The Performance of Printed Circuit Boards in the Presence of Production Errors: A Comparative Analysis Using Various DEA Models

Introduction

Data envelopment analysis (DEA), as initiated and developed by Charnes, Cooper, and Rhodes (1978) is a nonparametric method for identifying efficient production frontiers and evaluating the relative efficiency of decision making units (DMUs), each of which is an entity responsible for converting multiple inputs into multiple outputs. DEA has been widely used in the efficiency analysis of many business and industry applications. However, the presence of multiple inputs and outputs in DEA makes the comparison difficult. Boussofiane, Dyson, and Thanassoulis (1991) focused on some of the key issues that arise in applying DEA in practice. The application of DEA presents a range of issues relating to the homogeneity of the units under assessment, the input/output set used, the measurement of those variables, and the weights attributed to them in the analysis. Dyson et al. (2001) highlighted some of the pitfalls that have been identified in application papers and suggested protocols to avoid the pitfalls and guide the application of the methodology.

Once DEA identifies the efficiency frontier, DEA improves the performance of the inefficient DMUs by either increasing the current output levels or decreasing the current input levels (Charnes, Cooper, Lewin, & Seiford, 1994). However, both desirable (good) and undesirable (bad) output and input factors may be present in real applications. Commendable literature surveys can be found, for instance, in Seiford (1996) and Cooper, Seiford, Thanassaulis, and Zanakis (2004). The most well-known DEA models are the CCR model (Charnes et al., 1978), the BCC model (Banker, Charnes, & Cooper, 1984), the additive model (Charnes, Cooper, Golany, Seiford, & Stutz, 1985), and the Cone Ratio model (Charnes, Cooper, Wei, & Huhng, 1989). The said DEA models were all formulated for desirable inputs and outputs.

It was mentioned already in the seminal work of Koopmans (1951) that the production activities may often generate harmful side-effects that are discharged to the environment, referred to as undesirable outputs, such as pollution, waste, noise, etc. Motivated by the public and governmental environment, ecological efficiency measurement has recently attracted much interest (Allen, 1999). If inefficiency exits in the production, the undesirable outputs should be reduced to improve the inefficiencies, i.e., the undesirable and desirable outputs should be treated differently when we evaluate the production performance (Seiford & Zhu, 2002). We know that in the standard DEA model, decreases in outputs are not allowed and only inputs are allowed to decrease, similarly increases in inputs are not allowed and only outputs are allowed to increase. A symmetric case of input that should be increased to improve the efficiency can also occur (Allen, 1999). For example, the aim of the recycling process is to use the maximum quantity of input waste. For further discussion, one can refer Pittman (1981); Färe, Grosskopf, Lovell, and Pasurka (1989); Färe Grosskopf, Lovell, and Yaisawarang (1993); and Scheel (2001). Undesirable factors (inputs and/or outputs) may appear in ecological and non-ecological applications like health care (complications of medical operations) and business (tax payment), as pointed out by Smith (1990). Färe et al. (1989) discussed paper production system (pollutants such as biochemical oxygen demand, suspended solids, particulates, and sulfur oxides); Hailu and Veeman (2001) discussed Canadian pulp and paper industry (biological oxygen demand and total suspended solids); Yu (2004) measured the physical efficiency of the domestic airports in Taiwan with undesirable outputs (aircraft noise) and environmental factors; Hua, Bian, and Liang (2006) studied the eco-efficiencies of paper mills along the Huai River in China. Liang, Yongjun, and Shibing (2009) applied undesirable output modeling in the context of principal component analysis to measure the ecological performance of 17 Chinese sites in the Anhui province by considering all the indices from the system (ecology) pressure as undesirable outputs.