ON THE VALUATION OF GOODS AND SELECTION OF THE BEST DESIGN ALTERNATIVE docx

On the valuation of goods and selection of the best design alternative H.E. Cook, A. Wu Abstract In the planning and early design stages of new products, the value to the customer for the alternatives under consideration need to be quanti®ed in the same units as costs to make rigorous trade-off decisions. Ac- cording to the S-model, the value of a good is the price at which demand goes to zero and its demand curve shifts by a prescribed amount when its value changes. To test these ®ndings, we have investigated the simulated demand for two lottery tickets. This was necessary because the full demand curves and the values of commercial products are not known a priori. The so-called ``endowment effect'' for the lottery tickets was also observed and explained here as a direct result of the stochastic nature of the driving forces for buying and selling a good. The use of the S-model to examine product value trends over time is explored for two minivans competing in the real marketplace. The connections between the S-model and several other engi- neering design methodologies are discussed. Keywords Demand á Value á Endowment effect á QFD á SEU á Marketing research Introduction How potential customers value the features of a product is of great interest to a variety of ®elds including economics, psychology, marketing, ®nance, and engineering. The de®nition of value and the method of determining it are far from uniform across these ®elds, however. Even within the domain of engineering, which is our interest here, the de®nitions of value and its surrogates are not consistent. Value engineers, for example, de®ne value as worth di- vided by cost (Fowler 1990). In their seminal illumination of the robust design process, Taguchi and Wu (1980) used the term ``cost-of-inferior-quality'' to represent the loss of value which occurs when the level of a product attribute is off its ideal speci®cation. Practitioners of Quality Function Deployment (QFD) use a zero to ten scale to judge the value or worth of customer needs (Akio 1990). Utility is a classical, dimensionless measure of the appeal of a product (Thurston 1990; Locasio and Thurston 1993). These design support tools are used to make cost/ bene®t tradeoffs in their respective application domains. For example, Taguchi's robust design methodology is widely used in component design (Seventh Symposium on Taguchi Methods 1989, October 1989, Scottsdale, AZ, American Supplier Institute, Dearborn, MI). Value engi- neering methods are used extensively to wring non-value added costs out of preliminary designs (Tanaka et al. 1993). QFD is widely used to make design trade-offs be- tween alternatives (Tenth Symposium on Quality Function Deployment 1998, June 1998, Novi MI, QFD Institute, Ann Arbor, MI). Thurston and co-workers (Thurston 1990; Thurston 2001; Locasio and Thurston 1993; Carnahan and Thurston 1998) have pioneered the use of subjective ex- pected utility (SEU) theory in making design trade-offs when simultaneously considering bene®ts to the customer, the costs to the manufacturer, and environmental losses. The S-Model was developed with the objective of uni- fying Taguchi methods, value engineering, and QFD into an integrated tool-set having a common formalism for guiding the planning, design, and development of new products (Cook and DeVor 1991; Cook 1992; Kolli and Cook 1994; Cook and Kolli 1994; McConville and Cook 1996; Donndelinger and Cook 1997; Cook 1997; Pozar and Cook 1997). Aspects of several marketing research tools (Randall et al. 1974; Green and Ward 1975; Louviere and Woodworth 1983) were integrated with the S-model to make a direct assessment of value. As noted by Grif®n and Hauser (1993) conventional marketing research informa- tion is not suf®cient for making detailed cost/bene®t trade- offs. The guiding rationale for the S-model was to balance simplicity and rigor through the use of a phenomenolog- ical model of demand written as a Taylor expansion in terms of the values and prices of the competing products. There were several reason for taking this approach. The ®rst was that phenomenological models have had great success in other areas, the theories of diffusion and elas- ticity, being perhaps the two most notable examples. Secondly, a Taylor expansion is the simplest and least presumptive way to formulate the general problem. Thirdly, the formulation is rigorous in the limit if the function is analytic in the expansion variables. Received: 8 October 2000 / Revision received: 1 May 2001 / Accepted: 1 May 2001 / Published online: 14 July 2001 Ó Springer-Verlag 2001 H.E. Cook (&) Department of General Engineering, University of Illinois at Urbana-Champaign, 104 S. Matthews Ave., Urbana, IL 61801, USA E-mail: h-cook3@uiuc.edu Tel.: +1-217-244-7992 Fax: +1-217-244-5705 A. Wu Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, USA Original paper Res Eng Design 13 (2001) 42±54 DOI 10.1007/s001630100004 42 The purpose here is three-fold. The ®rst is to illustrate the use of the model to gain insight into competitive be- havior from the construction and analysis of the value trend curves for competing products. The second is to examine the S-model predictions that product demand goes to zero as the price of a product approaches its value and that demand shifts by a prescribed amount to a change in value of the good. The third is to examine and compare the interrelationships between the product de- velopment tools listed above and to discuss the general problem of selecting the best design alternative by incor- porating the S-model into the well-known QFD process. For the convenience of the reader, a review of the S-model formalism and its key equations are included. Review of S-model Market segments The S-model views customers as being within consumer segments, which are composed of persons who have sim- ilar tastes, lifestyle and demographics including, income, age, and gender. They are assumed to have a single, ag- gregate value for a good but it may represent an aggregate quantity taken over a range of multiple, distinct uses of the good. For example, when water is priced inexpensively, it is put to many marginal uses of lower value in comparison to its fundamental value for sustaining life. The use of market segments, as opposed to an individual perspective, is a convenient simpli®cation, which is widely used in planning mass-produced goods. The size of a segment could, of course, be reduced to the individual level where value would resemble but not be identical to the concept of consumer surplus. Product segments (e.g., minivans, televisions, personal computers, GPS devices) also exist. A buyer segment is de®ned as those persons who purchased items from a particular product segment and will generally be com- posed of several consumer segments. Marketing research can be used to determine how each consumer segment within a buyer segment values the product. The demand for the good is assumed to increase if price is reduced or if value is increased. If a person was ready to buy a speci®c brand today but found that the price had been increased, he or she might purchase a substitute brand or simply buy the ®rst brand chosen at a later date at the higher price. Fundamental and bottom-line metrics The coupling between the key elements in the product realization process is described in Fig. 1. For simplicity in presentation, the in¯uence of competitors is not shown. The loop on the right connects the needs of the customer to the needs of the manufacturer and the loop on the left connects the needs of society to the needs of the manu- facturer. A necessary but not suf®cient condition for the manufacturer to remain in business is to jointly satisfy the needs of its customers and society. The challenge to de- velopers of engineering design methodologies is to model the connections between the elements in the two loops in a manner that aids product planners and engineers to design pro®table products in the face of stiff competition. The S-model, because it includes only the linear terms in a Taylor expansion for demand, represents the simplest model of how the elements in Fig. 1 are connected when there are N competitors. For many products, societal needs are set by govern- mental regulations covering the manufacture, use, and disposal of the product. For this class of problems, it is both convenient and suf®cient to focus on the Customer and Manufacturer loop provided that the costs for meeting governmental regulations are included in computing the total cost of the product. Demand Demand and value are the key phenomenological variables to address in constructing a model of the Customer and Manufacturer loop because, when they are modeled sat- isfactorily, all of the other elements in the loop can be de®ned and readily modeled. Demand, price, and pro®t (or cash ¯ow) are well-known bottom-line, ®nancial met- rics. Value and cost along with the pace of innovation act as fundamental metrics (Cook 1997) in that they determine the outcomes for the bottom-line metrics. The demand of a product i given by D i is taken to be equal to the total amount of the product sold over a period of time, usually a year, the assumption being that sales are equal to demand. In other words, all of the customers who wanted to pur- chase the product should have been able to do so if they had the resources. This may not always be the case and it is important to assure that customers are not being turned away because of insuf®cient supply. Of course when sup- ply is insuf®cient, price will often rise to maintain a bal- ance with demand. The Taylor expansion is made about a so-called ``cartel point'' where the N competing products have the same prices, P i , values, V i , and market share, 1/N. The cartel point was chosen because its high degree of symmetry reduced the number of independent expansion coef®cients required by the model to one, noted as K, which, when divided by N, would be equal to the negative value of the slope of a cartel member's demand curve with price. Fig. 1. The product realization process couples customer and societal needs H. E. Cook, A. Wu: On the valuation of goods and selection of the best design alternative 43 The basic assumption of the S-model is that demand is an analytic function of the N values and prices of the competing products: D i  f i V 1 ; V 2 ; :::; V N ; P 1 ; P 2 ; P N 1 When the prices and values of the products change inde- pendently from their levels at the cartel, it follows that the change in demand for each product i=1, N is given by the following (Cook 1997): dD i  K dV i À dP i À 1 N  jTi dV j À dP j ÂÃ V ` X W a Y 2 provided that the price and value changes are small. On writing Eq. 2 as a function of the total variables: D i  KV i À P i À 1 N  jTi V j À P j ÂÃ V ` X W a Y 3 we obtain a useful hyper-plane approximation to the ac- tual demand surface as a function of the 2N variables of value and price. For a monopoly, Eq. 3 becomes as follows (Cook and DeVor 1991): D i  KV i À P i  4 It is seen from Eq. 4 that the price where demand goes to zero is equal to V i . The dashed lines in Fig. 2 illustrate the use of the linear approximation to a demand curve for a monopoly. The curve on the left is for a baseline product and the curve on the right is for an alternative formed from the baseline by adding a value improvement of $5. The value V i =$22 given by the intersection of the linear approximation for the baseline product with the zero de- mand line represents a marginal value for the product at a demand level of 8 and price level of $15. For a convex downwards demand curve, the marginal value will increase with price which is in keeping with the notion that mar- ginal uses of a product (uses of less value) decrease as price is increased. As the price of water is increased, for example, its marginal uses such as watering the lawn, washing the dog, etc. should become less and less preva- lent. As the ultimate value of water is priceless, its demand, as price increases, should approach the horizontal (in- elastic) level needed to sustain life. Value trends If the demands and prices of the products competing within a segment are known from historical data, the lin- ear set of simultaneous equations represented by Eq. 3 can be solved for the values of the products. The resulting expression is given by V i  ND i  D T  KN 1  P i 5 for product i, i=1, 2, N where D T is the total demand for the N competing products. In using Eq. 5, the demands over a given historical time period are taken to be equal to the sales over the period and prices are set equal to the historical transaction prices (not list prices). For any given time period, the average value,  V, of the N competing products is related to the average price of the products,  P, by the expression  V   P 1  E 2 E 2 ! 6 where E 2  Àd  D=  D dP=  P 7 de®nes a price elasticity in which the numerator represents how the fractional change in average demand changes when all of the N products change price by dP,  D being the average demand. If this elasticity is known, the negative slope of the demand curve, which appears in Eqs. 3, 4, and 5, can be computed from it using the expression K  NE 2  D  P 8 For automobiles, the price elasticity E 2 is approximately unity (Donndelinger and Cook 1997) and from Eq. 6, we see that the average value of the automobiles in a segment is approximately twice their average price. Note that when E 2 =1, the average demand for a segment will be reduced by 10% if the average price increases by 10%. The value given by Eq. 5 represents the buyer segment value for the good. It is a weighted average of the values over all of the consumer segments involved in the purchase of the good. Of particular interest is how value trends be- have when major product changes are made. Competition between two major brands, A and B, in the minivan market is examined in Fig. 3, where the values were determined from Eq. 5. The prices used in the computations are Fig. 2. Fit of a baseline demand curve by a linear approximation and the shift in the linear approximation resulting from a value improvement of $5 Res Eng Design 13 (2001) 44 considered proprietary by the manufacturer and are not included here for that reason. Prices and values were cor- rected for in¯ation. Also the brand names of the vehicles are not given here because the results do not apply to the current products as both have been extensively redesigned since the period covered in the plot. Minivan A, noted as mvA, had front wheel drive and was the recognized market leader in the 1992 model year. Minivan B, noted as mvB, was a rear wheel drive minivan for the 1992 and 1993 model years. During the 1994 model year, the manufacturer introduced a second brand that had front wheel drive. It also had an improved interior package, better ride, and fresher styling than the earlier model, which was more truck-like than car. This new minivan was in full production by the 1995 model year. However, both the new and the existing minivans were sold on the same showroom ¯oor during the 1994, 1995, and 1996 model years. The values for mvB shown for those years were com- puted using a sales-weighted-average for the two brands. It is seen that by the 1995 model year the value of mvB exceeded the value of mvA, which had not been upgraded for several years. In the 1996 model year, mvA received a major redesign with a signi®cant improvement in interior room, fresh styling, and the addition of a second rear sliding door, a feature which was not available on mvB. The value of mvA increased signi®cantly, becoming roughly $2,500 more than mvB in the 1996 model year. Direct value method Projections of future demand can be made using Eq. 3 provided that the values and prices of future products can be projected. In order to do this, key elements from choice theory (Louviere and Woodworth 1983), contingent valu- ation (Randall et al. 1974) and prospect theory (Kahneman and Tversky 1979; see also Tversky and Kahnemann 1981) have been used in conjunction with Eq. 3 to formulate the direct value (DV) method (Donndelinger and Cook 1997) of marketing research. In the DV method, one or more attributes of a baseline product are modi®ed to form an alternative product having a value V. The baseline and alternative are described in the survey and respondents are asked to make choices between the baseline and the al- ternative over a series of prices for the latter (McConville and Cook 1997). The use of four to six price points for each alternative under consideration strikes a good bal- ance, as a rule of thumb, between statistical accuracy and time to complete the survey. The price and value of the baseline product must remain ®xed at P 0 and V 0 , respec- tively, in keeping with the ®ndings from prospect theory. The fraction of respondents, f, choosing the alternative is plotted as a function of price. From the plot, a neutral price, P N , is determined. This is the price where half of the respondents choose the alternative and half choose the baseline. The products for the N±1 competitors are absent from the choice set and, because the two demands are equal, it follows from Eq. 2 that V À V 0  P N À P 0 9 The DV method has been used to determine the value of a variety of features for automobiles (McConville and Cook 1996; Donndelinger and Cook 1997; Cook 1997; Pozar and Cook 1997) construction equipment (Bush 1998; Freeman 2000; Herington 2000) farm equipment (Silver 1996) and aircraft (LeBlanc 2000). In using the method, respondents are usually asked only to consider one attribute change from the baseline at a time to minimize cognitive stress. A neutral price is found for each alternative whose value improvement is computed from Eq. 9. Note, in using Eq. 9 to determine the value change for the attribute, it is not necessary to know K. This is important, as the slope of f versus the price of the alternative need not and likely will not be equal to the slope of the demand curve for the baseline product in the marketplace. Value curves Once a customer need has been identi®ed, a value curve for the attribute should be developed. Value curves are expressed as exponentially weighted parabolas. When normalized by dividing through by the baseline value V 0 , they are of the general form vg Vg V 0  g C À g I  2 À g À g I  2 g C À g I  2 À g 0 À g I  2 45 c 10 The curve passes through three points: (1) the critical level for the attribute, g C , where value goes to zero; (2) the baseline level for the attribute, g 0 , where value is V 0 ; and (3) the ideal level of the attribute, g I , where value is at a maximum for the attribute. An example is shown in Fig. 4 for the interior noise level in a luxury vehicle cruising at highway speeds (Pozar and Cook 1997). Ten different noise levels were evaluated about a baseline noise level of g 0 =66 dBA using the DV method. The exponential weighting coef®cient c=0.59 was determined from the best ®t of Eq. 10 to the points. The values for g C =110 dBA and g I =40 dBA were pre-determined from human factor studies, which have demonstrated that 110 dBA is at the threshold of pain and that noise levels below 40 dBA start to become too quiet. An advantage of expressing value curves in the normalized form given by Eq. 10 is that they Fig. 3. The values for two production minivans as a function of model year as computed from Eq. 5 H. E. Cook, A. Wu: On the valuation of goods and selection of the best design alternative 45 can be used with a degree of con®dence for similar products whose baseline value V 0 differs somewhat from that used in developing the original curve. The empirical weighting coef®cient c is approximately the fraction of time that the attribute is important when using the product. Respondents took the survey sitting in front of a computer screen using headphones to listen to the noise levels. They had to sense if the alternative under consid- eration was louder or quieter than the baseline and to select the price increase they were willing to pay (WTP) for a noise reduction or the price reduction they were willing to accept (WTA) for a noise increase. The noise levels presented were from recordings of interior noise at high- way speeds in an actual luxury vehicle. The value of lottery tickets The products chosen for testing the theoretical relation- ship between the price intercept and value were two lottery tickets. Simulated markets for the tickets were used to develop demand curves. The pay-offs were chosen to be relatively small so as to avoid signi®cant changes in the wealth of the respondents had the purchase of the tickets and pay-offs actually occurred. The reason for this was to avoid the well-known situation typical of state lotteries in which potential buyers are offered a remote chance of winning a large sum if they purchase a ticket priced well in excess of the expected economic value (EEV) of the payoff. We do not presume, however, that buyers of such tickets are irrational. The added value for such a ticket over its EEV comes from the dream of what the outcome might be, not from what the outcome will likely be. Speci®cally, one simulated lottery ticket gave the holder a 50% chance to win $100 and the other offered an 80% chance to win $100, their respective EEVs being $50 and $80. The simulated lotteries were administered as surveys to 78 students enrolled in a course on product realization. Of these, 37 were either seniors or graduate students at the University of Illinois and 41 were graduate engineers taking the course as part of a continuing education pro- gram at a major U.S. company. The surveys used are shown in Appendix A. In using Eq. 4 to analyze the sim- ulation results, demand and supply were set equal to cu- mulative frequency f, for respondents willing to purchase or sell the tickets. The price, P, where a respondent changed from willing to pay to not willing was assumed to lie half-way between the respondents maximum stated willingness to pay, P*, and the next incremental price level. As each of the price increments was $5, we have P=P*+$2.50. To estimate the cumulative purchase frequencies for each lottery, we ®rst arranged the maximum price offered by each respondent in ascending order against a descending numerical index, n(P*), given by 78, 77, 76, 1. The cumulative frequen- cies were then computed using the standard relationship (DeVor et al. 1992) in the form fP P Ã  2:50 n m P Ã À0:5 n T 11 where n m (P*) was the (minimum) numerical index asso- ciated with price P* and n T was the total number of re- spondents. A similar process was used for sellers except that the index, n(P*), ran oppositely from 1 to 58, the number of respondents for the selling survey. Respondents as buyers The demand curves were initially constructed separately for the on-campus and off-campus respondents. The curves for both appeared equivalent, however, and no statistically signi®cant differences between the two sample means were found. Therefore, the responses for both groups were pooled together for the remaining analyses. In Fig. 5, the fractional demands for the two tickets are plotted versus P/EEV, de®ned as their prices divided by their respective EEVs. A least square ®t of a line through the quasi-linear P/EEV range from 0.6 to 1.05 intercepts the axis at 1.09. Points beyond P/EEV=1.0 represent risk- taking behavior. Fig. 4. The normalized value of a luxury vehicle as a function of its interior noise level as determined from a DV survey (Pozar and Cook 1997; Society of Automotive Engineers, reprinted by permission) Fig. 5. The demand curves for the simulated purchase of a lottery ticket Res Eng Design 13 (2001) 46 The fact that the values determined for the intercepts are close to the respective EEVs of the tickets supports the use of the S-model in representing the aggregate behavior of buyers in the purchase of a good. As price falls below value, demand increases with the increase in the driving force given by V±P. Whether or not these ®ndings apply to other, more complex goods is speculative because we do not know the economic values of other goods and are thus unable to test the prediction. However, the results found here are strongly supportive of the intercept as a mean- ingful measure of value. Use of the intercept as a phenomenological measure of the value of the product is also intuitive in the absence of the S-model. The use of V±P as a measure of the driving force for demand was suggested independently by An- derson and Naurus (1998), for example. The reservation price for an individual is widely used as a measure of value (Plott 1990). The intercept here represents the reservation price for the buyer segment. Demand according to the S- model is considered to be a stochastic process in which the probability that an individual in a segment would pur- chase a good is proportional to V±P (Cook and DeVor 1991). The resulting demand curve is the summation of the individual purchases. It also follows from the model, that when V±P is negative the driving force is to sell the good. Another key property of the S-Model is its prediction of how a piecewise, linear ®t to the demand curve over a small range in price shifts when the value of the good increases by a small amount dV. This property is also demonstrated in Fig. 5 by the overlap of the two curves in the vicinity of P/EEV%1. The model assumes that the slope of the demand curve does not change for a small change in value. The fact that the two curves superimpose in the quasi-linear region in Fig. 5 means that the two slopes are, in fact, not the same and suggests that the fractional change in K is directly related to the fractional change in V through the relation dK K À dV V 12 This empirical relationship does not contradict the S-model but supports its assumption that if the value change is small, then a possible change in slope can be ignored. The modest change in slope in the simulated experiment is a result of the large difference of $30 between the EEVs of the two tickets. Respondents as sellers Students in the same class also participated in a simulated market in which they were given the lottery tickets and then surveyed as to their selling price. For each ticket, the resulting supply curve, Fig. 6, intersected the demand curve at a price divided by the respective EEV of ap- proximately 0.75. The price P MC  0:75 EEV is known as the ``market-clearing price'' as it represents the price where the number of buyers of the ticket would just equal the number of sellers. This price is seen to lie within the quasi-linear portion of the curve in Fig. 5. Although the respondents were similar in many de- mographic aspects, the behaviors of the demand and supply curves in Fig. 6 cannot be explained by assuming that the respondents had a single value for a given lottery ticket equal to its EEV. If all the respondents had had the same value for a ticket, the two curves in Fig. 6 would have only touched at P/EEV=1 and no sales would have taken place. We postulate that the value differences arise from the respondent's differences in risk aversion. At the mar- ket-clearing price in Fig. 6, those who were most risk averse would be sellers and those who were least risk averse would be buyers. Based upon the curves, the buyers valued the tickets at V B %EEV. They would have purchased the tickets from sellers who valued the tickets at V s %0.4 EEV. Thus the S-model is suf®cient to describe the demand and supply curves in the market-clearing region in terms of aggregate behavior. It is useful at this juncture to point out that risk aversion is not the dominant factor causing buyers and sellers to have different values for massed produced goods. The manufacturer of an auto- mobile, for example, values this good less than a potential buyer because the manufacturer has many more automo- biles than required for his or her own use. The value of a mass produced good to the seller can be taken equal to its variable cost. The net value of a good to the seller is equal to the cash ¯ow generated. The average buy and sell prices for the 50% ticket were $29.17 and $45.43, respectively, and for the 80% ticket, they were $48.78 and $71.90. These differences and the shift in the supply curve to the right of the demand curve generated by the same respondents for the same good are expressions of the well-known ``endowment effect'' (Thaler 1980; Knetsch and Sinden 1984; Hanemann 1991; Kahn- eman et al. 1990; Morrison 1998; Kolstad and Guzman 1999), which has been widely observed in controlled ex- periments for both simulated and actual purchases. [We use the term ``endowment effect'' here only in a descriptive manner and do not necessarily imply that it arises solely from loss aversion (Kahneman et al. 1990)]. Simply stated, persons generally post a selling price for a good signi®- cantly higher than what they were WTP for the good only Fig. 6. Simulated demand and supply curves for the two lottery tickets H. E. Cook, A. Wu: On the valuation of goods and selection of the best design alternative 47 moments before. This is in contrast to the prediction from classical economic theory and the explanation remains unsettled (Morrison 1998). We wish to emphasize in what follows that the en- dowment effect is not anomalous behavior for any model in which the purchase of the good is considered to be a stochastic process. Consider a market segment of indi- viduals that have a single, true value, V T , for a good. Ac- cording to the S-model, the probability that a single individual buys the good is proportional to V T ±P>0 and the probability that he or she sells it is proportional to P±V T >0. Thus, if price is near but below V T , then the probability that any given individual in the segment will buy the good is small. Likewise, if price is near but above V T , then the probability that this same individual will sell the good, if it is in his or her possession, is also small. Therefore it is statistically likely that there will be a gap between a person's maximum buy price, P B , for a good and his or her minimum sell price, P S , for the same good. The true value of the good to the person can be taken to be equal to the average of the two limiting prices, V T =(P B +P S )/2. Whenever a transaction is freely consummated, the agreed upon price is such that both the buyer and the seller perceive receiving a net gain. Thus, when an indi- vidual becomes both buyer and seller, in the sense of purchasing a good and then immediately offering it for sale, he or she will post a higher price than the price just paid. The desire is to make a net gain in value from the sale similar to the net gain made by the purchase. The stochastic origins of the endowment effect given here are consistent with this view of human behavior. The gap between WTP and WTA resulting from the stochastic nature of demand can be simulated using Monte Carlo methods. An example is shown in Fig. 7 where the probability that an individual buys was taken to be p B =b(V T ±P) and the probability for selling was taken as p S =b(P±V T ). The simulated ®ndings are for b=1/5. The two lines representing p B and p S are also shown in Fig. 7. For the P±V T <0 region, the simulated choice is between buy or not buy and for P±V T >0, the choice is between sell or not sell. Points on the line equal to unity represent buy for P±V T <0 and sell for P±V T >0. Points on the line equal to zero represent not buy for P±V T <0 or not sell for P±V T >0. The particular simulations shown were made by starting at P À V T jj  4:5 and moving toward 0 in steps of 0.5. Once a transition was made from 1 to 0, the simulation was stopped and the remaining points were set to 0. If, using the same algorithm, a large number of simulations were made from 4.5 to 0 and an equal number made from 0 to 4.5, the resulting average demand fractions would follow the two lines shown. The magnitude of the slope b can be taken as a measure of the uncertainty that the individuals in the segment have in the value of the good. Thus, if individuals were absolutely certain of the value, the slope would be in®nite and there would be no gap between buy and sell prices. This represents the condition of classical economic theory. Comparisons to other models Taguchi's model Taguchi's model for robust design is based upon a quality loss function which is a sum of two quantities, the cost of inferior quality, W, and manufacturing cost, which we take to be equal to variable cost, C. As shown by Cook and DeVor (1991), the formal relationship connecting the S-model to Taguchi's model is the expression XgVg I ÀVg13 which equates the cost of inferior quality of an attribute at an arbitrary level g to the difference between the value for the attribute at its maximum or ideal level, g I , and the value for the attribute at level g. Taguchi suggested estimating W from the costs incurred to repair the product when the attribute is off target. This will generally be an underestimate of the true losses be- cause the customer also receives a loss in value when the product is performing less than expected and when it is out of service. The S-model expression for W given by Eq. 13 is a more fundamental way to arrive at this im- portant quantity using the value curve for the attribute of interest, such as the one shown in Fig. 4 for interior noise. The target speci®cation, g T , in Taguchi's model is the attribute level for the minimum in the loss function. The target speci®cation in the S-model is the level that maxi- mizes cash ¯ow or whatever bottom-line metric is of in- terest to the manufacturer. The two approaches to determining the target speci®cation give the same result when a monopoly is considered. However, for the general case in which there are several competitors, choosing the target speci®cation based upon a bottom-line metric is preferred because it fully accounts for demand, invest- ment, and pricing considerations. For this reason, S-model value and cash ¯ow considerations have been incorporated into Taguchi's Design of Experiments formalism (Cook 1997). Fig. 7. Monte Carlo simulations of the gap between a single individual's WTP and WTA Res Eng Design 13 (2001) 48 Value engineering Value engineers formally de®ne value as worth divided by cost, which is more in keeping with a value for the money measure. In practice they use a de®nition of functional performance divided by cost because of the dif®culty in quantifying worth in monetary units. Practitioners focus on discovering and eliminating non-value-added costs in preliminary designs (Fowler 1990). The connection be- tween value engineering and the S-model is that worth, as de®ned by value engineers, can be taken as being equiv- alent to value as de®ned by the S-model. Thus, use of the S-model would resolve the value engineer's problem of quantifying worth in monetary units. QFD The ®rst step in the QFD process is to use marketing re- search to obtain an ordinal rank of customer needs. Design alternatives are then judged on the basis of their ability to meet customer needs at low cost. The use of a zero to ten scale by engineers to rank how well the proposed alter- natives meet the customer needs is pragmatic in that it can be done quickly. It misses a key point, however, which is that potential customers should be more able to assess perceived bene®ts than the engineers can. Also, QFD, like value engineering, uses one set of units for bene®ts and another for costs, which compromises quantifying the difference between cost and bene®t in making trade-off decisions. Locasio and Thurston (1993) have shown how the problem of having costs and bene®ts in different units could be overcome in QFD by using SEU. Recently, Cook (2000) introduced the S-model formalism into the QFD House of Quality to attack this same shortcoming. A review of the S-model application to QFD is given here to demonstrate its use in making trade-off decisions using cash ¯ow as a metric. In doing this, it is necessary to relate changes in cost and value to changes in price. For a monopoly, the change in price needed to maximize cash ¯ow is equal to one-half of the sum of the value and variable cost changes: dP  dV  dC 2 ! : 14 This expression is also approximately correct for an oli- gopoly based upon Bertrand's classical theory of pricing if competitors do not change their value and variable cost. Similarly if competitors do not change value or cost, the forecast change in demand is given by dD  K dV À dC 2 ! : 15 The resulting change in annual cash ¯ow, A, for a given alternative under consideration is given by dA  D 0 dV À dC 2 !  dDP 0 À C 0 ÀdF À dM Y : 16 where F is ®xed cost and M is investment, assumed paid in equal installments over the life of the product Y. Incorporation of the S-model into the QFD process using a spreadsheet is illustrated in Table 1. Four alter- natives (factors), noted by the double index ij, are con- sidered for improving the cash ¯ow from the sale of a hypothetical automobile. The descriptions of the ij nota- tions for the factors are listed in Table 2. There are N=4 competitors in the segment having a total annual demand of 800,000 units. The baseline price of the vehicle under consideration is $20,000 and the average price of four vehicles is $21,000. Customer needs are listed under the ``What'' column and each factor represents a proposed ``How'' for meeting the customer needs. The results from the ®rst level of QFD are summarized in topmost section of Table 1. In rank order beginning with most important, customers want a more reliable, quieter, better performing, and more fuel- ef®cient automobile. A plus sign under a factor indicates that the factor is expected to have a positive in¯uence on the need, a minus sign is used to signify that a negative effect is expected, and a zero is used to indicate that no effect is expected. The second section of Table 1 lists the system level attribute of the vehicle judged to best meet the need expressed. In sections two and remaining, the base- line levels are shown in the ®rst column on the left. The baseline attributes would be determined from measure- ments on production vehicles. The deviations from base- line would be obtained either from measurements on prototype vehicles or from computer simulations of per- formance. Changes in the attributes are linked to changes in value from baseline in the third section of Table 1. A reduction of one repair was taken equal to $300 (Don- ndelinger and Cook 1997). The remaining value compu- tations are described in Appendix B. The ®nal section in Table 1 represents the computational steps leading to the forecasts of the change in cash ¯ow for each of the factors. The 2.2 liter inline-4 DOHC engine with balance shafts is seen to be preferred to the V-6. The reliability improve- ment package is seen to make a major improvement over baseline. Lightweight material A is seen to make a positive addition to cash ¯ow; whereas, material B makes a nega- tive contribution. At this point, it would be wise to build several prototype vehicles incorporating factors 11, 21, and 31 to verify the product improvements. In going through this simulated exercise, it is worth noting that the fundamental metrics of variable cost and value were not compared against each other in a tradi- tional cost versus bene®t manner. Instead, they were used to compute a forecast of cash ¯ow, a bottom-line metric which formed the basis for making the decisions. Only in this manner can the in¯uence of the investment level on the merits of a possible alternative be accounted for properly. Also the choices were made on how the factors impacted customer needs in the aggregate. No special weighting was given to a need based upon its importance ranking at the top of Table 1 as values determined from the DV method are complete for quantifying the impact of the design changes on each customer need. The ``House of Quality'' construction for QFD has a ``roof '' in which the strength of the interactions between the alternatives are noted. Such a construction is impos- sible using an orthogonal spreadsheet. Instead, interac- tions are displayed using additional columns to the right of those shown in the topmost section of Table 1. The H. E. Cook, A. Wu: On the valuation of goods and selection of the best design alternative 49 interaction column for factors 11 and 21 would be 1121 and so forth. Moreover, the QFD process shown here can be replaced with a design of experiments formalism (Cook 1997) and used to make a quantitative assessment of the interactions between alternatives. In fact, the entire pro- cess of alternatives from system to subsystem to compo- nent design can be expressed as a waterfall of experiments (Kolli and Cook 1994). Each level uses the same bottom- line metric for assessing the merits of the alternatives being considered whether they are subsystem or compo- nent alternatives. SEU A major difference between SEU and the S-model is that the SEU utilities are assessed from an interview with a particular individual (a so-called decision maker); whereas, S-model value represents an aggregate number determined from a survey of potential customers. The decision-maker, usually a key executive within the com- pany, is interviewed to assess the SEU utilities for both costs and bene®ts following a well-de®ned process (Thurston 1990). Using the approach presented by Koppleman (1975) [see the discussion on p. 134 in Ben-Akiva and Lerman (1985)], the decision maker's utilities can, however, be taken as representing those of an ``average individual'' thereby converting them into an aggregate form. (This is but one of several approaches proposed by Koppleman for arriving at aggregate utilities.) If the utilities are taken as an aggregate measure, then the SEU analysis is not compromised by the fact that several of the axioms by von Neumann and Morgenstern (1947) (required for an individual to maximize utility) have been refuted in experimental tests (Kahneman and Tversky 1979; see also Tversky and Kahneman 1981). In this re- gard, Scott and Antonsson (1999) have made a careful analysis to show that because of the necessity for aggre- gation, Arrow's Impossibility Theorem is also not a re- striction to making meaningful cost/bene®t trade-offs. Discussion and summary Market behavior For prices near but below the respective EEVs of the lot- tery tickets, the intercepts and the demand shifts observed in the simulated markets were in reasonable agreement with the predictions of the S-model. The S-model yielded a straightforward explanation of the market-clearing be- havior shown in Fig. 6. The most risk averse respondents would be the suppliers who valued the tickets less than their respective EEVs. The least risk averse would be the buyers who valued the tickets at their respective EEVs. As in any market, those who value the good the least would sell to those who value the good the most. The S-model's stochastic view of aggregate demand predicts an endowment effect as demonstrated here using Monte Carlo simulations. Explanations offered elsewhere for the effect have been based upon loss aversion (Kahn- eman et al. 1990), the nature of movements along indif- ference curves when there are not comparable substitutions for a good, which applies mainly to public goods (Hanemann 1991), and the uncertainty that bidders have in the value of the good (Kolstad and Guzman 1999). The explanation here does not rule out the other mechanisms listed above. The lack of a comparable substitution mechanism for the effect in Hanemann (1990), however, should be very weak in the type of market Table 1. QFD matrix including fundamental and bottom-line metrics (reprinted with permis- sion of the QFD Institute, Ann Arbor) Res Eng Design 13 (2001) 50 studied here. The EEVs of the lottery tickets were well understood by the respondents, which lessens the contri- bution to the effect proposed by Kolstad and Guzman (1999). However, their model is also stochastic and thus a gap between WTP and WTA should exist simply for this reason alone. Loss aversion could have contributed to our ®ndings here but we do not think it was necessarily dominant. The respondents were not told that they had to give up the tickets for a WTA price. They freely chose to sell at a price of their own choosing or not to sell. Thus, we do not see a strong element of seeking compensation for a perceived loss. Value trends The construction of value trends for competing products, Fig. 3, provides a quantitative assessment of the effec- tiveness of how design changes over time have impacted the values of competing products. Based upon conversa- tions with persons who have developed and analyzed value trends in proprietary applications of Eq. 5, value trend plots provide important insight into the competitive landscape, particularly when major product redesigns are introduced as seen here in Fig. 3. Values computed in this manner also provide the value for the baseline product, V 0 . Formulating the general problem of selecting the best alternative The general problem of selecting the best alternative re- quires an assessment of several types of costs (variable, ®xed, and investments in research, development, tooling and facilities) as well as a projection of prices and com- petitive actions. A bottom-line metric such as cash ¯ow, pro®t, breakeven time, return on investment, or internal rate of return needs to be used to assess properly the overall merit of each alternative for the general problem. The time required to develop an alternative for production is also a key metric. Taguchi's model, value engineering, and QFD, did not formally treat demand in their original formulations and this limited the range of problems that could be considered. However, both have been tightly linked to the S-model as described here and elsewhere (Cook 1997; Cook 2000), which opens these methods to treating the general problem. SEU can use the logit model (Ben-Akiva and Lerman 1985) to analyze market share to expand its range of applicability. In considering the possible actions of competitors, value trend plots of the type shown in Fig. 3 can be sup- plemented by the DV method to gain greater insight. For example, a DV study (Wu 1998) has shown that the value of the second rear sliding door is over $1200 per vehicle. This is almost one-half of the value difference found between mvA versus mvB in the 1996 model year. When evaluating a major feature such as the added door, a study of the impact on the bottom-line of each possible scenario should be made. With two competitors, competitor A adds the feature and competitor B either does or does not. Or A does not add the feature and B either does or does not. If the value of the feature is higher than its variable cost and if the investment required is not too large, the outcomes of such scenario studies will always be to add the feature. This conclusion, however, assumes that the added price increment does not make the price go above the maximum level for the market segment. Thus, under the price con- straint, it is necessary to prioritize possible new features on the basis of their projected pro®tability to determine which should be incorporated. The cut-off in adding fea- tures should be at the point where price approaches its upper limit for the segment of buyers targeted, assuming that the resources needed to design, tool, and facilitate the added features have not been fully consumed before this point. The forecast of the bottom-line metric is uncertain and the range of uncertainty should be evaluated. The most straightforward means for doing this is to examine the uncertainty in cash ¯ow using Monte Carlo methods. It is driven by the uncertainties in the values, prices, and price elasticities. Finally, we point out that, although almost all of the S-model applications to date have focused on in- cremental improvements to existing products, it can be applied to highly innovative products. A baseline repre- sented by an existing product or service still needs to be found. The DV method can then be used to develop value assessments for the innovative product. This will, of course, be greatly facilitated if respondents can evaluate prototypes of the innovative product. If the forecast changes in value, cost, and price are large, a non-linear model such as logit model may need to be invoked to make the demand forecasts. Appendix A Surveys regarding the simulated purchase of lottery tickets (Tables 3, 4). In each of the two surveys, you are asked to state your willingness to purchase a lottery at a series of different prices. Assume that your purchase of a ticket entitles you to be a potential winner in a single drawing (lottery) in which the chances of winngin $100 are shown at the top of each column. Each ticket is offered at 20 prices. For each of the prices shown, the box on the left should be checked if you would not the buy the ticket and the box on the right if you would buy the ticket. In each of the two surveys, assume you have been given a single ticket with the odds of winning a $100 prize listed at the top of the column. You have two options: (1) keep the ticket and participate in the lottery or (2) sell the ticket at the price offered. For each of the prices shown, please check tbe box on the right if you would sell your ticket at the price offered. Otherwise, check the box on the left if you would not sell your ticket at the price offered. Table 2. Explanation of attribute indices H. E. Cook, A. Wu: On the valuation of goods and selection of the best design alternative 51 [...]... expressing acceleration performance was Log(1/t) where t is the acceleration tine in seconds The reason for this choice is that a driver was assumed to sense H E Cook, A Wu: On the valuation of goods and selection of the best design alternative Table 7 Computation of the deviation in value from baseline for fuel economy 53 the acceleration force in a psychometric manner similar to noise The critical value... interior noise, acceleration performance, and fuel economy are given in Tables 5, 6, and 7, respectively, for each of the factors evaluated in the simulated QFD study Exponentially weighted three point value curves used for the interior noise and acceleration performance computations were taken from the results of Pozar and Cook (1997) and McConville and Cook (1996), respectively The attribute variable... 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Antonsson EK (1999) Arrow's theorem and engineering design decision making Res Engineering Design 11:218± 228 Silver RL (1996) Value benchmarking to improve customer satisfaction M.S thesis, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign Taguchi G, Wu Y (1980) Introduction to off-line quality control Central Japan Quality Control Association, Nagoya Tanaka M, . Wu: On the valuation of goods and selection of the best design alternative 43 The basic assumption of the S-model is that demand is an analytic function of. shown in the topmost section of Table 1. The H. E. Cook, A. Wu: On the valuation of goods and selection of the best design alternative 49 interaction column