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J Intell Manuf (2012) 23:517–531 DOI 10.1007/s10845-010-0390-7

Forecasting of manufacturing cost in mobile phone products by case-based reasoning and artificial neural network models

Pei-Chann Chang · Jyun-Jie Lin · Wei-Yuan Dzan

Received: 3 January 2010 / Accepted: 11 February 2010 / Published online: 25 February 2010 © Springer Science+Business Media, LLC 2010

Abstract The mobile phone manufacturers in Taiwan have made great efforts in proposing the rational quotations to the international phone companies with the ambition to win the bids by out beating other phone manufacturers. However, there are a lot of uncertainties and issues to be resolved in estimating the manufacturing costs for mobile phone man- ufacturers. As far as we know, there is no existing model which can be applied directly in forecasting the manufactur- ing costs. This research makes the first attempt to develop a hybrid system by integrated Case-Based Reasoning (CBR) and Artificial Neural Networks (ANN) as a Product Unit Cost (PUC) forecasting model for Mobile Phone Company. According to the cost formula of the mobile phone and experts’ opinions, a set of qualitative and quantitative factors are analyzed and determined. Qualitative factors are applied in CBR to retrieve a similar case from the case bases for a new phone product and ANN is used to find the relation- ship between the quantitative factors and the predicted PUC. Finally, intensive experiments are conducted to test the effec- tiveness of six different forecasting models. The model pro- posed in this research is compared with the other five models and the MAPE value of the proposed model is the small- est. This research provides a new prediction model with high accuracy for mobile phone manufacturing companies.

Keywords Mobile phone · Product cost prediction · Case-based reasoning · Artificial neural networks

P.-C. Chang (B) · J.-J. Lin Department of Information Management, Yuan Ze University, Taoyuan 32026, Taiwan, R.O.C e-mail: iepchang@saturn.yzu.edu.tw

W.-Y. Dzan Department of Naval Architecture, National Kaohsiung Marine University, Kaohsiung 81143, Taiwan

Introduction

The scale of global mobile phone market has the tendency to grow up quickly in recent years. The demand has already grown up steadily in developed country and even with the multiple numbers of growths in developing countries. The market demand can be categorized in two trends; i.e., high price mobile phone with high profit and low price mobile phone while with large amount of demand volumes. To satisfy large demand of the highly selected customer, the manufac- turing of mobile phone have changed towards higher quality, shorter delivery times and lower product costs. It is a key issue for the mobile phone manufacturer to come out with the accurate quotation for their phone products which can provide more opportunities in winning the bids from inter- national phone companies with famous brand such as Nokia, Motorola or i-Phone … etc. It is very important for the man- ufacturer to offer a reasonable quotations as mentioned by García-Crespo et al. (2010) otherwise even they win the bids however owing to the missed calculation in cost they might still lose money in these contracts. However, there are a lot of uncertainties and issues to be resolved in estimating the man- ufacturing costs for mobile phone manufacturers. As far as we know, there is no existing model which can be applied in forecasting the manufacturing costs. In tradition, the account will estimate the manufacturing cost based on their experi- ence and with the help of the experts in manufacturing to come out with the quotation for a particular phone product. Basically, they will apply the statistical tools to forecast the result in estimating the manufacturing cost. The model is very simple and the procedures are very tedious while the results are not that satisfactory.

The mobile phone manufacturers in Taiwan are very com- petitive and they are facing the challenges of fast changing model and new functions of the mobile phone provided by the

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phone company. The manufacturers have made great efforts in proposing the rational quotations to the international phone companies with the ambition to win the bids by out beat- ing other phone manufacturers. However, there are a lot of uncertainties and issues to be resolved in estimating the man- ufacturing costs for mobile phone manufacturers. As far as we know, there is no existing model which can be applied directly in forecasting the manufacturing costs. Case-Based Reasoning (CBR) includes both a cognitive and a compu- tational model of reasoning by analogy from past cases. It is often more efficient to solve a problem by starting with the solutions to previous similar problems than it is to gen- erate the entire new solution from the scratch. Back-prop- agation Neural Networks (BPN) is by far the most widely utilized for its relatively simple mathematical models and good generalization capabilities. The problem solving para- digm can be applied to a wide range of applications involv- ing classification, estimation, and prediction. Niazi et al. (2006) pointed out that BPN could be applied for training to deduce unprecedented problems by accumulated knowl- edge and information. Especially, it can find out solutions in uncertain circumstances and has satisfying results in deal- ing with non-linear problems. Therefore, BPN is the most popular neural network models being applied and it fits the best the nature of product cost estimation. Taking advan- tages of these two tools in old cases retrieving and gener- alizing from examples, CBR and BPN will be applied in this research for manufacturing cost estimation for a mobile phone.

The contribution of this study is to develop a novel hybrid system by integrated Case-Based Reasoning (CBR) and Arti- ficial Neural Networks (ANN) as a Product Unit Cost (PUC) forecasting model for Mobile Phone Company. Therefore, the proposed model can provide a timely and accurate prod- uct quotation for the mobile phone manufacturers in winning the orders from the international phone company. Some pro- duction variables during the manufacturing process cannot be derived before hand; hence this study will apply CBR to retrieve similar cases from the historic products and these variables then will be estimated based on these similar cases retrieved. In other words, the study applies CBR to retrieve manufacturing variables for a new mobile phone from his- toric products in estimating the PUC and then ANNs are used to train the model for discovering the relationship among the quantitative variables and the product unit cost. Therefore, the established model can be applied to predict the PUC for a new developed mobile phone.

The rest of the paper is organized as follows: “Literature survey” reviews the factors related to this research of the mobile phone manufacturing company. “The product unit cost of a mobile phone” is the framework in this study. “A Forecasting model of product unit cost for mobile phone” presents some experimental results of various models includ-

ing other compared methods. “Experiment results” is the final discussion.

Literature survey

Cost estimation techniques

Cavalieri et al. (2004) in their research discussing the spare parts cost estimation in auto industry pointed out that, at the final stage of the product life cycle, most product costs continuously arise because they have been determined at the product concept design stage. Some researches even point out that the product design initial stage has determined 70– 80% of the total product cost (Niazi et al. 2006; Ou-Yang and Lin 1997).

Product Unit Cost will affect sales price, sale volume and profit most directly. In addition, product cost estimation var- ies widely ranging from standard spare parts manufacturing cost estimation to the cost analysis of the optimized tech- nology and marketing fees of highly customized assembled products with appropriate product estimation models avail- able at stages from product concept design stage to the prod- uct design cycle final stages. Therefore, the available cost estimation technologies are surveyed as follows:

Zhang et al. (1996) categorized cost estimation techniques into traditional detailed breakdown, simplified-breakdown, group-technology-based, regression-based and activity- based cost approaches. Ben-Arieh and Qian (2003) divided cost estimation models into intuitive, analogical, parametric and analytical approaches. Shehab and Abdalla (2001) pro- posed intuitive, parametric, variant-based and generative cost estimating approaches. Cavalieri et al. (2004) proved three cost analyses of analogy-based, parametric and engineering approaches. Niazi et al. (2006) provided a category on the basis of the integrated cost estimation approaches into qual- itative and quantitative cost estimation techniques with key advantages and limitations of each cost estimation technique. This category is very informative for researchers interesting in the cost estimation model development.

New tools in soft computing

Recently, owing to the development in Computational Intel- ligences, tools in soft computing such as decision tree (DT), artificial neural networks (ANN), Support Vector Machines (SVMs) and Case-Based Reasoning (CBR) have been widely applied in the manufacturing companies for various moni- toring, planning and scheduling problems. A hybrid system which combines several techniques from soft computing into a model is a new trend in solving the complex manufactur- ing problems. CBR is a very useful tool in retrieving sim- ilar product and estimating the due date of a new product

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(Chiu et al. 2003). It is also applied in estimating the returned books from the retails which provides a very significant fore- casting result for wholesaler in keeping their book stocks (Chang and Lai 2005). In addition, back-propagation neu- ral networks (BPN) is more effective than some traditional direct procedures for manufacturing lead time forecasting since neural network can obtain a probable result even if the input data are incomplete or noisy (Chang and Hsieh 2003).

The hybrid CBR techniques have been widely applied in various applications including manufacturing planning, fault diagnosis, knowledge modeling and management, and med- ical diagnosis and application. Hui and Jha (2000) integrated NN, CBR, and rule-based reasoning to support customer ser- vice activities, such as decision support and machine fault diagnosis in a manufacturing environment. Liao integrated a CBR method with a multi-layer perception for the automatic identification of failure mechanisms in the entire failure anal- ysis process (Liao 2004a,b). Yang et al. (2004) integrated CBR with an ART-Kohonen NN to enhance fault diagno- sis of electric motors. Hua Tan et al. (2006) integrated CBR and the fuzzy ARTMAP NN to support managers in mak- ing timely and optimal manufacturing technology investment decisions. Saridakis and Dentsoras (2007) introduced a case- based design with a soft computing system to evaluate the parametric design of an oscillating conveyor. Chang et al. (2009) adopted an evolving CBR approaches to predict the flow time in semiconductor manufacturing factory.

Hybrid CBR has also been used in the medical planning and application areas. Garrell I Guiu et al. (1999) introduced a case-based classifier system to solve the automatic diagnosis of Mammary Biopsy Images. Hsu and Ho (2004) combined the CBR, NN, fuzzy theory, and induction theory together to facilitate multiple-disease diagnosis and the learning of new adaptation knowledge. Wyns et al. (2004) applied a modified Kohonen mapping combined with a CBR evaluation criterion to predict early arthritis, including rheumatoid arthritis (RA) and spondyloarthropathy (SpA). Ahn and Kim (2009) com- bined the CBR with genetic algorithms to evaluate cytologi- cal features derived from a digital scan of breast fine needle aspirate (FNA) slides. A hybrid algorithm with CBR and Neural Network was applied to forecast cost assessment of steel buildings (Lotfy and Mohamed 2002), and the research found that by presenting the closest retrieved cases to a neural network, the complex of the issues in domain problem will be reduced. The other hybrid algorithms in recent years also proved that the hybrid intelligent system is more efficient and more accurate (Chen and Burrell 2001; Zhang et al. 2008).

In addition, hybrid CBRs is also applied in the financial forecasting areas. Kim and Han (2001) presented a case- indexing method of CBR which utilizes SOM for the prediction of corporate bond rating. Li et al. (2009) intro- duced a feature-based similarity measure to deal with finan- cial distress prediction (e.g., bankruptcy prediction) in China.

Chang and Lai (2005) integrated the SOM and CBR for sales forecasts of newly released books. Chang et al. (2006) evolved a CBR system with genetic algorithm for wholesaler returning book forecasting and financial time series forecast- ing (Chang et al. 2009). Chun and Park (2006) devised a regression CBR for financial forecasting, which applies dif- ferent weights to independent variables before finding similar cases. Ravi Kumar and Ravi (2007) presented a comprehen- sive review of the works utilizing NN and CBR to solve the bankruptcy prediction problems faced by banks.

According to the literature survey above, this research makes the first attempt to develop a hybrid system by inte- grated Case-Based Reasoning (CBR) and Artificial Neural Networks (ANN) as a Product Unit Cost (PUC) forecasting model for Mobile Phone Company. According to the cost formula of the mobile phone and experts’ opinions, a set of qualitative and quantitative factors are analyzed and deter- mined. Qualitative factors are applied in CBR to retrieve a similar case from the case bases for a new phone product and ANN is used to find the relationship between the quantitative factors and the predicted PUC.

The product unit cost of a mobile phone

Mobile phone contractors are facing very competitive pres- sures in the market to provide low cost high-quality mobile phone in fast production time. They face with the problem of deciding the bidding price of a particular phone or sev- eral phones owned by one customer. They cannot make full design and explode the bill of material of the phone before they win the bid. Therefore, they have to make cost estima- tion of the phone based on their own experience in the man- ufacturing of previous phones. If the manufacturing cost is underestimated, a phone manufacturer will suffer a tremen- dous loss. If the information about the previously manufac- tured phones could be captured, stored and reused as a part of the estimation process, many estimation problems could be solved more easily and accurately.

The production of a mobile phone will go through a series of manufacturing processes and different type of mobile phones will be produced within a short period of times. Thus, the cost estimation for each product type is not a trivia prob- lem and it has caught a lot of attentions in industrial practi- tioners and academic researchers. These differences among different mobile phone cannot be accounted for simply by the change in size or type alone. Therefore, it is very meaningful to come out with a good estimation of the manufacturing cost for a particular mobile phone. The cost estimation of a mobile phone include the accumulation of all the costs related to the manufacturing of a mobile phone during the production pro- cesses and then divide the total cost by the total number of mobile phones produced in this period. However, there are

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various variables related to the manufacturing cost calcula- tion and the most difficult part is how to figure out these variables before hand so that a very accurate quotation can be provided to the sale manager for bidding. Related issues in calculating the PUC of a mobile phone can be described as follows:

The formula for calculating the product unit cost

The product unit cost of a mobile phone adopted by the com- pany is defined as follows:

PUC = PTC TPQ

(1)

PUC: Product Unit Cost for mobile phone i PTC: Total manufactured Cost for mobile phone i TPQ: Total Production Quantity for mobile phone i PTC is calculated as the total cost multiplies by the labor hour ratio and could be defined by (2)

PTC = TC × POHR (2)

TC: Total Cost, sum of labor cost and total manufacturing cost POHR: Product output ratio of working hours, defined as Product-Output/Hours Ratio POHR is equivalent to formula (3)

POHR = PTOH TOH

(3)

PTOH: Product Total Output Hours TOH: Total Output Hours. PTOH is defined by (4)

PTOH = ∑ {

TPQ × [

CT × SQ 60

]} (4)

TPQ: Total Product Quantity CT: Tact Time SQ: Production Station Quantity Hence, the PUC in formula (1) could be defined by (5)

PUC = {

TC × {∑ [

TPQ × CT × SQ 60

] /TOH

}} /TPQ

(5)

According to formula (5), to increase TPQ value or to decrease TOH value will help to minimize PUC. The product total manufactured cost (PTC) could be also calculated by the formula (6)

PTC = PEC + PNC (6)

PEC: Product Exception Cost PNC: Product Normal Cost PEC is defined by (7) and PNC is defined by (8)

PEC = PTC × PEHR (7) PNC = PTC × (1 − PEHR) (8)

PEHR: Product Exception/Hours Ratio According to formula (2), PTC could be as formula (9) and PTC could be also as formula (10) by applied formula (3)

PTC = [(POHR × TC) × PEHR] + [(POHR × TC) × (1 − PEHR)] (9)

PTC = [(

PTOH

TOH × TC

) × PEHR

]

+ [(

PTOH

TOH × TC

) × (1 − PEHR)

] (10)

In formula (10), the smaller PEHR value and the lower PTC value will be obtained. The lower PTC value means the lower PUC value from the management point of view. According to formula (1), (4) and (10), we know the product total output hours; total product quantity and the ratio of product excep- tion and hours are the important factors in deciding the prod- uct unit cost. In this study, we found the variables related to formula (10) can be categorized as quantitative factors. These variables are (1) yield rate of mobile phones as Y1; (2) Forecasted achieve rate as Y2 ; (3)The total production time of mobile phones as Y3 ; (4) Line balance as Y4 and (5) The interval between SR and MP as Y5.

Variables to be considered in the model

For a new product to be manufactured, it is impossible to directly forecast the quantitative factors as described in previ- ous section. Therefore, the cost accounting people and man- ufacturing engineers need to work together to come out with the values for these variables for PUC calculation. Three spe- cific variables including product total output hours (PTOH), total cost (TC) and the ratio of exceptional product to hours (PEHR) have to be figured out first. However, they are not available until the product, i.e., the mobile phone, is actually manufactured in the shop floor. However, in order to win the bid from the international phone company, the manufactur- ers have to provide a quotation for the new mobile phone. Therefore, the manager has to come out with the PUC of a new mobile phone very often and the accuracy of the estima- tion will not be verified until the products are manufactured. In addition, there are lots of qualitative variables needed to be decided in estimating the PUC and they are described as follows:

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Fig. 1 Mobile phone models Bar phone Flip phone Slide phone

Fig. 2 Keyboard built-in or not No hardware for keyboard (Apple

iPhone) Keyboard buit-in (BlackBerry)

(1) Mobile phone models (x1): including bar phone, flip phone and slide phone as listed in Fig. 1. In general, PTOH of bar phone is the smallest while slide phone takes the longest PTOH and flip phone is the middle of them.

(2) Number of functions built in the mobile phone (x2): For a cell phone, more functions built in means more items needed to be tested, and this leads to take longer PTOH time and higher PEHR rate, hence functional types are also an important factor in cell phone man- ufacturing. This research lists six common additional functions as functional types of mobile phone. They are Wi-Fi, GPS, Bluetooth, photo function, music player function and FM Radio and the number of func- tions included is the value of this variable.

(3) Type of Manufacturing (x3): including OEM (Original Equipment Manufacturing), ODB (Original Design- ing and Manufacturing) and OBM (Own Brand Man- ufacturing). Different types of manufacturing leads to different TC and PEHR, hence manufacturing types are an important factor in this research.

(4) Types of mobile phones (x4): Presently, the type of cell phone is not only a machine just for talking, particu- lar cell phones also have smarter abilities, like PDA, or even have its own operation system (OS), like Android, the open operation system from Google. Therefore, this research defines the types of mobile phones as three types: feature phone, PDA and Smartphone.

(5) Keyboard built-in or not (x5): The factors regarding how to reduce the PEHR include reducing the dif-

ferences among the products. Because of varied lan- guages in the world, the keyboard built-in or not becomes a main difference in manufacturing which includes different ways for user key-in and different types for keyboard on the cell phone.

(6) Figure 2 shows the different pictures of mobile phones with keyboard built-in or not. The training sample of qualitative factors in mobile phone production is list in Table 1.

(7) Yield of mobile phones, i.e., Y1 : Generally, it will be better if the yield of mobile phone is high and relatively speaking the high yield will cause little exception. The final PUC will be lower in such a high yield condition. Therefore, the yield is an important factor in determin- ing the PUC of a mobile phone.

(8) Forecast completion rate, i.e., Y2 : During the intro- duction of a new product, to make sure if there is enough capacity for the new order accepted, the pro- ject manager will estimate the production capacity needed for a new order. However, it may take more than three months for a new product from introduc- tion to a mass production and sometimes it even takes nine months. By that time, the order quantities may have changed owing to the market competition or eco- nomic situations. Therefore, it is preferred for the man- ufacturing engineering that the change of the order quantities will be as small as possible. Therefore, the forecasted capacities will be as close as the actual capacities needed. Therefore, the forecast completion rate is an important factor to be considered in estimating

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Table 1 The sample of qualitative factors in mobile phone production

Model x1 x2 x3 x4 x5

001 Bar phone 1 OBM Feature phone Y

002 Slide phone 3 OEM PDA phone N

003 Slide phone 2 OBM Smartphone Y

004 Bar phone 6 OEM PDA phone Y

005 Flip phone 4 ODM Feature phone Y

006 Bar phone 4 OEM PDA phone N

007 Slide phone 1 ODM Feature phone Y

008 Slide phone 3 ODM Feature phone Y

009 Flip phone 4 OEM PDA phone Y

010 Bar phone 1 ODM PDA phone N

the PUC of a mobile phone. The data collected will be from pilot run to mass production.

(9) Total production time of a mobile phone, i.e., Y3 : According to the PUC formula, the total production time of a mobile phone has a large effect on the final manufacturing cost of a mobile phone. It is assumed that all mobile products will go through the same work stations. Therefore, the difference in total production time will be caused by the difference in cycle time of each unit produced.

(10) Line balance rate, i.e., Y4 : Line balance is to arrange the operations within each work stations thus the dif- ference of production time among these stations are minimized. In addition, the production sequences from the beginning to the end are all fixed during the mass production stage. The more balance the work station is the more efficient the production line will be. As a result, the line balance rate is a key indicator and will affect the PUC of a mobile phone.

(11) Time interval between SR and MP, i.e., Y5 : From R&D to mass production, a mobile phone will go through a series of engineering testing. The shorter the engi- neering testing is, the lower cost the PUC will be since the cost of marketing, sales, overhead and production cost will be more effectively managed. According to Harper and Bell (1982), the engineering testing can be divided into four stages and they are EVT(SR), DVT(ER), PVT(PR), and MP. These four stages are described in the following:

(a) EVT: Engineering Verification Test In general, a engineering sample will be tested in this stage. A new product is just developed and there are a lot of issues to be resolved. The focus of the test is on the completeness of the design and the product is checked to see if it can com- pletely fit in the requirements of the customer.

(b) DVT: Design Verification Test This is the second stage of the test and the empha- sis is to find out all the design problems to ensure that the design can follow the customer’s speci- fication.

(c) PVT: Production Verification Test In this stage, product design is finished and the entire design tests are completed. It is just a final check out before the mass production to make sure all standard operation procedures will be fol- lowed according to the original design.

(d) MP: Mass Production The new product goes through the R&D process and will begin its new stage, i.e., the mass pro- duction. The stability of the product will reach a certain quality level after a certain amount of production. We call it a “mass production” for a particular mobile phone.

As described in the section above, these qualitative fac- tors i.e. x1 . . . x5 will be inputted to CBR for retrieving sim- ilar cases in the production of a mobile phone. Then, these five quantitative factors, i.e.Y1 . . . Y5, include yield of mobile phones, forecast completing rate, the total production time of mobile phones, line balance rate, the time interval between SR and MP which are used to forecast the PUC since there are close relationship among these factors and the PUC of the mobile phone.

A forecasting model of product unit cost for mobile phone

As described in the previous section, there is a need to develop a forecasting model to provide timely and accurate PUC for the manager to win the beat from the international phone

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Fig. 3 The overall framework of the CBR-ANN model

Stage 2: Atrificial Neural Network

Stage 1: Case based reasoning (K-NN)

Yield of mobile phones

Forecasted achieve rate

The total production time of

mobile phones Line balance

The interval between SR

and MP

Neural Network

Y1 Y2 Y3 Y4 Y5

Predicted PUC

Training Data Collection

Test Case

Retrieve similar K data Train ANN

company. This research makes the first attempt to develop a hybrid system by integrated Case-Based Reasoning (CBR) and Artificial Neural Networks (ANN) as a Product Unit Cost (PUC) forecasting model for Mobile Phone Company. According to the cost formula of the mobile phone and experts’ opinions, a set of qualitative and quantitative factors are analyzed and determined. Qualitative factors are applied in CBR to retrieve a similar case from the case bases for a new phone product and ANN is used to find the relation- ship between the quantitative factors and the predicted PUC. Therefore, the established model can be applied to predict the PUC for a new developed mobile phone. A detail framework of our approach in estimating the PUC of a mobile phone can be described in Fig. 3.

The first stage is Case-Based Reasoning stage, and K-Nearest-Neighbor method is adopted for predict the quan- titative factors. The final stage is BPN forecasting stage. For BPN training stage, the training data of input layer is quanti- tative factors and output neuron is PUC and in testing stage, the data for input layer is the quantitative factors predicted

by KNN and the result calculated by BPN will be compared with the actual PUC value for evaluating MAPE. A pseudo code of the proposed model is described as follows: Stage 1: Case-based reasoning (K-nearest-neighbor)

A CBR system may perform ineffectively in retrieving cases when the features are irrelevant for cases matching. Therefore, to minimize the bias associated with the features, it is crucial to identify the most salient features leading to effective case retrieval. Generally, the performance of the similarity metric and the weighting of features are keys to this reasoning process.

KNN has widely used in the area of pattern recognition (Xu et al. 1992), classification, and prediction. KNN is labor intensive when given large training sets. In this research, we use KNN algorithm to predicting the value of quanti- tative factors. KNN is based on learning by analogy, that is, test case is compared to the given training cases that are similar to it. The “similar” means there is a distance mea- surement function between test case and training case. For example, if the cases are described by n attributes and the dis-

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tance measurement function is Euclidean distance. The case X 1 = (x11, x12, . . . , x1n ) and X 2 = (x21, x22, . . . , x2n ) and the Euclidean distance between these two cases is calculated as follows:

dist(X 1, X 2) = √√√√

n∑

i =1 (x1i − x2i )2 (11)

As showed in Table 1, qualitative factors in this research include non-numeric value, so called as nominal or cate- gorical value, cannot be calculated by Euclidean distance function, hence we choose a simple way to compare the corresponding value of the attribute in case case1 and case case2. If the two cases have identical, for example OBM in manufacturing types, then the distance (difference) between the two is taken as zero. If the two are different (e.g. case1 has attribute value as OBM but case2 has OEM), then the distance is considered to be one. By this way, the distance between each case can be calculated if they are similar to each other or not.

After determining the similarity, the next job is predicting the value of unknown tuple. For K-NN, the value of K means how many K cases closed to the unknown tuple. When K is equals to one, the unknown tuple is assigned the class of the training one that is closest to it in the case base and 1-NN

returns a real-valued prediction for the given unknown tuple. For instance, if the patterns with value of yield rate of mobile phones are as Table 2.

In this research, K = 1, K = 3 and K = 5 are tested to determine which one is the best number of groups with minimum MAPE value. When K is equal to three and the test case is in Table 3. The distance measurement is calcu- lated as in Table 4.

As shown is Table 4, the most similar cases are 001, 007 and 008, therefore the predicated yield rate of mobile phones is the average value of these three cases, that is (0.9265 + 0.8853 + 0.7165) /3 ≈ 84.28%.

Repeat these steps, we can predicate other four quantita- tive factors, forecasted achieve rate, the total production time of mobile phones, line balance and the interval between SR and MP, by 3-NN, as shown in Table 5.

After predicting quantitative factors, this research assumes that there exists a non-linear relationship between the quan- titative factors and production unit cost (PUC), therefore a Artificial Neural Network (ANN) is adopted for forecasting the PUC value. Stage 2: Artificial neural networks forecasting

An Artificial Neural Network (ANN) is a simplified simu- lation of biological neural networks in human brains. ANN is capable of “learning”; that is, it can be trained to improve its

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Table 2 Ten sample patterns of mobile phones with different yield rates

Model X 1 X 2 X 3 X 4 X 5 Yield rate of mobile phones (%)

001 Bar phone 1 OBM Feature phone Y 92.65

002 Slide phone 3 OEM PDA phone N 89.54

003 Slide phone 2 OBM Smartphone Y 82.54

004 Bar phone 6 OEM PDA phone Y 70.45

005 Flip phone 4 ODM Feature phone Y 75.43

006 Bar phone 4 OEM PDA phone N 76.54

007 Slide phone 1 ODM Feature phone Y 88.53

008 Slide phone 3 ODM Feature phone Y 71.65

009 Flip phone 4 OEM PDA phone Y 90.65

010 Bar phone 1 ODM PDA phone N 92.56

Table 3 A test case

Model X 1 X 2 X 3 X 4 X 5

T01 Bar phone 2 ODM Feature phone Y

performance by either supervised or unsupervised learning. ANN appear to be particularly suited for financial time series forecasting, as they can learn highly non-linear models, have effective learning algorithms, can handle noisy data, and can use inputs of different kinds (Chang and Wang 2006; Krolzig and Toro 2004). Kimoto et al. applies Back-Propagation Neu- ral Network to predict the stock price then determine buying and selling time for Tokyo Stock. They used six input indexes, vector curve, interest rate, New York Dow-Jones average, turnover, foreign exchange rate and a teaching data, to suc- cessfully predict the stock price(Kimoto et al. 1990). Due to the high accuracy and quick solving effect, lot of research- ers adopted BPN to be a forecasting method (Radhakrishnan and Nandan 2005). The BPN and the supervised learning, i.e., learned by samples, are chosen to train the forecasting process. After training, the trained weight can be used for the prediction of future occurrences. The BPN is an ANN using back-propagation algorithm and is one of the popu- lar ANNs, which has been widely applied to many scientific and commercial fields for nonlinear analysis and forecasting. The structure of ANN in this research contains three layers: input layer, hidden layer and output layer as shown in Fig. 4.

Each layer contains i and j nodes denoted respectively by circles. The node is also called neuron or unit. The circles are connected by links, denoted by arrows in Fig. 4, each of which represents a numerical weight. The wi j is denoted as numerical weights between input and hidden layers and so is w j 1 between hidden and output layers as also shown in Fig. 4. The processing is performed in each node in the hidden and output layers. As for the number of layers and number of nodes, they will be further decided using design

Table 4 The similarity matrix

Model X 1 X 2 X 3 X 4 X 5 Similarity

001 0 1 1 0 0 1.41

002 1 1 1 1 1 2.24

003 1 0 1 1 0 1.73

004 0 16 1 1 0 4.24

005 1 4 0 0 0 2.24

006 0 0 1 1 1 1.73

007 1 1 0 0 0 1.41

008 1 1 0 0 0 1.41

009 1 4 1 1 0 2.65

010 0 1 0 1 1 1.73

of experiment. The back-propagation learning algorithm is composed of two procedures: (a) a feed forward step and (b) a back propagation weight training step. These two separate procedures will be explained in detailed as follows:

(a) Feed forward

Assume that each input factor in the input layer is denoted by xi ,y j and zk represent the output in the hidden layer and the output layer, respectively and y j and zk can be expressed as follows:

y j = f (xi ) = f (

w0 j + I∑

i =1 wi j xi

) (11)

and

zk = f ( y j

) = f ⎛

⎝w0k + I∑

j =1 w j k y j

⎞

⎠ (12)

where the w0 j and w0k are the bias weights for setting thresh- old values, f is the activation function used in both hidden and output layers; xi and y j are the temporarily computing

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Table 5 Predicated quantitative factors

Model Predicated—yield rate of mobile phones (%)

Predicated—fore- casted achieve rate (%)

Predicated—the total production time of mobile phones ( min)

Predicated—line balance (%)

Predicated—the interval between SR and MP (week)

T01 84.28 71.84 17.25 86.15 15.2

T02 82.87 70.81 21.65 83.11 12.4

T03 82.50 68.55 21.72 83.44 16.6

T04 80.09 67.04 18.55 83.95 17.1

T05 78.54 70.51 19.08 83.44 14.8

Fig. 4 The structure of artificial neural network Hidden Layer

x1 wij

wj1 x2

x3

x4

x5

yield rate of mobile

phones

Forecasted achieve rate

production time of mobile

phones

Line balance

The interval between SR

and MP

y1

y2

y3

z1 Predicted PUC value

Input Layer Output Layer

results before applying activation function f . In this research, a sigmoid function (or logistic function) is selected as the activation function. Therefore, the actual outputs y j and zk in hidden and output layers, respectively, can be also written as:

y j = f (xi ) = 1

1 + e−xi (13)

and

zk = f ( y j

) = 1 1 + e−y j (14)

The activation function f introduces the non-linear effect to the network and maps the result of computation to a domain (0, 1). This sigmoid function is differentiable. The derivative of the sigmoid function in formula (13) and (14) can be easily derived as:

f ′ = f (1 − f ) (15)

(b) Back propagation weight training

The error signal e j at the output of neuron j in this research at iteration n is defined by (16)

e j (n) = d j (n) − y j (n) (16)

where d j (n) is predefined network output and y j (n) is the neuron network output value.

The error energy is defined by (17)

E = 1 2

∑ e2 (n) (17)

The goal is to minimize E so that the weight in each link is accordingly adjusted and the final output can match the desired output. To get the weight adjustment, the gradient descent strategy is employed. In the link between hidden and output layers, computing the partial derivative of E with respect to the weight w j 1 uses the following formula:

∂ E

∂w j k = ∂ E

∂ zk

∂ zk ∂Yk

∂Yk ∂w j k

= −ek ∂ f (Yk )

∂Yk y j

= −ek f ′(Yk )y j = −δk y j (18)

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Table 6 Training data for ANN Model Y1 (%) Y2 (%) Y3 ( min) Y4 (%) Y5 (week) PUC (US)

001 92.65 81.43 14.65 90.55 14.6 7.54

002 89.54 54.56 25.45 84.43 19.4 26.33

003 82.54 73.65 19.56 83.45 13.4 18.54

004 70.45 91.43 28.54 73.65 22.4 33.34

005 75.43 77.45 20.14 82.44 15.6 25.54

006 76.54 62.54 26.73 73.14 18.4 27.55

007 88.53 78.43 15.45 87.45 13.7 11.65

008 71.65 55.65 21.65 80.44 18.5 22.65

009 90.65 61.34 25.25 83.45 17.3 30.96

010 92.56 74.38 21.05 85.65 15.7 18.56

where

δk = ek f ′(Yk ) = (tk − zk ) f ′(Yk ) (19) The weight adjustment in the link between hidden and output layers is computed by the following:

�w j k = α · y j · δk (20) where α is the learning rate, a positive constant between 0 and 1. The new weight herein can be updated by the following

w j k (n + 1) = w j k (n) + �w j k (n) (21) where n is the number of iteration. Similarly, the error gradi- ent in links between input and hidden layers can be obtained by taking the partial derivative with respect to wi j

∂ E

∂wi j =

[ K∑

k=1

∂ E

∂ zk

∂ zk ∂Yk

∂Yk ∂ y j

] · ∂ y j ∂ X j

· ∂ X j ∂wi j

= −� j xi (22)

where

� j = f ′(X j ) = K∑

k=1 δk w j k (23)

The new weight in the hidden-input links can be now cor- rected as:

�wi j = α · xi · � j (24) and

wi j (n + 1) = wi j (n) + �wi j (n) (25) Training the BPN with many samples is a very time-consum- ing task. The learning speed can be improved by introducing the momentum term η. Usually, η falls in the range [0, 1]. For the iteration n, the weight change �w can be expressed as following:

�w(n + 1) = η × �w(n) + α × ∂ E ∂w(n)

(26)

The formulas described above are applied to derive the weight between output layer and input layer. This procedure is repeated with each training pattern. Each pass through the training pattern is called as an epoch. The goal is to mini- mize the mean square error of predefined output and ANN output value after executing a certain amount of epochs.

During the training stage, ANN is employed to the actual data. For example, a set of training data is listed in Table 6.

In the testing stage of ANN, the input layer receives the value predicted by KNN. The experimental result is described in the next section.

Experiment results

With regard to the product cost estimation of a mobile phone, this study is to establish a hybrid model to forecast the new product manufacturing unit cost. The data collected in this research started from 2004/1 to 2007/6 and total number of data is 72. This research included two stages, gathering sim- ilar data in CBR stage and forecasting product manufactur- ing unit cost in BPN stage. This research assumes that the productions of each type of mobile phone are independent. Using CBR to retrieve similar cases, we compared predicated

Table 7 Comparing predicted and actual value (take yield rate of mobile phones as the example)

Model Predicated—yield rate of mobile phones (%)

Original—forecast yield rate (%)

T01 84.28 92.25

T02 82.87 82.55

T03 82.50 87.45

T04 80.09 93.65

T05 78.54 82.53

MAPE 6.80

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Table 8 The MAPE value for different K value

K = 1 K = 3 K = 5

MAPE 13.45% 8.14% 11.65%

Table 9 The result calculate by ANN and the actual PUC value

Model Predicated PUC Original PUC

T01 US$13.07 US$14.54

T02 US$24.47 US$26.43

T03 US$24.26 US$23.65

T04 US$15.91 US$14.06

T05 US$18.51 US$19.74

MAPE 7.90%

Table 10 RMSE value (iteration = 1,000)

α η

0.2 0.4 0.6

0.3 0.0466 0.0469 0.0474

0.5 0.0466 0.0469 0.0474

0.7 0.0466 0.0469 0.0474

Table 11 RMSE value (iteration = 3,000)

α η

0.2 0.4 0.6

0.3 0.0459 0.0460 0.0460

0.5 0.0461 0.0461 0.0462

0.7 0.0462 0.0463 0.0464

value and the real value of yield rate of mobile phones and the experimental results are shown in Table 7.

To verify the accuracy of CBR approach in the first stage, 60 data of mobile phones as applied as training data for the NN model and 12 data for testing. As for the KNN, we choose K = 1, 3 and 5 for nearest neighbors and compute the MAPE value for each combination. The MAPE of the experimental results is shown in Table 8.

As shown in Table 8, k = 3 has the minimal MAPE value; hence we select K = 3 and use the predicated values of these five quantitative values as input variables of ANN. The final results predicted by ANN are shown in Table 9.

There are many parameters to be decided in applying ANN such as learning rate α, momentum η and the number of iteration for learning. In this research, the design of experi- ment is conducted to decide the best set up for these param- eters. The RMSE values of different experiments are shown in Tables 10, 11 and 12.

Table 12 RMSE value (iteration = 3,000)

α η

0.2 0.4 0.6

0.3 0.0458 0.0458 0.0458

0.5 0.0459 0.0458 0.0459

0.7 0.0460 0.0460 0.0460

Table 13 Parameters setting

Parameter setting Value

The number of hidden layer 1

The number of neuron in hidden layer 3

Transfer function Sigmoid

Learning rule Delta rule

Learning rate 0.5

momentum 0.4

The number of NN learning iteration 50,000

Table 14 Predicted and original PUC of each mobile phone model

Model Predicated PUC Original PUC

T01 US$16.74 US$15.56

T02 US$23.50 US$24.88

T03 US$26.00 US$27.75

T04 US$17.79 US$15.87

T05 US$29.43 US$31.96

T06 US$16.41 US$14.93

T07 US$22.31 US$24.23

T08 US$22.88 US$20.32

T09 US$18.42 US$17.59

T10 US$18.34 US$19.14

T11 US$30.95 US$31.44

T12 US$23.80 US$24.67

MAPE 6.824%

The final parameters according to DOE are decided and they are shown in Table 13. The number of hidden layer is 1 and the number of neuron in each layer is 3. Learning rate is 0.5 and the momentum is 0.4. The transfer function is Sig- moid and with Delta as learning rule. The number of NN learning iteration is 50,000.

For these 12 testing data (mobile phones), we list the pred- icated and original PUC of each mobile phone model and the average MAPE of these two different PUC is shown in Table 14.

To ensure the performance by combining CBR and KNN, other five models in predicting PUC are also developed as follows:

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Table 15 Experimental results for all models Test data Predicted value

No. Actual value CBR-ANN Model 1 Model 2 Model 3 Model 4 Model 5

T01 15.56 16.74 18.39 15.17 16.08 15.79 15.48

T02 24.88 23.50 25.93 29.31 23.32 28.67 26.88

T03 27.75 26.00 26.28 30.17 27.01 29.37 28.92

T04 15.87 17.79 17.15 20.02 16.86 20.04 20.25

T05 31.96 29.43 29.89 33.17 27.68 31.79 28.92

T06 14.93 16.41 16.57 16.97 16.70 17.61 18.45

T07 24.23 22.31 20.81 25.91 22.11 25.44 25.25

T08 20.32 22.88 21.45 16.82 22.45 17.55 20.45

T09 17.59 18.42 19.58 24.20 19.36 23.84 24.35

T10 19.14 18.34 18.91 25.21 19.36 25.45 25.48

T11 31.44 30.95 32.06 31.29 29.58 30.47 28.92

T12 24.67 23.80 20.74 27.16 26.48 26.72 28.72

MAPE 6.82% 8.61% 12.54% 7.28% 11.60% 14.53%

Model 1: using CBR only to forecast the PUC of mobile phones with qualitative factor. In this model, we use PUC value instead of the quantitative factors in order to compare the per- formance with the two-phase forecasting model in this research.

Model 2: using ANN only to forecast the PUC of mobile phones with qualitative factor. Because of the attributes (factors) in each case has nominal type value, we encoding each value as cardinal number. For example in attribute Mobile phone model, bar phone is numbered as one and slide phone is two.

Model 3: using CBR to forecast the quantitative factors and using CBR to predict the PUC. Because of CBR has significant effect in deal- ing with quantitative factors using similar cases. Therefore, CBR is applied again to predict the final PUC for comparison with the prediction by ANN.

Model 4: using ANN to forecast the quantitative factors and using ANN to predict the PUC. ANN has the ability to handle the nonlinear rela- tionship between variables and forecasted vari- ables. Therefore we use ANN to forecast the quantitative factors and then estimate the PUC directly.

Model 5: using ANN to forecast the quantitative factors and using CBR to predict the PUC.

To compare the CBR ability in predicting the PUC, we replace the ANN with CBR in model 4. In forecasting quan- titative factors, the procedure of qualitative factors is similar

to Model 4, and in the CBR stage, the parameters and simi- larity measurement is similar to Model 3.

Finally, the overall performance of each model is listed in Table 15. It can be observed obviously that the proposed approach in combining CBR and ANN performs the best among others.

Conclusions

A hybrid model by integrating Case-Based Reasoning and Artificial Neural Networks is studied in this research. This study concludes that CBR provides a significant ability for calculating the quantitative factors by using similar cases and ANN can be used to find the nonlinear function for forecast- ing problem.

As shown in Table 15, comparing Model 1 with Model 2, CBR has better performance than ANN when the approach is adopted to predict PUC value. Because CBR can handle the nominal attributes as numbered one or zero, different or equal value respectively, but ANN limits at processing nom- inal attributes as cardinal number and the vague definition leads to higher MAPE value. The same situation occurs in Model 4 and Model 5, the ANN forecasting stage results in worse result than CBR in this research and Model 3. The CBR model was more effective with respect to these trade- offs, especially its clarity of explanation in estimating man- ufacturing costs, than the other models. An important aspect of the construction cost model is its long-term use, for which ease of updating and consistency in the variables stored are major factors. In these respects, the CBR model can be more useful for estimating manufacturing costs.

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In this research, the CBR approach can reach a better result than ANN approach in Model 2, 4 and 5, but ANN gives an improved result in forecasting PUC value stage. That is cause of CBR only uses the quantitative factors by Euclidean dis- tance or Boolean measurement and ANN can find the fittest function to describe the relation between quantitative factors and PUC value. As shown in Table 15, using CBR to fore- cast the PUC directly has worse result than adding another CBR forecasting approach, it also proves that the two-phase forecasting approach is necessary and ANN can deal with the nonlinear relation when input variables and target variables are all cardinal numbers.

This research investigates the pros and cons of CBR and ANN approaches and combines these two approaches in pre- dicting the mobile product unit cost. In the future, not only the number of data set but also different data mining approaches, like decision tree and support vectors, can be further inves- tigated in the near future. Especially, fuzzy similarity com- bined with CBR and ANN will be very interesting subjects in forecasting manufacturing costs. A hybrid model integrating the various tools, such as fuzzy reasoning (Liao 2004a), NNs, case-based reasoning, genetic algorithms, fuzzy rule classifi- cation (Chang et al. 2005) and in particular, a NN model incor- porating genetic algorithms or random neural network (Kark- oub 2006) for obtaining both the optimal NN architecture and its parameters will be an interesting direction to engage on.

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