This study applies the Analytic Network Process (ANP) to forecast the sales volume of printers in Taiwan for adjusting the recycling and treatment fee as an incentive for recycling industries. When historical data are lacking and when a broad spectrum of social impact is involved, the ANP, with the capacity to manage dependence and feedback among the factors, can serve as a tool to forecast outcomes by using expert judgment. The priorities derived from numerical judgment are similar to probabilities. They are obtained from the limit supermatrix of the ANP that represents forecasts for the next period. The result of back testing has shown that the ANP’s percentage error is small compared with those of some naïve statistical techniques. Sensitivity analysis is also made to ensure robustness of the model. Finally, the characteristic strengths of the Analytic Hierarchy Process (AHP) and ANP in forecasting are discussed to simplify their use in future applications.
Global warming and environmental deterioration have drastically forced people to make compensatory decisions for survival on our Earth as well as prompting them to be concerned about sustainable and green issues for humans. In 1971 the Environmental Protection Administration (EPA) of the Republic of China (ROC) in Taiwan initialized some actions on waste clean-up and resource recycling by establishing regulations to force people to recycle waste. To consider environmental costs, the Recycling Fund Management Board (RFMB) of the EPA was established in 1998. The RFMB collects funds from manufacturers and importers when they sell goods (33 categories announced so far) to customers and subsidizes recycling industries with a recycling and treatment fee as an incentive to increase the recycling rate of waste goods, containers, and packages [1].
Electronic waste (e-waste) is the major target in environmental policy making, because it contains many hazardous materials that are not easily disposed of and decay over a long period of time. Such waste requires industries to specialize in dissolving and cleaning to prevent environmental pollution, particularly for end-of-pipe recycling [2]. In 2001 the RFMB set forth a regulation on recycling used printers due to the fact that waste printers make up a large part of the e-waste from consumers. To balance the input and output of funds, sales volume and volume of waste printers collected are the two major factors for setting up a fee, and both rely heavily on forecasting for the next year so that the fee can be predetermined on a yearly basis. However, the amount of printers for selling and recycling is difficult to estimate due to the state of the economy and customer behavior at the time of the forecast, along with the availability of sparse historical data.
The RFMB has estimated the sales volume for the purpose of fund allocation in the past. Wen [3] employed three techniques to evaluate sales volume and volume of waste collected for announced recyclable items: trend functions with quadratic and cubic forms, a simple moving average, and a modified moving average from the growth rates of the nearest two periods. Liu [4] made use of a simple moving average and trend techniques for estimating the volume of waste cars in Taiwan, but the forecasting results were not good enough due to the complexity of the economic factors. The current work still relies heavily upon expert judgment. Thus, a reliable technique is in demand, because it has a significant impact on decision making with regard to environmental policy.
Forecasting is an analytical technique used to assist managers to develop a business plan or to proceed with decision-making with uncertainties, and a forecast of the sales volume is closely related to a business’ competitive strategy [5]. Traditional forecasting approaches have been found difficult to use in predicting the sales volume and the amount of waste because of the inadequacy of historical data, the extensiveness of the social dimension, and because of unforeseeable factors. To conduct a forecast, this study therefore applies the Analytic Network Process (ANP), which is a generalization of the Analytic Hierarchy Process (AHP) that deals with dependence and feedback among the factors, combines qualitative and quantitative analyses through expert judgment, and relies on the constraining attributes mentioned above. Moreover, the AHP and AHP can be used to forecast general events whose actual outcomes have not yet been observed, e.g., predicting a chess winner [6] or market share in the hamburger industry [7]. We concentrate the forecasting on a time basis and apply the ANP to forecast printer sales volume for the next period based on the data from the RFMB since 2002. It is hoped that this study can be used as another choice for solving the current problem.
The paper is organized as follows. After the introduction, a literature review on forecasting using the AHP and ANP is provided in Section 2. Forecasting-related applications of AHP and ANP are also collected for ease of understanding. Then, the detailed procedure of the ANP model for forecasting is proposed in Section 3. A case study is then illustrated in Section 4, and sensitivity analyses are performed to ensure that the model is robust. In Section 5 some common statistical techniques are applied to the same problem for comparison. The essence of utilizing AHP/ANP for forecasting is discussed in Section 6. In the final part, some concluding remarks are made for ease of future applications.
When historical data are lacking and when a broad spectrum of social impact is involved, the ANP, with the ability to handle dependence and feedback among factors, is a valuable technique for forecasting the next period via expert judgment. This study exploits the ANP as a forecasting tool to predict the sales volume of printers in Taiwan. Through a back test, the percentage error of the result from the proposed model is −1.297%, which is minimal compared to the errors from five naïve statistical techniques. In addition, the results of sensitive analysis show that the model is almost insensitive to a change in the priorities, within plus or minus 40% of the original values, of the cluster weights.
After a comprehensive review, the applications of the AHP and ANP for forecasting are given in a table in which the numbers of levels or clusters, the period of forecasting, the forecasting targets, and the alternatives are displayed. The forecasting-related applications of the AHP and ANP are then classified as seven areas under two categories of explicit or implicit representation of time. The two tables clarify possible applications for the reader.
The last part discusses how to use the ANP for forecasting. There are three topics, including the selection of the AHP or ANP, the possible uses of the AHP and ANP for forecasting-related applications, and how to define the alternatives for direct forecasting. These observations provide a straightforward direction for ease of future applications in forecasting.
Although there are many criteria for judging the adequacy of the usage of various forecasting techniques [31], for simplicity this study chooses the percentage error as the index for measuring the accuracy of techniques. In addition, this work concentrates on how to use the ANP or AHP for forecasting through a case study, and some criticisms of the AHP, e.g., Belton and Goodwin [32], are left out. The issues of choosing a suitable measure for errors and of dealing with the criticisms of the AHP or ANP are left for a future study.
