A two-stage DEA model with partial impacts between inputs and outputs: application in refinery industries
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A two‑stage DEA model with partial impacts between inputs and outputs: application in refinery industries Mohammad Nemati1 · Reza Kazemi Matin1 · Mehdi Toloo2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Conventional data envelopment analysis (DEA) methods are useful for estimating the performance measure of decision making units (DMUs) that each DMU uses multiple inputs to produce multiple outputs without considering any partial impacts between inputs and outputs. Nevertheless, there are some real-world situations where DMUs may possess several production lines with a two-stage network structure that each production line use inputs according to their needs. The current paper extends the recent work by Ma (Expert Syst Appl Int J 42:4339–4347, 2015) to consider partial impact between inputs and outputs for two-stage network production systems. Toward this end, we consider several input–output bundles in each stage for production lines. We formulate a couple of new mathematical programming models in the DEA framework with the aim of considering partial impact between inputs and outputs for calculating aggregate, overall, and subunit efficiencies along with resource usage by production lines for a two-stage production system Finally, an application in refinery industries is provided as an example to illustrate the potential application of the proposed method. Keywords Data envelopment analysis (DEA) · Two-stage network DEA · Partial impact · Free intermediate measures
* Reza Kazemi Matin [email protected] Mohammad Nemati [email protected] Mehdi Toloo [email protected] http://homel.vsb.cz/~tol0013/ 1
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2
Department of Systems Engineering, Faculty of Economics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic
13
Vol.:(0123456789)
Annals of Operations Research
1 Introduction Data envelopment analysis (DEA) is a linear programming (LP) procedure to estimate the relative performance among a set of decision-making units (DMUs). It was introduced by Charnes and associates (1978). In particular, DEA estimates the performance of a unit under assessment relative to a set of homogenous production units which consume several inputs to generate several outputs. Traditional DEA approach makes no assumption about the procedures within the DMUs. As discussed by Sexton and Lewis (2003), traditional DEA considers DMU as a “black-box” which consumes inputs to generate outputs without contemplation of the internal procedure. In addition, in some situations such as supply chain structure, DEA methods include two or more stages and outputs of Stage 1 are considered as intermediate measures which are given as inputs to Stage 2. The primitive notion of two-stage DEA methods is according to the novel idea of Färe and Grosskopf (1996) who introduced the Network DEA structures. In the two-stage DEA model, all outputs of Stage 1 are inputs for Stage 2. This structure in DEA was also studied by Wan
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