مقاله سال ۲۰۱۶

 مجله امگا – Omega

Standard or black-box data envelopment analysis (DEA) is a set of mathematical programming techniques for measuring the efficiency performance of decision making units (DMUs) that convert exogenous inputs into final outputs. In standard DEA, the internal production processes of DMUs are ignored and the exogenous inputs consumed and final outputs produced by the DMUs are the only consideration for efficiency evaluation. On the other hand, network DEA (NDEA) attempts to formulate the internal operations of the evaluated DMU and thus intermediate products (which are outputs coming from divisions (sub-processes) and inputs utilized by others) are explicitly taken into account. In other words, NDEA intends to open the black box so as to provide adequate detail to management and can provide detailed information on the efficiency of divisions (or sub-DMUs) at the assessed DMU as well as its efficiency status. NDEA can be thought of as a generalization of standard DEA.

DEA researchers developed various NDEA models for evaluating the efficiency of DMUs (Färe and Grosskopf (1996, 2000); Lewis and Sexton (2004); Prieto and Zofio (2007); Kao (2009, 2014); Tone and Tsutsui (2009); Lozano (2011); Du,Chen and Huo (2015)) and other researchers focused on the efficiency performance of DMUs which have internal series (e.g., two-stage or three-stage) structures (Sexton and Lewis (2003); Kao and Hwang (2008); Liang, Cook and Zhu (2008); Fukuyama and Weber (2010) ; Cook, Liang and Zhu (2010); Fukuyama, Weber and Xia (2015); Halkos, Tzeremes and Kourtzidis (2014); Akther, Fukuyama and Weber (2013)). A review of the NDEA models can be found in Kao (2014). The management of the DMU often would like to know the sources of inefficiency within it, but some of the existing network DEA methods do not fully provide information on the DMU’s overall efficiency status that is consistent with Pareto-Koopmans efficiency with the full consideration of internal flows or intermediate products. Obviously, adoption of Pareto-Koopmans efficiency stems from the possibility principle or free disposal hull which is for example given in the A3 postulate of Cooper, Seiford, Tone and Zhu (2007). In NDEA Tone and Tsutsui (2009) used the possibility principle for only exogenous inputs and final outputs similar to standard DEA which doesn’t have intermediate products.

In the DEA literature, there are two efficiency notions: weak efficiency and Pareto-Koopmans efficiency. The Farrell-Debreu measure is calculated based on the weakly efficient frontier and hence possibly existing nonzero slacks are ignored in its efficiency measurement. By contrast, the original model by Charnes, Cooper and Rhodes (CCR, 1978) is developed with the intension of incorporating the notion of full efficiency or Pareto-Koopmans efficiency. Charnes, Cooper and their associates have incorporated this efficiency notion with the use of the non-Archimedean infinitesimal. In a black-box setting, a DMU is Pareto-Koopmans efficient if and only if it is impossible to make an improvement in the utilization of any input or output without worsening some of the other inputs and/or outputs. Hence, Charnes, Cooper and their associates relate the CCR model to the notion of Pareto-Koopmans efficiency. See Charnes and Cooper (1984, 1985), Charnes, Cooper, Golany and Seiford (1985) and Cooper, Seiford, Tone and Zhu (2007) for detailed discussion of the difference between the two notions. The additive model, Russell models and slacks-based models are alternative methods to incorporate Pareto-Koopmans efficiency.