Taiwanese motherboard manufacturers create 98.5% of the world’s desktop motherboards and dominate the global desktop motherboard market (Market Intelligence Center (MIC), 2012). However, this industry’s growth rate has slowed due to the trend of replacing desktops with laptops and tablets. In addition, aggressive pricing by laptop/tablet manufacturers has diminished desktop motherboard sales. Forecasting plays an important role in many business activities, such as the volume of demand in order and inventory management, production planning in manufacturing processes, capacity usage in production management, and the diffusion patterns of new products and technological innovations. The market is changing rapidly and a new forecasting model is required. Forecasted results can assist manufacturers in making better decisions on future expansion and investment.
In recent years, the Bass diffusion model (Bass, 1969) has been used successfully to describe the empirical adoption curve for many new products and technological innovations. This model provides good predictions on the timing and magnitude of the sales peaks of the products to which it is applied. Bass, Krishnan, and Jain (1994) proposed a generalized Bass model that included marketing mix variables (e.g., price and advertising variables). This generalized model can produce the best model fit and forecasting performance. Bass (1969) used the ordinary least squares (OLS) method to estimate the parameters of the Bass diffusion model. However, the OLS approach has a bias when estimating continuous time models. In contrast, Schmittlein and Mahajan (1982) proposed the maximum likelihood estimation (MLE) method to improve the estimation. However, the maximum likelihood formulation considers only the sampling error and ignores all other sources of error, hence the computed standard error estimates may be too optimistic. Many researchers have tried to improve the problem. For example, Srinivasan and Mason (1986) applied the nonlinear least square (NLS) method to obtain valid error estimates. Venkatesan and Kumar (2002) presented genetic algorithms (GAs) to estimate the parameters of the Bass diffusion model. The parameter estimates they obtained from the GAs were consistent with the NLS method. Wang, Chang, and Hsiao (2013) proposed an evolutionary approach based on a GA/particle swarm optimization (PSO) hybrid to obtain the parameter estimates of the modified Bass model. This hybrid evolutionary approach has been successfully applied to real-world engineering design problems (Nagi et al., 2011 and Niu et al., 2010).
The support vector machine (SVM) developed by Vapnik (1998) is based on statistical learning theory. SVMs have been widely applied in the fields of pattern recognition, bioinformatics, and other artificial-intelligence-related applications. SVMs have also been used to solve nonlinear regression estimation problems, a process known as support vector regression (SVR). SVR models have been used successfully to solve forecasting problems (Cao, 2003, Che et al., 2012, Chou et al., 2013, García and García, 2012, Hong and Pai, 2007, Huang, 2012, Huang et al., 2011, Jiang and He, 2012, Khashei and Bijari, 2012, Pai and Lin, 2005 and Štěpnička et al., 2013). Empirical results have indicated that the selection of the three parameters, including C, ɛ, and γ, in an SVR model significantly influences its forecasting accuracy. SVRs with evolutionary algorithms (e.g., GA, simulated annealing, PSO, chaos-based PSO, chaos-based firefly, and hybrid) are used to determine appropriate parameter values ( Hong, 2009, Kazem et al., 2013, Wu, 2010 and Wu and Law, 2011).
We implement an SVR model with a differential evolution (DE) algorithm (Price et al., 2006 and Storn and Price, 1997) to improve the forecasting performance of motherboard shipments. In addition, we use a hybrid evolutionary algorithm that combines PSO with a quasi-Newton method to improve the parameter estimates of the generalized Bass diffusion model. In the following section, we present the forecasting models. Section 3 explains the SVR model with the DE and hybrid PSO (HPSO) algorithms. Section 4 denotes our use of data on motherboard shipments from Taiwanese firms to demonstrate the application of our proposed forecasting model. Finally, we offer a conclusion and suggestions for future studies in Section 5.
Various forecasting activities are involved in making business decisions, and forecasting accuracy plays an important role. In this study, we propose using an SVR model based on the DE algorithm to improve the fitting and forecasting processes for motherboard shipments. We compared two SVR models with the Bass diffusion and generalized Bass diffusion models. Whereas the SVR-1 model considers only the time variable, the SVR-2 model considers the time variable and market value. In our study, the SVR-2 model outperformed the other models on both model fit and forecasting accuracy. We therefore conclude that an SVR model with a DE algorithm is suitable for forecasting in the motherboard industry. In practice, a combined forecast of the Bass and SVR models should be considered in the motherboard industry.
Future research should attempt a modeling comparison of our approach with other methods such as hybrid forecasting and evolutionary algorithm-based SVR models.
