, Spain;1. Industrial Management & Business Administration Department, School of Engineering, University of Seville, Spain;2. Centre for Management Studies, Instituto Superior Técnico, Technical University of Lisbon, Portugal
Abstract:In the usual data envelopment analysis (DEA) setting, as pioneered by Charnes et al. (1978) [1], it is assumed that a set of decision making units (DMUs) is to be evaluated in terms of their relative efficiencies in converting a bundle of inputs into a bundle of outputs. The usual assumption in DEA is that each output is impacted by each and every member of the input set. One particular area of recent research is that relating to partial input to output impacts where the main issue addressed is that in many settings not all inputs impact all outputs. In that situation the authors view the DMU as consisting of a set of mutually exclusive subunits, with each subunit having its own unique bundle of inputs and outputs. Examined as well in this area, is the presence of multiple processes for generating sets of outputs. Missing from that earlier work is consideration of the presence of outputs in the form of by-products, giving rise to a parent-offspring phenomenon. One of the modeling complications there is that the parent assumes two different roles; as an input affecting the offspring, while at the same time being the dominant output. This gives rise to a model that we refer to as conditional two-stage. Another complication is that in the presence of multiple processes, by-products often arise out of only a subset of those processes. In the current paper we develop a DEA-type of methodology to handle partial input to output impacts in the presence of by-products.
Keywords:DEA  Multiple processes  By-products  Dual role factors  Partial impacts  Conditional two-stage DEA
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