Proceedings of the TMCE 2004, April 12-16, 2004, Lausanne, Switzerland, Edited by Horváth and Xirouchakis 2004 Millpress, Rotterdam, ISBN
AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING
Jeremy J. Michalek Department of Mechanical Engineering University of Michigan USA [email protected]
Fred M. Feinberg School of Business Administration University of Michigan USA [email protected]
Panos Y. Papalambros Department of Mechanical Engineering University of Michigan USA [email protected]
ABSTRACT scope, perspective, product representation, and metrics of performance and success. An overview of Marketing and engineering design decisions are these differences is provided in Table 1, excerpted typically treated as separate tasks both in the from a comprehensive literature review of product academic literature and in industrial practice, and development decision research by Krishnan and their interdisciplinary interactions are not well- Ulrich (2001). Separating these disciplines helps in defined. In this article, analytical target cascading the organization and management of information but (ATC), a hierarchical optimization methodology, is can also cause communication difficulties and used to frame a formal optimization model that links disjoint decision-making resulting in inferior product marketing and engineering design decision-making decisions. Krishnan and Ulrich note this as a models by defining and coordinating interactions weakness, particularly for complex or technology- between the two. For complex products, engineering driven products. However, the two communities do constraints typically restrict the ability to achieve some desirable combinations of product characteristic targets, and the ATC process acts to Marketing Engineering Design A product is a A product is a complex guide marketing in setting achievable targets while Perspective bundle of assembly of interacting designing feasible products that meet those targets. on Product The model is demonstrated with a case study on the attributes components “Fit with market”, Typical “Form and function”, design of household scales. market share, Performance technical performance, consumer utility, Metrics innovativeness, cost KEYWORDS profit Dominant Customer utility Geometric models, Analytical target cascading, marketing, optimal Representa- as a function of parametric models of tional product planning, design optimization, discrete product attributes technical performance choice models, logit, conjoint analysis Paradigm Example Product size, shape, Product attribute Decision configuration, levels, price 1. INTRODUCTION Variables function, dimensions Product Creative concept and Marketing and engineering contributions to product Critical positioning and configuration, development are typically treated separately both in Success pricing, collecting performance Factors and meeting industry and in the academic literature. Research on optimization product development decision-making in the customer needs marketing community has historically differed from Table 1 Comparison of Marketing and Engineering research in the engineering design community in Design Perspectives
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have different foci and areas of expertise, and solution is a Pareto set of optimal products, and the attempting to integrate them completely may be choice of a single product from that set requires disadvantageous. This article offers a method to explicit expression of preferences among objectives. formally link decisions by the two communities Such preferences are notoriously difficult to define in while maintaining their disciplinary identity; the practice. Some methods use interactive, iterative resulting model employs the formalism of Analytical searches to elicit preferences, relying on intuition in Target Cascading (ATC) (Kim, 2001). An expanded navigating the Pareto surface and choosing an version of this paper (Michalek et al., 2004) provides appropriate design (Diaz, 1987). Recent efforts in the further depth from a marketing perspective and design literature take the approach of resolving demonstrates that coordinating marketing and tradeoffs among technical objectives by proposing engineering decision models using ATC results in models of the producer’s financial objective solutions superior to those obtained through disjoint (Hazelrigg, 1988; Li and Azarm, 2000; Gupta and decision-making. Samuel, 2001; Wassenaar and Chen, 2001). Gu et al. (2002) build on this work using the collaborative 1.1. Marketing Product Planning Models optimization framework to coordinate decision models in the engineering and business disciplines. Kaul and Rao (1995) provide an integrative review of Here we propose a related methodology, but we product positioning and design models in the coordinate product planning and engineering design marketing literature. They differentiate between models using the ATC methodology, which has product positioning models, which involve decisions proven convergence characteristics for arbitrarily about abstract perceptual attributes, and product large hierarchies (Michelena et al., 2002; Michalek design models, which involve choosing optimal and Papalambros, 2004), and we draw upon levels for a set of physical, measurable product techniques from the marketing literature to develop characteristics. In this article we work only with explicit mathematical models of demand based on measurable product characteristics; however, a data. comprehensive framework similar to the one proposed by Kaul and Rao could be used to include 2. METHODOLOGY perceptual attributes, product positioning, and consumer heterogeneity. In this article, conjoint- Using the ATC framework, discussed in detail based “product design” models from the marketing below, the joint product development problem is literature will be referred to as product planning decomposed formally into a product planning models. subproblem and an engineering design subproblem. The product planning subproblem involves choosing Optimal product planning in the marketing literature the desired target product characteristics and price is typically posed as selection of optimal price and that will maximize the producer’s expected profit, product characteristic levels that achieve maximum where profit depends on demand. The engineering profit or market share. For complex products, where design subproblem involves choosing a feasible engineering constraints may prevent some design that will achieve the target product combinations of product characteristic levels from characteristics as closely as possible. Using the ATC being technically attainable, it is difficult to define process, the two subproblems are solved iteratively explicitly which combinations of characteristics are until a consistent optimal product design is achieved. feasible. For such products, planning decisions made without engineering input may yield inferior or infeasible solutions. 2.1. Analytical Target Cascading Analytical target cascading is an optimization 1.2. Engineering Product Design Models methodology for systems design that works by decomposing a complex system into a hierarchy of The engineering design optimization literature interrelated subsystems (Kim 2001). ATC requires a focuses on methods for choosing values of design mathematical model for each subsystem that variables that maximize product performance computes the subsystem response as a function of the objectives. Papalambros and Wilde (2000) provide decisions at that subsystem. The subsystem models an introduction to engineering design optimization are organized into elements of a hierarchy, as in the modeling techniques, strategies and examples. When example shown in Figure 1, where the top level multiple conflicting optimization objectives exist, the represents the overall system and each lower level
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VEHICLE 2.2. The Marketing Product Planning Subproblem ... ELECTRONICS POWERTRAIN BODY CHASSIS ... In the product planning subproblem, a simple model of profit Π is calculated as revenue minus cost, such that ... CLUTCH ENGINE TRANSMISSION ... Π =−−qp( cVI) c, (1)
... BLOCK CYLINDER HEAD CRANKSHAFT ... where q is the quantity of the product produced and sold (product demand), p is the selling price, cV is the Figure 1 Example ATC hierarchy for a vehicle design variable cost per product, and cI is the investment cost. This model is simplified, and it ignores such represents a subsystem of its parent element. finance-related concerns as the time value of money, Papalambros (2001) provides an overview of the fixed costs, risk and uncertainty; however, this ATC literature, and Michalek and Papalambros simple model will suffice to demonstrate broad (2004) provide details of the generalized ATC trends and provide insight into the general forces at formulation. work. The price p is treated as a decision made by the firm, and for simplification in this article c and c are In the ATC process, top-level system design targets V I considered constant across all possible product are propagated down to subsystems, which are then designs. Product demand q depends on the price p optimized to match the targets as closely as possible. and characteristics z of the product, and discrete The resulting responses are then rebalanced at higher choice analysis and conjoint analysis are used to levels by iteratively adjusting targets and designs model and predict q as a function of z and p. It is throughout the hierarchy to achieve consistency. assumed in this article that the producer is a Michelena et al. (2002) and Michalek and monopolist; however, game theory could be used to Papalambros (2004) proved under assumptions of model oligopoly competition following Michalek, convexity that by using certain classes of Skerlos and Papalambros (2003). coordination strategies to coordinate elements in the ATC hierarchy, the ATC formulation will converge, Discrete Choice Analysis within a user-specified tolerance, to the same A set of statistical methods largely unfamiliar to solution as if all variables in the entire system were engineering audiences has been developed, first in optimized simultaneously (or, “all-at-once”). Using logistics and urban planning and then in economics, ATC can be advantageous because it organizes and to predict choices made in uncertain environments separates models and information by focus or (Louviere et al., 2000; Train, 2003). The chief discipline, providing communication only where theoretical edifice is that of random utility models. In necessary. Some problems that are computationally such models, a decision-maker is presumed to derive difficult or impossible to solve all-at-once can be utility from each alternative in a set of possible solved using ATC, and in some cases ATC can result alternatives, to an extent partially predictable in in improved computational efficiency because the terms of observed covariates. In marketing formulation of each individual element typically has applications, these covariates are typically product fewer degrees of freedom and fewer constraints than (or household-specific) characteristics, whose values the all-at-once formulation. can be used to obtain an overall ‘attraction’ for each In the formulation and example presented in this alternative, where attraction refers to the observable, article, there are only two elements: the marketing deterministic component of utility. Because we product planning subproblem M and the engineering cannot predict consumer utility perfectly, these design subproblem E, which is the child of M. attraction values are combined with stochastic error However, for complex systems ATC allows the terms in order to determine choice probabilities for flexibility to model the engineering subproblem as a each alternative (and the probability that none of the hierarchy of subsystems and components rather than alternatives is chosen, often called the “outside with a single element. For examples of complex good”). systems engineering design using ATC, see Kim et al. (2002), and Kim et al. (2003). Formally, there is a set of product alternatives numbered 1 through J with attraction values {v1, v2,
AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 3
… vJ} and associated errors {ξ1, ξ2, … ξJ} plus an mapping is assumed a linear function of discrete outside good, indexed as alternative 0, with error ξ0 price and product characteristic levels. The attraction and attraction value v0 normalized to zero (v0 = 0). vj for product j is then written as The probability Pj that we observe a choice of K Lk alternative j is the probability that alternative j has (5) vZjkljkl= ∑∑β , the highest utility: kl==11
′ . where Z is a binary dummy variable such that Z =1 Pvjjjjj=+≥+∀∈Prξξ v′′ , j (2) jkl jkl indicates alternative j possesses characteristic/price k Computational efficiency depends critically on the at level l, and βkl is the “part-worth” coefficient of distribution assumed for the ξ random error terms in characteristic/price k at level l. In Z the elements of Eq.(2). Errors can take several forms, and it generally the product characteristic vector z are enumerated as requires extremely large samples for assumptions k = {1, 2, ... K-1}, and price p included as the last about distributional error to have any substantive term, k=K. Each product characteristic/price k is impact; consequently, researchers often work with discretized into Lk levels, l = {1, 2, ... Lk}. One error specifications allowing the most tractability. advantage of using discrete levels is that it does not For example, if errors are assumed to be normally presume linearity with respect to the continuous distributed, then the form of Pj is called the variables. For example, we cannot assume that a $5 multinomial probit model, which does not admit of price increase has the same effect for a $10 product closed-form expressions for choice probabilities in as it does for a $25 product. terms of underlying attractions. However, if ξ terms Given a set of observed choice data, values can be are assumed to be Type II extreme-value (or found for the β parameters such that the likelihood of Gumbel) distributed (i.e., Pr[ξ < x] = exp[-exp(-x)]), the model predicting the observed data is maximized. then it can be shown that A great deal of research in marketing is devoted to ev j recovering model parameters through latent classes, Pj = finite mixtures or using Hierarchical Bayes methods v j′ (3) 1+ ∑ e (Andrews, Ainslie, and Currim, 2002); however, here j′∈ we simply use the standard maximum likelihood formulation (Louviere et al., 2000). The log of the when the utility of the outside good v0 is normalized to zero (see Train 2003, Chapter 3 for proof). This sample likelihood for a particular individual on a form is called the multinomial logit model (MNL). particular choice occasion n is: The MNL model allows a convenient closed-form K Lk solution for choice probabilities P that is especially j exp∑∑βklZ jkl attractive in terms of optimization. Using Eq.(3), kl==11 Φnj ln , (6) choice probabilities for any subset of products can be ∑ K Lk j∈ calculated easily. Even if all products are offered by 1exp+ ∑∑∑βklZ j′ kl ′ a single entity (i.e., a monopolist), the presence of the jkl∈== 11 outside good ensures that demand for a set of where Φ =1 if the observed choice on choice unattractive products will be low, with probability of nj occasion n is alternative j and Φ =0 if j is not the not choosing a product given by: nj observed choice. Here n is the set of alternatives 1 available on choice occasion n. Eq.(6) is maximized P0 = . 1+ ∑ ev j′ (4) with respect to the β terms after summing across all j′∈ individuals and choice occasions. In this way, the part-worth coefficients βkl are obtained for each level It is assumed that v can be measured as a function of l of each product characteristic/price k. observable quantities such as price, product characteristics, consumer characteristics, etc. In this In all random utility models, such as the logit used paper we consider only price and product here, one must careful about model identification: for characteristics. Any number of rules for mapping example, adding a constant term to all attraction price p and product characteristic values z onto values v shifts them upward to the same extent and attraction values v are possible. In practice, product does not change choice probabilities predicted by the characteristics and price are discretized, and the logit model. Thus, in using Eq.(5), there are an
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infinite number of solutions for optimal beta values Conjoint Analysis that predict equivalent choice probabilities and Maximum likelihood estimation can be used to fit therefore have identical likelihood values. Standard beta parameters to any set of observed choice data; practice is to impose an identification constraint on however, collinearities in the characteristics and price the system of coefficients, which unambiguously of the choice sets can make accurate parameter chooses just one among all possible 'optimal' estimation difficult and can cause problems solutions. Such constraints typically set a linear generalizing to new choice sets (Louviere et al., combination of the coefficients to zero. For clarity, 2000). Conjoint analysis (CA) has been widely used we select from the infinity of equivalent solutions the to develop efficient, orthogonal and balanced survey one solution where the mean beta value Σ β /L is the l kl k designs (experimental designs) to determine which same for all k. By adding this constraint, the model product characteristics are important to consumers, has 1 + Σ (L – 1) degrees of freedom, and the k k and appropriate levels for each characteristic. There solution is uniquely defined. is vast literature on conjoint analysis and appropriate The part-worths retrieved with maximum likelihood experimental designs, and we direct the reader to any estimation correspond to discrete values of the of the classic or recent articles, notably Louviere’s product characteristics and price. For example, we (1988) expository article and Kuhfeld’s (2003) may have a certain part-worth for a price of $10 and exhaustive account. another for a price of $15. To optimize over Conjoint studies present subjects with a series of continuous values of price (as well as characteristics products or product descriptions, which they simultaneously), it is necessary to estimate utility for evaluate. Products can be presented in various ways, intermediate values, such as $12. There are several but characteristic levels are always made clear, either possible methods allowing interpolation between in list form, pictorially, or both. Subjects can indicate these discrete part-worth values for each their preferences among products by ranking (i.e., characteristic and price, ordinarily a type of spline putting in an ordered list), rating (for example, on a function. We avoid linear splines due to their 1-10 scale) or choosing their favorite from a set. indifferentiability at knots (the estimated values) and Each method has certain advantages; however, instead use higher-order polynomial splines, either choice-based conjoint is considered most natural, quadratic or cubic, depending on which provides a since this is what real consumers do. Consequently, closer fit. Finally, the attraction can be written as a we follow that approach here, offering successive function of the continuous variable product sets of products and asking which is most preferred characteristics values z and price p using a spline in each, or whether none is acceptable (the “no function Ψ of the part-worths β for each k kl choice” option). To avoid the combinatorial characteristic/price k. If price is represented as k=K, explosion required if all possible pairings of attribute the attraction v is written as values are used, an efficient design is generated. K −1 Efficient designs specially tailored to conjoint studies vp=Ψzz, = Ψ +Ψ p, (7) jkjK()∑ ()k () are supported in a number of software packages, such k =1 as Sawtooth, SPSS and SAS. In our case study th where the angle bracket notation
v e j 2.3. The Engineering Design qsPsjj== . 1+ ∑ ev j′ (8) Subproblem j′∈ In the engineering subproblem, design characteristics Market potentials can be given exogenously at the z are calculated as a function of the design variables outset or estimated through a variety of techniques x using the response function r(x), where x is based on historical data or test markets (Lilien, constrained to feasible values by constraint functions Kotler and Moorthy, 1992). g(x) and h(x). General procedures for defining design variables x, response functions r(x), and constraint functions g(x), and h(x) to define a product design
AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 5
space are well established in the design optimization literature (Papalambros and Wilde, 2000); however, Marketing Product Planning Subproblem maximize modeling specifics are entirely product dependent. Π −ε with respect to The objective function of the engineering zM ,,p ε 2 subproblem is to minimize deviation between the subject to wzD()ME−≤ z ε product characteristics achieved by the design zE and 2 the targets set by marketing z . Using ATC notation M where Π =−−qp( cVI) c introduced in Michalek and Papalambros (2004), this v objective function is written as e
qs= v 2 1+ e wzD()ME− z , (9) 2 vp=Ψ(zM , ) 2 where || ||2 denotes the square of the l2 norm, w is a z M weighting coefficient vector, and ○ indicates term- z E by-term multiplication. For complex products, engineering constraints typically restrict the ability to Engineering Design Subproblem meet some combinations of product characteristic 2 minimize wzD()− z targets, and the ATC process acts to guide marketing ME2 in setting achievable targets while designing feasible with respect to x products that meet those targets. subject to gx( ) ≤ 0 2.4. Complete ATC Formulation hx( ) = 0 where Figure 2 shows the complete ATC formulation of the zrxE = ( ) product development problem for a single-product- producing monopolist. There is only one product in Figure 2 ATC Formulation of the Product Planning and the formulation, so the index j is dropped for Engineering Design Product Development simplicity. In the product planning subproblem, price Problem p and product characteristic targets zM are chosen to maximize profit Π, where Π is calculated as revenue minus cost as in Eq.(1), and demand q is calculated 3. CASE STUDY using the logit model in Eq.(7)-(8), subject to the The demonstration case study involves dial-readout constraint that the targets zM cannot deviate from the household scales. This particular durable consumer characteristics achieved by the engineering design zE product was chosen because scales have high by more than ε, and ε is minimized. In the penetration, are not highly differentiated, are engineering design subproblem, design variables x inexpensive, and have clearly identifiable are chosen to minimize the deviation between components and consumer benefits. The complete characteristics achieved by the design zE and targets model including survey data is available at set by marketing zM subject to engineering http://ode.engin.umich.edu. constraints g(x) and h(x). These two subproblems are solved iteratively, each using standard nonlinear 3.1. Marketing Product Planning programming techniques (Papalambros and Wilde, Subproblem 2000) to solve each subproblem until the system converges. The weighting update method (Michalek Five product characteristics were adopted because of and Papalambros, 2004) is used to find weighting their design relevance and the ability to define coefficient values w that produce a solution metrics to measure them. These factors, shown in satisfying user-specified tolerances for inconsistency Table 2, are also advertised or visible in online scale between marketing and engineering for each term in e-commerce. Other factors, such as brand name and z. This method is important for producing consistent warranty, were not included in the study in order to solutions in cases where the top level subproblem focus on factors affected by the design of the does not have an attainable target: In this case profit product. Factors that are difficult to measure or is maximized rather than setting an attainable profit difficult for consumers to assess before use, such as target. “easy to clean,” were ignored.
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Figure 3 Screen shot of the online scale conjoint survey
price), and the logit model was used to calculate An efficient choice-based conjoint analysis survey demand q for the monopolist using Eq.(7)-(8). was used to collect data on consumer preferences. The survey was implemented online to simulate Based on discussions with a scale manufacturer, a aspects of online purchase decision-making. The variable cost cV of $3 per unit and an investment cost survey can be found at http://ode.engin.umich.edu, cI of $1 million was assumed for this example. The and a screen capture is provided in Figure 3. The market size s was assumed to be five million people, survey includes fifty questions, each of which asks the approximate yearly market for dial scales in the the respondent to choose among three scales or select United States. the “no choice” option. The scales are described by numerical values, a drawing, and a close-up of the Weight Capacity (z1) Interval Mark Gap (z4) dial. The survey includes some scales with physically 200 lbs. -0.534 2/32 in. -0.366 infeasible characteristic combinations because 250 lbs. 0.129 3/32 in. -0.164 responses to these questions serve to infer trade-offs 300 lbs. 0.228 4/32 in. 0.215 in consumer preferences. Five levels were chosen for 350 lbs. 0.104 5/32 in. 0.194 each product characteristic in the conjoint analysis as 400 lbs. 0.052 6/32 in. 0.100 shown in Table 2. The levels were chosen to span the range of values of products in the market, based on a Platform Aspect Ratio (z2) Size of Number (z5) sample of 32 different scales sold on the internet, to 0.75 -0.058 0.75 in. -0.744 ensure realism and to capture anticipated trade-offs. 0.88 0.253 1.00 in. -0.198 1.00 0.278 1.25 in. 0.235 Data were collected from 184 respondents, who were 1.14 -0.025 1.50 in. 0.291 solicited from online newsgroups and from 1.33 -0.467 1.75 in. 0.396 engineering and business students at the University Platform Area (z3) Price (p) of Michigan. Respondent data from the survey was 2 used to estimate the model’s β parameters using 100 in. 0.015 $10 0.719 2 Eq.(6) summed over all respondents and all survey 110 in. -0.098 $15 0.482 2 questions with a modified Newton-Raphson search 120 in. 0.049 $20 0.054 2 algorithm (Greene, 2003). The resulting β values are 130 in. 0.047 $25 -0.368 2 provided in Table 2. Six cubic splines Ψk were fit to 140 in. -0.033 $30 -0.908 these β values (one for each characteristic and one for Table 2 Logit coefficient part-worth β values
AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 7
x8 (rack length) 3.2. Engineering Design Subproblem x (pitch diameter) x12 (dial diameter) 9 The engineering design model was developed through reverse engineering: three scales were x1 disassembled, and the components and functionality x5 were studied, as shown in Figure 4. We chose to x14 x4 restrict our focus to rectangular dial-readout scales to x2 keep the demonstration simple; however, the model x3 could be expanded to include digital scales. x7
The model of the dial-readout scale is based on the x13 topology of scales found in the market: levers A x6 (spring x10 (pivot horizontal arm length) constant) x (pivot vertical arm length) provide mechanical advantage and transfer the force 11 of the user’s weight from the cover B onto a coil Figure 5 Design variables for the scale spring C which is displaced proportionally to the applied force. Another lever D is used to transfer the vertical motion of the spring to the horizontal motion geometric and mechanical relationships. We omit of a gear rack E. The pinion gear F translates linear these derivations here for brevity and focus; motion of the rack to rotational motion of the dial G. however, the entire engineering model is provided in This basic topology is common among the products the Appendix. observed, but dimensions vary, and the ratio of dial- turn per applied force depends on the dimensions of 3.3. Results the levers, the rack and pinion, and the spring The engineering design and marketing subproblems properties. This design topology was parameterized were solved iteratively until convergence using a and modeled using fourteen design variables, eight standard nonlinear optimization algorithm based on constraints to maintain feasible geometric and the Generalized Reduced Gradient method mechanical relationships among the variables, and (Papalambros and Wilde, 2000) to solve each five response functions that calculate product subproblem. At the solution, shown in Table 3, the characteristics as functions of the design variables. optimal scale design is bounded by active Figure 5 shows the design variables used for the engineering constraints that ensure the dial, spring scale. Other dimensions were considered fixed plate, and levers are small enough to fit inside the parameters, and the dial number size and tick mark scale. Detailed variable descriptions are provided in gap were calculated based on scale dimensions. The the appendix and shown in Figure 5. None of the response and constraint functions were derived using variable bounds was active at the solution, and the optimal scale characteristics are within the range of
A scales found in the online market. This design represents the joint optimal solution obtained through coordinated communication between marketing and G engineering models, and the expanded version of this F paper (Michalek et al., 2004) demonstrates that it is E superior to the solution obtained by considering D disjoint marketing and engineering decision models C B sequentially.
A Mkt. Variables Engineering Design Variables
F p $26.41 x1 0.71 in. x8 5.00 in. E z1 254 lbs. x2 11.10 in. x9 0.31 in. D z2 0.997 x3 0.72 in. x10 0.52 in. z 134 in2 x 4.46 in. x 1.59 in. C 3 4 11 B z4 0.116 in. x5 4.20 in. x12 9.36 in. G z5 1.33 in. x6 23.41 lb./in. x13 11.56 in. x7 0.50 in. x14 11.60 in.
Table 3 Optimal scale design Figure 4 Disassembled dial readout scale
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4. CONCLUSIONS ACKNOWLEDGMENTS This article presented and demonstrated a The authors gratefully acknowledge Laura Stojan for methodology for defining a formal link between her efforts in supporting the case study through marketing product planning and engineering design research, modeling of the scale, and implementation decision-making. The ATC framework is especially of the survey. The authors also acknowledge Feray suitable in allowing disciplinary separation while Adigüzel and Peter Ebbes for their help computing retaining rigorous linking and coordination. the efficient choice-based conjoint design for the case study. This work was sponsored by the For the marketing community, this method will help Rackham Antilium interdisciplinary project at the in working with complex products where some University of Michigan and the Reconfigurable combinations of desired characteristics are Manufacturing Systems Engineering Research Center technologically impractical or physically impossible at the University of Michigan. The support of these to produce. The infeasible set is typically a function sponsors is gratefully appreciated. of the technical decisions of the product and is difficult to express as a function of the target NOMENCLATURE characteristic levels without exhaustive enumeration. Using this method allows constraints to be derived in ○ Term-by-term vector multiplication terms of design decisions and then linked through the cI Investment cost model to product characteristics. cV Variable cost per product For the engineering design community, this method g Vector function of inequality constraints will help to put design decisions into the larger h Vector function of equality constraints context of the firm and its objectives. This context j Product index can help to resolve tradeoffs among competing performance objectives in multiobjective J Number of product alternatives optimization by providing information about the k Product characteristic index relative importance of each engineering objective in l Product characteristic level index the context of explicit models of demand and the n Choice occasion number producer’s objectives. p Selling price This article focused on the basic elements of the links Pj Probability of choosing alternative j between marketing and engineering design. The q Product demand methodology can be extended in several ways. Vector response function that calculates Models of demand heterogeneity can be introduced r to design product lines. Multiple product topologies product characteristics can be included for product variety, and design s Size of the entire market topologies could potentially be generated v Deterministic component of utility automatically (Campbell, Kotovsky and Cagan, w Vector of weighting coefficients 1998). Cost models can be integrated to the engineering subproblem such that the marketing x Vector of design variables product planning subproblem sets target production Vector of product characteristics achieved by zE cost and the engineering design subproblem designs engineering products that meet the cost targets. In addition, Vector of product characteristic targets set by z models of product families can be used to study M marketing commonality effects on product cost structure Z Binary characteristic level indicator variable (Fellini, Kokkolaras and Papalambros, 2003), and β Part-worth coefficient manufacturing investment decisions, particularly considering reconfigurable and flexible equipment ε ATC deviation tolerance variable (Koren et al., 1999), can be included in the model. Π Profit Finally, if the conjoint analysis survey can be Spline function to interpolate part-worths for Ψ designed optimally to avoid questions about k characteristic/price k infeasible product characteristic combinations, then Φ Binary variable indicating observed choice the expense of the survey can be reduced and the accuracy improved. ξ Random (error) component of utility
AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 9
APPENDIX: MARKETING AND ENGINEERING SUBPROBLEMS Marketing Model Maximize profit with respect to price and product characteristic targets
Objective Function Name Description Value Units Scaled Formula Maximize profit while minimizing deviation f -67900986 - -6.790 f = −Π +ε from engineering design
Π Profit $67,990,273 $ Π =−−qp( cVI) c 2 ε 89,287 - ε =−wzD z Weighted deviation ()ME2
Decision Variables : zM,p Eng. Design : zE Name Description Units Scaled Min Max Value Dev. % Dev w
z 1 Weight Capacity 255 lbs 0.273 200 400 254 -0.4 -0.183% 1.0E+05
z 2 Platform aspect ratio 0.996 - 0.422 0.75 1.333 0.997 0.001 0.089% 1.0E+05
z 3 Platform Area 134.0 in^2 0.851 100 140 134.0 0.0 0.045% 1.0E+05
z 4 Size of gap between 1-lb interval marks 0.1159 in 0.427 0.063 0.1875 0.1156 -0.0003 -0.211% 1.0E+05
z 5 Size of number (length) 1.334 in 0.584 0.75 1.75 1.334 0.000 -0.036% 1.0E+05 p Price $26.41 $ 0.820 10 30
Intermediate Calculations Name Description Value Units Formula v Ψ z 1 Interpolated part worth of capacity 0.162 - 1 ( 1 ) v Ψ z 2 Interpolated part worth of aspect ratio 0.282 - 2 ( 2 ) v Ψ z 3 Interpolated part worth of area 0.017 - 3 ( 3 ) v Ψ z 4 Interpolated part worth of gap 0.127 - 4 ( 4 ) v Ψ z 5 Interpolated part worth of number size 0.281 - 5 ( 5 )
v 6 Interpolated part worth of price -0.507 - Ψ6 ( p) v Total deterministic component of utility 0.362 - Ψ (z, p) ev S Market Share 58.95% - S = 1+ ev ev q Demand 2,947,575 units qs= 1+ ev
Parameters Name Description Value Units s Size of market 5,000,000 -
c V Variable cost per unit $3.00 $
c I Investment cost $1,000,000 $ v Attraction of the outside good 0 - 0
10 Jeremy Michalek, Fred Feinberg and Panos Papalambros
Engineering Model Minimize deviation from target product characteristic values Objective Function Name Description Value Scaled Formula Last 2 f 8.9E+04 8.9E-06 f =−wzD z ##### Minimize normalized squared target deviation ()ME2
Product Characteristics : zE(x,y) Targets : zM Name Description Value Units Formula Min Max Target % Dev w
4π xxx69101( x++ x 2)( x 3 x 4) z 1 Weight Capacity 254 lbsz1 = 200 400 255 -0.183% 1.0E+05 xxxx11() 1()() 3++ 4 xxx 3 1 + 5 −1 z 2 Platform aspect ratio 0.997 -zxx21314= () 0.75 1.333 0.996 0.089% 1.0E+05
z 3 Platform Area 134.0 in^2zxx31314= 100 140 134.0 0.045% 1.0E+05 −1 z 4 Size of gap between 1-lb interval marks 0.1156 inz4121= π xz() 0.063 0.188 0.1159 -0.211% 1.0E+05 2tan π yz−1 1 x− y ( ( 11() 1))()2 12 10 z 5 Size of number (length) 1.334 inz5 = 0.75 1.75 1.334 -0.036% 1.0E+05 12+ yyz−−11 tanπ ( ()12() 11 () 1 ) Design Variables (x) Name Description Value Units Ref. Values (from rev. eng.) Min Max
x 1 Length from base to force on long lever 0.71 in 0.63 0.125 36
x 2 Length from force to spring on long lever 11.10 in 9.25 0.125 36
x 3 Length from base to force on short lever 0.72 in 0.63 0.125 24
x 4 Length from force to joint on short lever 4.46 in 4.50 0.125 24
x 5 Length from force to joint on long lever 4.20 in 4.19 0.125 36
x 6 Spring constant 23.41 lb/in 23.44 1 200
x 7 Distance from base edge to spring 0.50 in 0.50 0.5 12
x 8 Length of rack 5.00 in 5.00 1 36
x 9 Pitch diameter of pinion 0.31 in 0.25 0.25 24
x 10 Length of pivot's horizontal arm 0.52 in 0.50 0.5 1.9
x 11 Length of pivot's vertical arm 1.59 in 1.00 0.5 1.9
x 12 Dial diameter 9.36 in 5.75 1 36
x 13 Cover length 11.56 in 10.00 1 36
x 14 Cover width 11.60 in 10.25 1 36 Constraints (g(x,y),h(x,y)) Name Description Value Units Formula
g 1 Dial diameter must be less than base width -1.64 in x12≤−xy 142 1 g 2 Dial diameter must be less than base length minus spring and plate 0.00 in x12≤ xyxy 13−−−2 1 7 9
g 3 Length of short lever has to be less than base length -2.30 in ( x45+≤−xx) 1312 y g 4 Joint position on the long lever must be shorter than the length -7.62 in x512≤ xx+ g 5 Rack shorter than base when pivot is rotated 90 deg -2.76 in x79118131+ yx++≤− xx2 y g -1.97 in 1 6 Rack length must be sufficient to span between pivot and center of dial x8131≥−( xy2 ) −( xyxyx 1277910 +−−−) 2 2 g in 221 7 Long lever must attach to top of scale (Pythagorean Theorem) 0.00 ()(2)xx1+≤−−+ 2 x 13 yx 1 7()2 x 14 − y 1 222 g 8 Long lever must attach to base a minimum distance y13 from centerline -14.23 in ()()x13−−2yx 1 7 +≤+ y 13 xx 1 2
x8 (rack length) Parameters (y) x (pitch diameter) x12 (dial diameter) 9 Name Description Value Units y1 Gap between base and cover 0.30 in y2 Minimum distance between spring and base 0.50 in x1 y3 Internal thickness of scale 1.90 in x y4 Minimum pinion pitch diameter 0.25 in 5 y5 3.00 in x14 Length of window x4 y6 Width of window 2.00 in x2 y7 Distance btwn top of cover and window 1.13 in y8 Number of lbs measured per tick mark 1.00 lbs x3 x y9 Horizontal distance between spring and pivot 1.10 in 7 y10 Length of tick mark + gap to number 0.31 in x13 y11 Number of lbs that number length spans 16.00 lbs x6 (spring x10 (pivot horizontal arm length) y12 1.29 - Aspect ratio of number (length/width) constant) x11 (pivot vertical arm length) y13 4.00 in Min. allowable dist. of lever at base to centerline
AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 11
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12 Jeremy Michalek, Fred Feinberg and Panos Papalambros