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

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.. The second is to exam

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

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 agag-gregate

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 Diis 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, Pi, values, Vi, 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

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:

Diˆ fi…V1; V2; :::; VN; P1; P2; PN† …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):

dDiˆ K dVi dPi 1

N

X

j6ˆi

dVj dPj

8

<

:

9

=

provided that the price and value changes are small On

writing Eq 2 as a function of the total variables:

Diˆ K Vi Pi 1

N

X

j6ˆi

Vj Pj

8

<

:

9

=

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):

It is seen from Eq 4 that the price where demand goes to

zero is equal to Vi 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 Vi=$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

ViˆN DK N ‡ 1‰‰i‡ DTŠŠ‡ Pi …5†

for product i, i=1, 2, N where DTis 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 ˆ P 1 ‡ E2

E2

…6† where

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 ˆNE2D

For automobiles, the price elasticity E2is 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

E2=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

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 P0 and V0, 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, PN, 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

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 V0, they are of the general form

v…g† V…g†

V0 ˆ ‰gC gIŠ2 ‰g gIŠ2

gC gI

‰ Š2 ‰g0 gIŠ2

…10†

The curve passes through three points: (1) the critical level for the attribute, gC, where value goes to zero; (2) the baseline level for the attribute, g0, where value is V0; and (3) the ideal level of the attribute, gI, 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

g0=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 gC=110 dBA and

gI=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

45

can be used with a degree of con®dence for similar

products whose baseline value V0 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

f P ˆ P… ‡ 2:50† ˆnm… † 0:5Pn

where nm(P*) was the (minimum) numerical index asso-ciated with price P* and nTwas 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

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/EEV1 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

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 PMC 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 VBEEV They would have purchased the tickets from sellers who valued the tickets at

Vs0.4 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

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, VT, for a good

Ac-cording to the S-model, the probability that a single

individual buys the good is proportional to VT±P>0 and

the probability that he or she sells it is proportional to

P±VT>0 Thus, if price is near but below VT, then the

probability that any given individual in the segment will

buy the good is small Likewise, if price is near but above

VT, 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, PB, for a good and

his or her minimum sell price, PS, 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,

VT=(PB+PS)/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

pB=b(VT±P) and the probability for selling was taken as

pS=b(P±VT) The simulated ®ndings are for b=1/5 The two lines representing pBand pS are also shown in Fig 7 For the P±VT<0 region, the simulated choice is between buy or not buy and for P±VT>0, the choice is between sell

or not sell Points on the line equal to unity represent buy for P±VT<0 and sell for P±VT>0 Points on the line equal to zero represent not buy for P±VT<0 or not sell for P±VT>0 The particular simulations shown were made by starting at

P VT

j j ˆ 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'smodel

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

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, gI, 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, gT, 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

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 ˆ dV ‡ dC2

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 ˆ K dV dC2

The resulting change in annual cash ¯ow, A, for a given

alternative under consideration is given by

dA ˆ D0 dV dC

2

‡ dD P‰ 0 C0Š dF dMY : …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 improveimprove-ment 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

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 agggation, 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)

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, V0

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

51