Product cost estimation during design phase D. Mourtzis1, K. Efthymiou1, and N. Papakostas1 Laboratory for Manufacturing Systems and Automation, Dept. of Mechanical Engineering and Aeronautics, University of Patras, Patras, Greece
1
Abstract The research work presented in this paper deals with the cost estimation of new products during the design phase. A short overview of the cost modeling techniques is presented, emphasizing on those methods used during the design step of new products. The proposed cost estimation method, which consists of the Case Based Reasoning methodology along with the Regression Analysis, is presented. The proposed methodology is applied to a case study, coming from the automotive industry, namely cost estimation of a side door. Finally, a software tool, based on web technology, is developed for implementing the proposed methodology. Keywords: Cost, Knowledge Based, Automotive
1 INTRODUCTION According to life cycle theory, the majority of product costs are spent during the manufacturing phase, however most of these costs are mainly determined in the design phase. More specifically, during the early phases of product development only 10 to 15% of the product has been developed, but 80% of costs have been committed. In addition, the possibility to influence cost during the design phase is much higher than the other phases, while at the same time the modification cost is substantially smaller compared with other stages of lifecycle. Thus, good cost estimation as early as possible assists controlling the parameter of cost, which subsequently implies that the performance and the effectiveness of an enterprise is significantly influenced positively [1]. In the literature, a variety of different cost estimating techniques can be found, while numerous classification schemes have been proposed for the taxonomy of these cost methods. However, it seems that there is common consensus concerning classification of cost estimation methods in quantitative and qualitative techniques [19]. In the design phase, the available information is limited, since the product is never fully defined [2], imposing a great obstacle for the cost evaluation. Quantitative approaches, based on a detailed analysis of the product design and the manufacturing processes, demand a lot of information [3]. In parametric techniques, cost is expressed as an analytical function of constituent variables based on statistical methods [4]. Activity Based Costing (ABC), introduced by Kaplan and Cooper [5], focuses on calculating the costs incurred on performing the activities to manufacture a product [6]. In [7] three different times (setup, operation and non operation time), material cost and factory expenses are taken into account, following the operation based approach, also considered as a quantitative technique. In contrast to quantitative techniques, qualitative methods seems to be more effective for cost estimation during the design phase, since they do not require detailed information of the product design nor the manufacturing
processes. Case Based Reasoning (CBR), decision support techniques, regression analysis and Artificial Neural Networks (ANNs), are mainly based on a comparison between the new product and the past products in order to provide a first draft cost estimation. Duverlie et al [8] investigates the relationship between the product cost (i.e. a piston) and product’s features, utilizing linear, logarithmic and polynomial regression models. In [2], ANNs are trained, utilizing data from past products, in order to evaluate the cost of a new brake disk. Similarly, in [9] the estimation of packaging cost is performed with the application of ANN model which incorporates the geometrical characteristics of the packaged product. Moreover, rule based approaches and fuzzy algorithms have been employed for the estimation of the process time and cost [10, 11]. In [8] a CBR methodology is employed, in order to perform the economic evaluation of a piston. Another CBR application during the design step is presented by Ficko et al [12], for the cost prediction of manufacturing tool, extracting the similarity between the new product’s features and the geometrical features of past CAD models stored in databases. Finally, it must be noted that CBR methodology has also been successfully applied to construction cost estimation [13, 14]. In conclusion, quantitative techniques may lead to useful cost estimations, but their application during the design step is difficult or even impossible due to the lack of information, since the product design and the manufacturing processes are not yet fully defined. Among the qualitative techniques, CBR seems to be the most promising for the current stage of the product lifecycle, since ANNs [14] and regression analysis techniques [8] do not excel CBR in terms cost estimation accuracy.
2 METHODOLOGY 2.1 Overview The present product cost estimation methodology is based on two pillars. The first one, and basic core of the approach, is the CBR methodology, enhanced by the second pillar, the Regression Analysis techniques. Case representation, similarity measurement and case adaptation - revision are included in the CBR method steps, while regression analysis provides the weighting factors, which are necessary for the calculation of the similarity measurement and the case revision as well. CBR is a problem solving methodology [15] based on experience, organized as a set of past cases stored in a case base. Each case is characterized by numerical or alphabetic features. The most similar cases are recalled either to resolve problems or to provide recommendations for current problems. The CBR cycle consists of the following four activities: 1. Retrieve similar cases to the problem case. 2. Reuse a solution suggested by a similar case. 3. Revise or adapt that solution to better fit the new problem. 4. Retain the new solution once it has been confirmed or validated. Regression analysis refers to techniques for modeling and analysis of numerical data consisting of values of a dependent variable and one or more independent variables [16]. The dependent variable in the regression equation is modeled as a function of the independent variables which are incorporated into the model as predictor or explanatory variables. In addition to independent variables, all models include unknown constants called parameters, which control the behaviour of the model, since the parameters’ estimation is made for the optimization of the model fitting to the data.
Figure 1: Product cost estimation methodology. Figure 1 depicts the overall methodology of the proposed product cost estimation method, illustrating the CBR components and their cooperation with the Regression Analysis techniques. The first step is the definition of the new problem; in our case the definition of the new product features. Afterwards, the new product is compared with all the past products, i.e. the past cases stored in casebase, and the most similar past case is retrieved. The weights for the similarity measurement have been derived employing regression analysis. The cost value of the retrieved case is used as the reference value for the cost estimation of the new product, utilizing the weight factors again. Finally, the new problem becomes a past case and it is stored automatically in the case memory.
2.2 Case representation A case is a contextualized piece of knowledge representing an experience and typically consists of: • •
the problem: description of the world’s state when the case occurred the solution: problem’s derived solution
Figure 2: Subassembly’s hierarchical structure of the ontology. Cases can be represented in a variety of forms using the full range of Artificial Intelligence (AI) representational formalisms including frames, objects, predicates, semantic nets and rules. In the current approach, cases are represented with the help of a simple ontology, i.e. a formal representation of a set of concepts. Forasmuch as the present work is oriented to product cost modeling, and more specifically to car’s closures or Body In White subassembly products, the characteristics of the ontology are formalized from this point of view, employing a hierarchical structure. Thus, product features (joints, material, geometry, number of parts) constitute the problem, while product cost is the solution. Product feature is a key attribute characterizing the assemblies and subassemblies. Feature
Description
Type
RSW
The number of Remote Spots Welding
Numerical
Laser
The number of laser stitches
Numerical
Adhesive
The number of indirect spots joining
Numerical
Anti-fluter
The meters of antifluter joining
Numerical
Frame
Subassembly’s frame material type
Text
Skin
Subassembly’s frame material type
Text
Coating
Subassembly’s frame material type
Teext
Length
Subassembly’s maximum length [mm]
Numerical
Width
Subassembly’s maximum width [mm]
Numerical
Thickness
Subassembly’s maximum thickness [mm]
Numerical
Number of Parts
The number of the different part types of subassembly
Numerical
Table 1: Description of product’s features
2.3 Similarity measurement A great number of similarity measures exist, applying to specific demands. Nearest neighbour technique, perhaps the most widely used technology in the CBR retrieval process, computes the similarity between past cases stored in the case memory and the new case i.e. new product, based on weight features. In the current approach the following form of similarity measurement is used. SimG
T, S
∑
w
f x ,x
(1)
T: the new (Target) case
•
S: the past (Source) case.
•
j: one of the past cases.
•
n: the number of features in each case.
•
i: one of the n individual case feature.
•
wi: the weighting factor for the ith feature.
•
f: the similarity function.
•
xit : the ith feature of the target (new) case.
•
xi : the ith feature of the source (past) case.
The similarity function depends on the type of the feature. If the product feature is alphabetical (text), equation 2 is applied. If the new case feature is identical to the past case feature, the similarity is 1, otherwise it is equal to 0. 1, T S f T, S (2) 0, T S In case that the product’s features are numerical, a slight modification of Minkowski measurement is employed as a similarity function, providing normalized values within a range from 0 to 1, where 1 means totally similarity in contrast to 0 meaning totally dissimilar. 1
T
S /T
C
∑
a
x
(4)
Where: •
Y: the product cost
•
xi: the ith product feature.
•
C: the constant parameter in the regression analysis model.
w
s
f T, S
Y
• αi: the regression coefficient for each product feature. The weighting factors are derived after the normalization of αi based on the following equation:
Where: •
experts. The general form of the linear regression equation applied to this study is presented hereafter.
(3)
Hence, each one of the past (source) cases is compared with the new (target) case, utilizing equation 3 for numerical characteristics and equation 2 for alphabetical characteristics. The past case with the greatest similarity value, i.e. nearest to 1 is selected to be the reference case for the cost estimation. 2.4 Weight factors determination Perhaps, the greatest obstacle of the nearest neighbour approach for similarity measurement is the determination of the weighting factors [17]. Weighting can be defined in an empirical way, reflecting either the degree of certainty of the characteristic value or the degree of importance in the similarity measurement [8]. Analytical Hierarchy Process (AHP) seems to be the most accurate and reliable method for determining relative important weights, compared with Equal Weights and Gradient Descent method [14], however AHP still remains to be based on experts’ experience and is not able of capturing past knowledge from the cases stored in casebase automatically without users’ interference. The proposed method attempts to determine the weighting factors by capturing the trend between the cost and the features of the product, utilizing multivariate regression analysis, in order to overcome the issue of the subjective weighting by
|a |
∑
(5)
|a |
The coefficient ai of the linear equation (eq 4) is the slope of the line, i.e. the rate of change in product cost per unit change of i-th feature. In other words, this coefficient can be regarded as the impact factor of each product feature to product cost. Therefore each coefficient, after the proper normalization can be used as a weighting factor, since it is denoting the effect of each feature to product cost. 2.5 Case revision Case revision is an adaptation process of adjusting the solution of the retrieved case to fit the current case. Adaptation looks for prominent differences between the retrieved case and the current case and then applies formulae or rules that take those differences into account when suggesting a solution [17]. In the proposed methodology the parameter adjustment process, belonging to structural adaptation, is applied. Specified parameters (i.e. product features) of the retrieved and the current case are compared, in order to modify the retrieved case in an appropriate direction. Each feature’s value of the new case is divided by the feature value of the most similar past case. Afterwards, these ratios are multiplied by the respective weighting factor as it has been derived by the regression analysis. Finally, given that the product cost is affected by the current economic condition, including the materials requirements, labour forces, government rates and fees etc, a business cost index is employed [18]. Cost N 3
C
∑
w
IN
C
IP
C
Cost P
C
(6)
INDUSTRIAL EXAMPLE
3.1 Side door In order to present the applicability of the present product cost estimation methodology, a real manufacturing case, from the automotive industry, has been selected. The specific closure, as all hang on parts is a standalone subassembly, not related to the rest of the car. It is chosen for the current application of the CBR cost estimation methodology, because the side door is one of the core elements of a car appearance, and is therefore changed every 2-3 years (face lifting) and many efforts are provided to allow the maximum decision support to designers.
3.2 Results The cost of four different side door types is estimated, following the proposed methodology. Confidentiality issues do not allow the presentation of the real actual cost nor the CBR estimated cost of each side door. Therefore, the values of cost have been normalized based on the greatest cost value and multiplied by 100. Table 2 presents the actual cost, the estimated cost employing the proposed approach and the similarity of each side door. The cost evaluation for all the four side door types is quite close to the actual cost, providing engineer - designer a rather helpful information for the cost order of magnitude at least. Side Door
Similarity
Actual Cost
Estimated Cost 57.61
A
0.83
65.89
B
0.85
90.97
100
C
0.85
83.38
69.16
D
0.79
66.26
60.76
•
analysis. Data are extracted from the casebase by using the Java Database Connectivity. rd Presentation layer (3 tier): is a client part of the application. It consists of a web browser that is used to communicate with the business layer through Internet.
Table 2: Product Cost Estimations Figure 4: System Architecture.
The deviation, calculated by equation 7, for each case is presented in figure 3. The deviation of four test cases fluctuates between the maximum and the minimum deviation, 16.5% and 8% respectively, while the mean deviation is approximately 14% and the standard deviation is 3.82%.
20
Deviation (%)
15 10 5
Product Cost
Test Cases
0 -5
0
1
2
3
Figure 5: Print Screen of the Web Based Product Cost Estimation System.
-10 -15
Figure 3: Deviation diagram of the four side door types. Deviation
C
C
A
C
A
E
100
(7)
4 WEB APPLICATION A web application, that can be accessed without constraints of time and place, was developed in order to assist end users to manipulate the model in a user friendly way. The architecture of the Product Cost Estimation System, as presented in figure 4 follows the three-tier example and includes the following three layers. •
•
4
Data layer (1st tier): includes the application’s casebase management system and the connections with all the other external systems, namely an external database for the recovery and storing of data. nd Business layer (2 tier): is that in which the business logic resides. The business layer provides data manipulation and data management functionality, and includes the similarity mechanism, and the regression
5 CONCLUSION This paper introduces a methodology based on CBR enhanced with regression analysis, for assessing the product cost during the design phase. The basic steps of the proposed methodology, i.e. case representation, similarity measurement, weight factors determination and case revision are presented in detail. A subassembly oriented ontology has been employed for the case representation. Similarity measurement, which can be considered as the core component of the CBR methodology is enhanced with the application of regression analysis. In particular, regression analysis provides automatically the weight factors for each feature, overcoming the issue of the subjective weighting by experts. It must be noted that the weight factors are also utilized for the case revision as well. Future research will focus on the comparison of the current approach with former methods. The applicability of the current approach is verified by its application to a real industrial case, i.e. the cost estimation of four different types of side door. Finally, a software tool, based on web technology, developed for implementing the proposed methodology, is
presented. The proposed system presents a mean deviation from the actual cost 14% approximately, allowing the engineer during the design phase a first rough estimation of product cost. 6 ACKNOWLEDGEMENT This work has been partially supported by “the research project “MyCar”, funded by the CEU. 7 REFERENCES [1] Chryssolouris, G., 2006, Manufacturing Systems: Theory and Practice, 2nd Edition, Springer-Verlag, New York. [2] Cavalieri, S., Maccarrone, P., and Pinto, R., 2004, Parametric Vs Neural Network Models for the Estimation of Production Costs: A Case Study in the Automotive Industry, International Journal of Production. Economics, 91/2:165–177. [3] Niazi, A., Dai, J.S., Balabani, S. and Seneviratne, L., 2006, Product Cost Estimation Technique Classification and Methodology Review, Journal of Manufacturing Science and Engineering, 128:563 – 575. [4] NASA, Parametric Cost Estimating Handbook, http://cost.jsc.nasa.gov/pcehg.html [5] Cooper, R., Kaplan, R. S., 1988, How Cost Accounting Distorts Product Costs, Manage. Account., 69/10: 20–27. [6] Tatsiopoulos, I., P., and Panayiotou, N., 1999, The integration of activity based costing and enterprise modeling for reengineering purposes, International Journal Production Economics 66:33-44 [7] Jung, J.-Y., 2002, Manufacturing Cost Estimation for Machined Parts Based on Manufacturing Features,” Journal of Intelligent Manufucaturing., 13/4:227–238. [8] Duverlie, P., Castelain, J. M., 1999, Cost Estimation During Design Step: Parametric Method versus Case Based Reasoning Method, The International Journal of Advanced Manufacturing Technology 15:895–906. [9] Zhang, Y. F., Fuh, J. Y. H., Chan, W. T., 1996, Feature-Based Cost Estimation for Packaging Products Using Neural Networks, Computers in Industry, 32:95–113. [10] Gayretli, A., and Abdalla, H. S., 1999, A Featured Based Prototype System for the Evaluation and Optimization of Manufacturing Processes, Computers in Industry Eng., 37:481–484. [11] Shehab, E. M., and Abdalla, H. S., 2001, Manufacturing Cost Modeling for Concurrent Product Development, Robotics and Computer Integrated Manufacturing, 17: 341–353. [12] Ficko, M., Drstvensek, I., Brezocnik, M., Balic, J., Vaupotic, B., 2005, Prediction of Total Manufacturing Costs for Stamping Tool on the Basis of CAD-Model of Finished Product, Journal of Materials. Processing. Technology, 164–165:1327– 1335. [13] Wang, H. J., Chiou, C. W. and Juan, Y. K. 2008, Decision support model based on case-based reasoning approach for estimating the restoration budget of historical buildings, Expert Systems with Applications, 35:1601-1610.
[14] An, S. H., Kim, G. H., Kang, K. I., 2007, A casebased reasoning cost estimating model using experience by analytical hierarchy process, Building and Environment 42:2573–2579. [15] Riesbeck C.K., Schank R., 1989, Inside Case-based Reasoning, Erlbaum, Northvale, NJ,. [16] Rawlings, J. O., Pantula, S. G., Dickey, D. A., 1998, Applied Regression Analysis: A Research Tool, 2nd Edition, Springer-Verlag, New York. [17] Watson, I., and Marir, F., 1994, Case-Based Reasoning: A Review, The Knowledge Engineering Review, 9/4:355-381. [18] Singapore Department of Statistics, ,2009, Unit Business Cost Index of the Manufacturing Sector: Rebasing to Year 2000”, Information Paper on Economic Statistics July 2009 [19] Chryssolouris, G., Papakostas, N., Mavrikios, D., 2008, A perspective on manufacturing strategy: Produce more with less, CIRP Journal of Manufacturing Science and Technology, 1:45-52 [20] Partha, P.D., Rajkumar, R., 2010, Cost Modelling techniques for availability type service support contracts: A literature review and empirical study, CIRP Journal of Manufacturing Science and Technology