Utility Based Optimization Model for Deriving Optimum Target of Functional Requirements Cucuk Nur Rosyidi† Industrial Engineering Department Sebelas Maret University, Surakarta 57126 INDONESIA Email:
[email protected],
[email protected] Dradjad Irianto1, Andi Cakravastia2, Isa Setiasyah Toha3 Department of Industrial Engineering Bandung Institute of Technology, Bandung 40132, INkNESIA Email:
[email protected] [email protected] [email protected] Abstract.This paper addresses optimum target derivation of functional requirements. In deriving the target, designer faces multi attribute decision making under risk. The risk in product design can be represented using utility function that reflects designer attitude toward the risk related to the cost and time needed for product design. From customer view point, utility function reflects their attitude toward risk in product value. The objective of this paper is to develop a utility based optimization model which balances the designer and customer utility. Hence the objective function is to minimize utility gap between customer and designer, considering time and cost provided by company as the constraints. The customer utility is derived using technical competitive assessment matrices in the QFD, while the designer utility is derived using their attitude toward the cost and time. Optimizing both utilities simultaneously will lead to a compromised decision in product design, especially in deriving optimum target of FRs . Keywords: QFD, utility function, optimization, functional requirement.
1. INTRODUCTION Current competition in market place challenged companies to improve quality product that satisfies their customer needs. The improvement has to be conducted in order to survive and to be profitable (Vanegas and Labib, 2001). QFD is a popular tool for product development in industry (van de Poel, 2007). It has been adopted in many fields, such as health, education, software, construction, and airplane industries (Kumar et al. 2006). QFD implementation consists of four stages: product planning, parts deployment, process planning and production planning. The basic concept of the QFD is to translate Customer Requirement (CR) into technical attributes or engineering characteristics ( Fung et al. 2003). Another design methodology such as axiomatic design using different terminology to represent the design process. In axiomatic design, the design process starts with mapping of customer needs to Functional Requirement (FR) (Suh, 2001). Different authors use different terminology for CR and engineering characteristics in QFD (van de Poel, 2007). In this paper, we use FR instead of engineering characteristics
as in the research of El-Haik (2005). In general there are two main purposes in QFD implementation. The first is to determine the CR or FR priority, and the second is to obtain the optimum target value of FR. This paper addresses the second purpose. In deriving the optimum target, designer faces multi attribute decision making under risk. Most of the decisions in engineering design are made using imperfect models, imprecise information, and limited knowledge (Gurnani and Lewis, 2005). The risk in product design can be represented using utility function, which explains a decision maker’s attitude towards risk resulting from any risky activities or decisions. In this view, utility function transfers objective value of the design into customer satisfaction level using mathematical formulation (Yang et al. 2003). The function can also be used to represent the product value from the customer point of view. According to Askin and Dawson (2000), there is a difference between utility function and value function. The value function assumes riskless event, while in the utility function there is an uncertainty in the result of an event.
†Corresponding Author
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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference This paper develops an optimization model for deriving optimum target of FR. The model integrates customer and designer utility functions into one objective function. The objective function is to minimize gap between customer and designer utilities considering time and cost provided by the manufacturer.
2. RELATED RESEARCH Engineering design always involves a decision making problem. The decision involves many attributes and variables with different units of measures. Decision making problem requires three components, i.e. choices, information, and preferences (Takai and Ishii, 2002). Choices are the alternatives that decision-maker faces at the time of decision making, information is the modeling of decision problem, while preferences can be summarized by utility function. Utility analysis is used to help a decision maker in making real valued function that encodes the decision maker’s preference for all possible outcomes (Scott, 2004). Since a utility function is a representation of the decision maker preference, it serves two important purposes in engineering design (Scott, 2004). First, it allows the designer to construct a single-valued objective function that incorporates all the attributes and reconcile them on a single scale. Second, the objective function is based upon outcomes for each alternative that are given as probability distributions. Locascio and Thurston (1998) developed a multiattribute utility function to formulate multiobjective optimization towards QFD. In the research, CR is redefined as design attributes, while engineering characteristics are redefined as design variables. The objective is to maximize multiattribute design utility considering the constraints which derived from natural laws as transfer functions. The functions are used to relate design attributes and design variables. The research assumed the designer has a complete understanding about CR in deriving optimum target of the design variables, and the CR has quantitative metric units. In real world, most of the CRs are qualitative in nature and does not have metric units. Askin and Dawson (2000) developed a model to maximize product value to customer using value function. The function is derived using normalization which maps the minimum and maximum target value of FR into the range value between zero and one. The research involved cost, time and technical difficulty as constraints. Gurnani and Lewis (2005) developed a decision making optimization model considering risk and uncertainty in engineering design. The model used hypothetical equivalent and inequivalent method as a basis to build the real model, and the utility function is involved in the model assuming that each criteria is independent.
Yeh et al. (2005) developed an optimization model to maximize designer utilities in a negotiation support system. The optimization is conducted iteratively until a consensus is reached among designers. Lin and Wei (2005) developed an optimization model for selecting product design improvement using linear programming. The objective is to maximize total weighted effect value of product features to the customer and designer considering cost and time provided by manufacturer to accomplish the design.
3. MODEL DEVELOPMENT In designing a product, designer has to consider the design constraints. The constraints which usually considered are cost, time, and technical difficulty. Each constraint can be represented by designer utility function that reflects designer attitude towards the cost, time, and technical difficulty in accordance with the risk of design accomplishment. In developing the model, this paper only considers cost and time as constraints. Customer utility function is derived using technical competitive assessment matrices of QFD. The function reflects customer view towards product value which is represented by its FRs target. For larger the better case, customer utility function will be monotonically increasing since larger FR target gives more value to customer. The designer function will be monotonically decreasing since the manufacturer has to spend more money for designing larger FR target. For example, higher car efficiency gives more value to customer, and it means more money has to be spent by manufacturer in designing the product.
3.1 Objective Function The objective function of the model is to minimize gap between customer and designer utilities which can be expressed as follows: ∑
,
(1)
denotes cost (for r=1) and where denotes j-th FR and time (r=2) of the j-th FR. Weight of the j-th FR is denoted by which resulted from the QFD. denotes customer utility of the j-th FR, while the designer utility function for the j-th FR is denoted by . The weight, , can be obtained from the QFD matrices using the following equation: ∑ ∑
∑
,
(2)
denotes the relationship weight between i-th CR where and j-th FR.
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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference The designer utility consists of two functions, cost and time utility functions. Hence, the functions need to be scaled using constant scales. Assuming that preference and utility are independent, then the utility can be expressed as in equation (3). ∏
1
1,
4. Total weight used in equation (1) has to be equal to one, which can be stated as in equation (9). ∑
1
(9)
3.3 Complete Model (3)
where denotes the normalization scale, is the r-th is the designer utility constant scale for j-th FR, and towards cost and time. The value of K can be obtained using equation (4) (Keeney and Raiffa, 1993).
As a result, the optimization model then can be stated completely as the following: Min ∑
(10)
subject to 1
∏
1
(4)
1 then the equation will If in equation (3), ∑ be simple and become an additive function as the following (Keeney and Raiffa, 1993): ∑
.
∑ ,
(5)
∑
1
4. AN ILLUSTRATED EXAMPLE
3.2 Constraints The constraints used in the model are as follows: 1. Upper and lower limit values of target FR which can be expressed as in equation (6), ,
(6)
A pencil design is used for the numerical example which taken from the research of Askin and Dawson (2000). Figure 1 shows the QFD of the design. We assume there are no relationships exist among FRs, and the designer only considering cost as a constraint in the design.
where and denote the lower and upper limit values of FR respectively. The limit values of Equation (6) are bounded by the availability of technology. 2. The second constraint is the budget cost and time needed in designing a product. In general, both constraints can be stated as follows: ∑
,,
1,2
(7)
where denotes cost and time needed in designing j-th FR of a product, while denotes maximum cost or time given in the design. 3. The third constraints are the cost and time needed in the design which expressed in term of FR target value. Equation (8) expresses the constraint. The equation is needed to bring the designer and customer into the same unit measure or scale, i.e. FR target value, so their utilities can be compared. , 1,2 (8)
Figure 1.QFD for pencil design (Adapted from Askin and Dawson (2000))
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Table 1. Utility functions used in numerical example
Customer
Designer
.
2 1
0.667
.
1.25 1
1.05 1
3.667
Equation (11) shows a widely used utility function in the form of exponential shape (Yang et al. 2003). The exponential utility function will be used to represent most of the customer and designer utility functions. Table 1 shows a set of assumed utility functions with the afore-determined relationship coefficients and their graphics representation. 1
(11)
The technical competitive assessment involves of four competitors, i.e. Product A, B, C, and D as can be seen in Figure 1. The assessment matrices is used as a basis to set the upper and lower level of FR target values. For example, the lower and upper level of FR1 are 4 and 5.5 (FR1 of Product C and D). The upper and lower level of the FR will also be used as a boundary to derive customer utility function. The function can be derived by asking the customer about their preference concerning the FR (Scott, 2004). The cost factor in Figure 1 is used to obtain the function of equation(8). For example, the cost factor of FR2 is 1.667. It means that design cost of one unit of that
.
.
.
.
2.45 1
.
.
1.5
.
.
FR is 1.667. Assuming linear relationship between cost 1.667 . and FR, the function of equation (8) will be The weights can be obtained by equation (2) using data in Figure 1. The weights for FR1, FR2, and FR3 are 0.359, 0.314, and 0.327 respectively. The equality constraints in the form of equation (8) has to be substituted into the objective function to result a non linear optimization problem subject to cost constraint and bounds of feasible region. Assuming the maximum design cost is 20 monetary units, the model for deriving optimum target of FRs for the pencil design can be expressed as follows: Min | 0.359
2 1
.
1.25 1 2.45 1 0.359 1.05 1 1.5 Subject to 4 2.5
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. .
. .
.
0.667 .
.
.
0.314 0.327
.
|
3.667 0.314 0.327
5.5 6
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4 1.667
0.5
REFERENCES
17
The solution of the model can be seen in first row of 4.97, 3.69, and 2.97 The Table 2, i.e. solution will be compared to the results of the model where the customer and designer utility functions are treated as individual model. The models are then solved individually to maximize the utilities using related constraints. The second and third rows of the table show the optimal solution for the individual model.
y1 4.97 5.5 4
y2 3.69 3.95 2.5
El-Haik, B. (2005) Axiomatic Quality:Integrating Axiomatic Design with Six-Sigma, Reliability, and Quality Engineering, Wiley Interscience. Fung, R. Y. K., Tang, J., Yiliu, P., and Chen Y. (2003) Modelling of Quality Function Deployment Planning with Resource Allocation, Research in Engineering Design, 14.
Table 2. Solution of the model Model Customer Designer
Askin, R. G., and Dawson, D.W. (2000) Maximizing Customer Satisfaction by Optimal Specification of Engineering Characteristics, IIE Transactions, Vol. 32, pp. 9-20.
y3 2.97 2 3.9
The solution of the individual model shows that FRs target of the customer is higher than FRs target of the designer. It resulted from the fact that maximizing designer utility means choosing the lowest level of FR target values, because the maximum value of the designer utility is in the lowest cost. The FR target value for customer can not reach its maximum value since cost constraints are imposed into the model. The solution of the developed model in this paper is in the range between the individual models. It reveals that the developed model in this paper can be used to trade off customer against designer utilities. This trade off shows the need for both customer and designer to be interacted in making design decision, especially in determining FR target values. This interaction results in compromised values in determining the FR target and balancing both customer and designer interests.
5. CONCLUSIONS This paper proposed an optimization model for deriving optimum target of FRs considering cost and time provided by manufacturing company in designing a product. The model integrates customer and designer utilities into one objective function. Hence, minimizing gap between customer and designer utilities is set to be the objective function of the model. The numerical example shows a comparison between the model developed in this paper and model where customer and designer utilities are solved partially. The objective function of the individual model is to maximize the utility. The comparison of the models shows that the model developed in this paper trades off customer against designer utility. The model results in compromised values of FR, and balancing both customer and designer interests.
Gurnani, A.P., and Lewis, K. (2005) Robust Multiattribute Decision Making Under Risk and Uncertainty in Engineering Design., Engineering Optimization, Vol. 38, No.7, pp 813-830. Keeney, R. L., and Raiffa, H.(1993) Decision with Multiple Objectives, Cambridge University Press. Kumar, A., Antony, J., and Dhakar, T.S. (2006) Integrating Quality Function Deployment and Benchmarking to Achieve Higher Profitability, Benchmarking: An International Journal,Vol 13, No.3, pp.290-310. Lin, S., and Wei, C. (2005) A Study on the Linear Programming in Time Cost Analysis of Product Improve Design-a Focus on Computer Mouse Products, Journal of American Academy of Business, Vol.7, No. 2. Locascio, A., and Thurston, D.L. (1998) Transforming the House of Quality to a Multiobjective Optimization Formulation, Structural Optimization, Vol. 16, 136-146. Scott, M. J. (2004) Utility Methods in Engineering Design. in E. Nikolaidis and D. Ghiocel (ed), CRC Handbook on Reliability Design (CRC Press). Suh, N. P. (2001) Axiomatic Design Advances and Applications, Oxford University Press. Takai, S., and Ishii, K. (2002), Setting Target Product Requirements: Decision Analytic Approach, Proceedings of DETC’02, ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Montreal, Canada. van de Poel, I. (2007), Methodological Problems in QFD and Directions for Future Research, Research in Engineering Design, 18:21-36.
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APIEMS 2008 Proceedings of the 9th Asia Pasific Industrial Engineering & Management Systems Conference Vanegas, L.V., and Labib, A.W. (2001), A Fuzzy Quality Function Deployment (FQFD) Model for Deriving Optimum Targets, International Journal of Production Research, Vol. 39, No. 1, 99-120. Yang, Y.S., Jang, B.S., and Yeun, Y.S., Lee,K.Y.(2003) Quality Function Deployment-Based Optimization and Exploration for Ambiguity, Journal of Engineering Design, Vol. 14, No. 1. Yeh, J., Shih, W., and Lin. B.H. (2005) Prototyping A Negotiation Support System for New Product Development, Journal of Chinese Institute of Industrial Engineers, Vol.22, No.3, 252-261.
Author Biographies Cucuk Nur Rosyidi is a lecturer in Industrial Engineering Department of Sebelas Maret University Surakarta. Currently he is a Ph. D candidate at Department of Industrial Engineering, Bandung Institute of Technology, Indonesia. He received a Master degree from Department of Industrial Engineering, Bandung Institute of Technology in 2005. His dissertation topic is about the determination of key characteristics priority. His email address is
[email protected], or
[email protected] Dradjat Irianto is a lecturer in Department of Industrial Engineering, Bandung Institute of Technology, Indonesia. He received a master degree from Keio University, Japan in 1993, and doctoral degree from Twente University, Nederland. His teaching and research interests include quality engineering, process quality control, and the implementation of quality management. His email address is
[email protected] Andi Cakravastia is a lecturer in Department of Industrial Engineering, Bandung Institute of Technology, Indonesia. He received a doctoral degree from the Graduate School of Engineering at Hiroshima University, Japan in 2004. His teaching and research interests include supply chain management and applied operations research. His email address is
[email protected] Isa Setiasyah Toha is a Professor in Department of Industrial Engineering, Bandung Institute of Technology, Indonesia. He received a doctoral degree from Department of Industrial Engineering, Bandung Institute of Technology. His teaching and research interests include manufacturing systems design, manufacturing planning and scheduling, and manufacturing automation with special emphasis on engineering and make to order systems. His email address is
[email protected]
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