Semiconductor manufacturing plays one of the most important roles in the global economy. Tremendous capital investment is required to build and equip a production line (Andersen et al., 1993). Also, the high reinvestment of total revenue into capital expenses is required. For competitive prices and adequate return on the investment against above two issues, the strategy to shorten order lead times with a fair degree of flexibility in the product mix and a significant periodical increase in productivity is critical. In other words, managements must make a right decision in a short time after analyzing the performance. Not only that, the performance analysis can help stockholders, loaners, employees, suppliers, customers, and future employees to understand the condition they possess. Thus, one of motivations is assessing the performance accurately; another is comparing their advancement and trend from management viewpoints.
DEA is a multiple input-output efficient technique that measures the relative efficiency of decision-making units (DMUs) using a linear programming based model. The technique is non-parametric because it requires no assumption about the weights of the underlying production function. DEA was originally proposed by Charnes et al. (1978) and this model is commonly referred to as a CCR model. The DEA frontier DMUs are those with maximum output levels for given input levels or with minimum input levels for given output levels.
DEA provides efficiency score θo*, a ratio efficiency of the DMUo. At the same time, the optimal solution reveals slacks, if any of excesses in inputs and shortfalls in output exists. If its full ratio efficiency, θo*=1, and with no slacks in any optimal solutions is called
CCR-efficient. Otherwise (0<θo*<1), the DMU has a disadvantage against the DMUs in its reference-set.
Färe et al. (1992, 1994a) developed the DEA-based Malmquist productivity index by CCR model. The DEA-based Malmquist productivity is a combined index that can be extended to measures the productivity change of DMUs over time. It has been applied in many ways, as described in Färe et al. (1994b), Löthgren and Tambour (1999a), Grifell-Tatjé and Lovell (1996), and Fulginiti and Perrin (1997) and others. The two components embedded in Malmquist productivity, measuring the changes in technology frontier and technical efficiency, are also further examined in this research. By the technology frontier shift (FS), the development or decline of all DMUs is able to measure. Technical efficiency change (TEC) is used to measure the change in technical efficiency. It is also a measure of how much closer to the frontier the company (DMU) is when crossing the two consecutive times. We define TEC and Malmquist iproductivity as R3 and R4 respectively in Section 4.1 for the performance measurement.
Chen and Ali (2004) applied the DEA Malmquist productivity measure to the computer industries by the CCR model to assess the four distance functions of Malmquist productivity.
Moreover, they discovered more information about the two components that obscure in the Malmquist productivity index. We define them as R1 and R2 in Section 3 for the performance measurement in this research and account for the attributes. Their approach not only reveals
patterns of productivity change and presents a new interpretation along with the managerial implication of each component, but also identifies the strategy shifts of individual DMUs in a particular time period. They determined whether such strategy shifts were favorable and improving. However, the ratio efficiency θo* by the CCR model is not able to take account of slacks. For instance, the optimal solution θo*=1 might be with slacks≠0. In the DEA Malmquist productivity, the DMUo is regarded as efficient but actually, it should be regarded as inefficient. Therefore, it is important to observe both the ratio efficiency and the slacks.
Some attempts have been made to unify θo* and slacks into a scalar measure.
Charnes et al. (1985) developed the additive model of DEA, which deals directly with input excess and output shortfalls. But this model has no scalar measure (ratio efficiency) per se. Thus, although this model can discriminate between efficient and inefficient DMUs by the existence of slacks, it has no means of gauging the depth of inefficiency, similar to θo* in the CCR model.
Tone (2001) developed a slack-based measure (SBM) of efficiency in DEA, which takes account of scalar measure and slacks. Further, Tone (2002) developed a slack-based measure of super efficiency (Super-SBM) in DEA for discriminating between efficient DMUs. Super efficiency measures the degree of superiority that efficient DMUo possesses against other DMUs.
So far, all the studies using DEA Malmquist productivity measurement are still not
employing the slacks-based measurement. Using the SBM/Super-SBM model to measure Malmquist productivity is an unprecedented approach. The method could attain more accurate and complete results. Liu and Yang (2004) applied the CCR model to assess the performance of Semiconductor’s packaging and testing firms in Taiwan from 2000 to 2003. Instead, we employ the SBM measurement and the Super-SBM model in this research. In addition to TEC (R3) and Malmquist productivity (R4) which existed in the traditional Malmquist productivity measurement, we also investigate the two components- R1 and R2 proposed by Chen and Ali (2004) to interpret a more detailed management implication.
The next section reviews how the DEA-based Malmquist productivity index works. We also present the Malmquist productivity approach.