130 
 
 J385 
 
 ,028 COPY 2 
 
 STX 
 
 FACULTY WORKING 
 PAPER NO. 1028 
 
 A Laboratory Comparison of Two Methods of 
 Optimal New Product Concept Generation: 
 Toward Validation 
 
 D. Sudharshan 
 
 v*fc u ' 
 
 #1 
 
 W!fl» 
 
 College of Commerce and Business Administration 
 Bureau of Economic and Business Research 
 University of Illinois. Urbana-Champaign 
 
BEBR 
 
 FACULTY WORKING PAPER NO. 1028 
 College of Commerce and Business Administration 
 University of Illinois at Urbana- Champaign 
 March 1984 
 
 A Laboratory Comparison of Two Methods of Optimal 
 New Product Concept Generation: Toward Validation 
 
 D. Sudharshan, Assistant Professor 
 Department of Business Administration 
 
Digitized by the Internet Archive 
 
 in 2011 with funding from 
 
 University of Illinois Urbana-Champaign 
 
 http://www.archive.org/details/laboratorycompar1028sudh 
 
Abstract 
 
 While several analytical methods for optimal new product concept 
 generation have been reported in the literature, no empirical comparison 
 of their performance has been documented. This paper reports a labora- 
 tory comparison of two such methods. The results reported here add 
 further validity to a computer simulation based comparison. 
 
INTRODUCTION 
 
 This paper reports on a comparison of two critical modelling assump- 
 tions in the generation of optimal new product concepts. While several 
 algorithms have been proposed in the analytical marketing literature, 
 so far the only reported comparisons have been performed using computer 
 simulations. Here, we report on a laboratory simulation study in which 
 optimal new product concepts as generated by two different methods were 
 constructed and compared. The criteria for comparisons were both pre- 
 dicted preference shares and actual preference shares in a sample. 
 
 Development of optimal new product concept generating methods is 
 attracting increasing attention for the purposes of better directing 
 marketing planning and strategy. In 1974, Shocker and Srinivasan pro- 
 posed an analytic framework for the generation of optimal new product 
 ideas. Since then several optimization algorithms have been proposed 
 in the analytical marketing literature to generate optimal new product 
 concepts. 
 
 These methods (algorithms) are: GRID SEARCH (suggested for this 
 problem by Shocker and Srinivasan (1974)); PROPOSAS, Albers and 
 Brockhoff (1977) — this method is now called PROPOPP (Albers and 
 Brockhoff (1982)); ZIPMAP due to Zufryden (1977); the methods due to 
 Gavish, Horsky and Srikanth (GHS) (1983), and PRODSRCH due to May, 
 Shocker, and Sudharshan (1982), Sudharshan (1982). Each algorithm 
 tries to find the optima of an objective function (depicting incremen- 
 tal preference share or incremental revenue) which is derived based on 
 a model of consumer preferences. A general formulation of the problem 
 is provided in Appendix A. 
 
-2- 
 
 One of the major differences between the methods compared here, 
 lies in the preference model incorporated in the respective methods. 
 All the methods except GRID SEARCH and PRODSRCH, assume that it is suf- 
 ficient to allow only a single choice model (k = 1, in the notation 
 used in Appendix A), i.e., it is assumed to be enough to treat each 
 consumer or segment as choosing the same product at all times from an 
 assortment of products. GRID SEARCH and PRODSRCH are more flexible in 
 permitting models which allow consumer preferences to be computed prob- 
 abilistically (k > 1) . The model assumes that over many occasions it 
 is possible that a consumer could choose several products and that all 
 his chosen products come from a subset of the products in the market 
 called his consideration set (the size of which set is denoted by the 
 parameter k) . 
 
 Which of these methods leads to better new products? Answering 
 this question is tantamount to answering the question of which model- 
 algorithm combination best represents reality and solves the problem 
 best. In a computer simulation, it is possible to define reality and 
 test the alternate methods' performances, knowing reality. May, Shocker, 
 and Sudharshan (1982), Sudharshan (1982) report such a comparison of 
 the different methods, in which it was shown that methods that allowed 
 probabilistic choice measures (k > 1), performed better (their new pro- 
 duct concepts obtained better numerical preference shares) than those 
 methods that did not allow such measures in market situations where in 
 reality consumer preferences were defined to be probabilistic. While 
 this was an important result, several questions were left unanswered. 
 If one were to perform such comparisons in real markets, would such 
 
-3- 
 
 findings hold? In real markets would the different product concepts 
 result in "perceptually" different products? 
 
 As a first step toward answering these questions we performed a 
 laboratory study, in which we developed physical realizations of the 
 product concepts generated by two methods and compared their relative 
 performances. We chose the two methods that May, Shocker, Sudharshan 
 (1982) and Sudharshan (1982) found to do best in the single choice case 
 (Gavish, Horsky and Srikanth) and the probabilistic case (PRODSRCH) . 
 
 The Laboratory Study Method 
 
 In this study we carried out all the steps of the market charac- 
 teristics based framework for generating optimal new product concepts 
 (Shocker and Srinivasan (1974)). In brief, we chose a product market 
 and obtained consumer preferences for, and perceptions of, existing 
 products, and then generated optimal new product concepts using two 
 search methods. These concepts were translated into new products and 
 consumer preferences obtained for them also. This permitted us to know 
 that we could create new products from concepts generated by PRODSRCH, 
 and to compare the relative performance of the two "new products" to 
 each other and to their respective predicted performances. 
 
 A schematic showing the general flow of this study leading from 
 calibrating preference models for consumers, constructing a market of 
 existing products, generating "optimal" new products, obtaining consumer 
 preferences for the products in the simulated market, through analyses 
 of the data is presented in Exhibit 1. 
 
-4- 
 
 Exhibit 1 
 Scheme of Laboratory Study 
 
 Stimulus 
 Construction 
 
 Preference 
 
 Judgments for 
 
 Calibration 
 
 and Verbal Report 
 
 Parameter 
 Estimation 
 Using 
 
 LINMAP 
 
 \y 
 
 Existing Products 
 Generation and 
 New Product 
 Generation 
 Using Two 
 Methods and 
 Performance 
 Prediction 
 (Of New Products) 
 
 V 
 
 Stimulus 
 Construction 
 
 v 
 
 Preference 
 
 Judgments 
 
 \<L 
 
 Verbal Reoort 
 
 ( Analysis ) 
 
 Existing Products 
 
 V 
 
 Calibration 
 Measurement 
 
 Calibration 
 
 Market Generation 
 
 and 
 Prediction 
 
 V 
 
 New Product 
 Formulation 
 
 Observation 
 
 Observation 
 
 i 
 
 Analysis 
 
-5- 
 
 As we had to formulate new products from new product concepts 
 gathered during the study, we would not know them a priori. We had to, 
 therefore, use a product type which could be formulated in the labora- 
 tory. 
 
 The translation of concepts gathered from the analysis into new 
 products requires a transformation from the perceptual space of the 
 concepts to the physical space of the products. That is, for a given 
 concept in perceptual space, it might be possible to find more than one 
 location in physical characteristics space. To avoid this problem we 
 chose product characteristics for which psychophysical transformations 
 have been generally standardized. 
 
 The product type we chose was a non-carbonated beverage, with two 
 flavors — raspberry and lemon. Different existing products were formu- 
 lated using different combinations of intensities of the two flavors. 
 Earlier work in sensory optimization (e.g., Moskowitz (1972, 1978) using 
 cherry flavored beverages) and in marketing (e.g., Huber (1975) using 
 lemon-tea beverages) indicated the existence of a distribution of sub- 
 jects' preferences for different flavor intensity levels. 
 
 The particular flavors chosen were such that they (a) presented a 
 plausible combination, and (b) were not available as a combination to 
 the marketplace (McBurney (1981)). 
 
 Also, since all the methods (exceptions being PRODSRCH and GRID 
 SEARCH) are not designed to handle interactions among attributes, we 
 restricted our product type to one combination of two flavors. While 
 sugar was added to each beverage, the concentration of sugar was main- 
 tained at a constant level for all beverages to avoid possible inter- 
 action effects of sugar concentration with the different flavors. 
 
-6- 
 
 Given the model structure incorporated in Gavish, Horsky and 
 Srikanth's (1983) method we had to consider a product type for which we 
 could expect finite ideal points for the different subjects. And, last 
 but not least, for the product type we chose, we had to have reason to 
 believe that the ideal point model, around which the different search 
 methods have been built, would be valid for predicting preferences. 
 
 The robustness of the linear compensatory model which underlies the 
 ideal point model has been demonstrated in the literature (e.g., Dawes 
 and Corrigan (1974); Green and Devitta (1975); Wilkie and Pessemier 
 (1973); and Bettman (1971, 1979)). Additionally, Huber's work (1975) 
 demonstrated a high degree of "predictive validity" (internal) for the 
 "ideal-point" model in predicting subjects' preferences of lemon- tea/ sugar 
 combinations using logarithm transforms of physical (concentration) space. 
 Satisfaction of the above criteria provided us with encouragement to pro- 
 ceed with a "raspberry-lemon" beverage in this study. 
 
 Choice of Subjects 
 
 Subjects for this study were a convenience sample of freshman stu- 
 dents enrolled in introductory psychology courses at a large Eastern 
 public university. While diverse demographic groups may differ in their 
 preference for raspberry-lemon combinations, it is less likely that a 
 difference will be observed in the type of models that are most appro- 
 priate to modeling preference structures for each group (Huber (1975)). 
 
 We needed to have subjects who would be available for both the 
 phases of measurement. We were able to recruit 23 subjects for the 
 study. 
 
-7- 
 
 While we wanted to compare the relative, observed and predicted 
 performance of two methods of optimal new product concept generation, 
 we were also sensitive to studying and reporting at least some aspects 
 of consistency and validity of the data gathering and estimation methods 
 used. We were also sensitive to various possible confounds. Our 
 methodology was designed to reflect such concerns. 
 
 Stimulus Construction 
 
 The stimuli used for calibrating the preference models were fifteen 
 combinations of four levels (25%, 50%, 100%, and 200%) each of raspberry 
 and lemon beverage powders. These were chosen to represent a wide and 
 feasible range of each attribute. Commercially available (Kool-Aid 
 Brand) unsweetened beverage flavors were used. These percentages are 
 relative to the manufacturer's recommended concentration (treated as 
 100% concentration) . The sugar concentration used was also that recom- 
 mended by the manufacturer. In order to avoid respondent bias caused 
 by the color differences of the various calibration stimuli, we colored 
 all the combinations with a food coloring to attain uniformity. 
 
 Preference Measurement 
 
 Subjects performed pairwise taste comparisons of all possible pairs 
 of the fifteen calibration stimuli using standard taste testing proce- 
 dures. To present satiation/dullness of taste buds, participants were 
 instructed to rinse their mouths after each beverage was tasted (a pilot 
 test was carried out with eight subjects to ensure that this procedure 
 had the desired effects with these products). They compared one pair 
 of beverages at a time. 
 
-8- 
 
 Estimation of "k" (Consideration size parameter) 
 
 Verbal reports were obtained from the subjects. These reports pro- 
 vided information to permit estimation of the value of k for this group 
 and also to obtain feedback regarding reactions to the study methodology. 
 
 Consistent with the laboratory study by Pessemier et. al. (1971) a 
 common "k" was estimated for all the subjects. In that study the para- 
 meter "beta" was estimated for all subjects for a particular product 
 class, the assumption being that "beta" was a parameter associated with 
 product type. The parameter k (consideration set cardinality) may be 
 expected to vary with product type and with individual consumers. It 
 could vary with product type since each type might embrace a different 
 number of brands, possess varied degrees of differences between brands, 
 and the degree of involvement of consumers with products in each product 
 type. Across individual consumers, the size of the set of products 
 considered for purchase could also vary. When aggregation of consumers 
 into homogeneous segments is done, perhaps our assumption of a common 
 value of k across segments, but differing across product types, may be 
 borne out. The question requires an empirical answer. 
 
 In the literature, the terms "evoked set," "consideration set," 
 "awareness set," have often been (erroneously) referred to collectively 
 as "evoked set." Consideration/evoked sets have been operationalized 
 quite differently by various researchers. Campbell (1969), and Ostlund 
 (1973), for example, measured "the alternatives that were considered." 
 The phase in the decision process at which such consideration was Co have 
 taken place was not specified. Parkinson and Reilly (1979) measured 
 those alternatives that subjects "would consider buying." Belonax and 
 
-9- 
 
 Mittelstaldt (1978) measured the number of products that were "accept- 
 able." And, Homans, Maddox and May (1977) measured the alternatives 
 that were actively considered. In the stream of modeling efforts focused 
 on in this research, the parameter k represents the set of brands that 
 would be purchased by at least some members of a segment over a suffi- 
 ciently long period of time. This would take into consideration the 
 differences in preferences over situations and some situational exi- 
 gencies such as stockouts, etc. (Shocker and Srinivasan (197-^)). To ^ > , 
 estimate the value of k from observed purchase data requires that such 
 a product be available in the market. Further, at least ten obser- 
 vations would have been required per subject (Blattberg, Buesing and 
 Sen (1980)). Given our choice of product and the time frame for this 
 project, we relied upon each subject's estimate of "the number of dif- 
 ferent fruit flavored beverages (non-alcoholic) that the subject had 
 consumed in the last few months," as the measure for k. 
 
 This measure had the advantage that it involved only the subject's 
 consumption. While such consumption could have occurred in the company 
 of others, most often a range of alternative soft drinks is available 
 for a subject to choose from based on his preference. Also, such occa- 
 sions would provide a broader range of consumption situations. This 
 measure also had the advantage of being relevant to a product type some- 
 what analogous to the product under study. 
 
 Calibration of Decision Models 
 
 The estimation of the parameters for the ideal point model for each 
 
 subject was performed using LINMAP (Srinivasan and Shocker (1976). In 
 
 particular, the strict paired" comparison option in LINMAP IV was to be 
 
-lO- 
 used to provide increased accuracy in the estimations (see Srinivasan 
 (1981)). 
 
 For each subject, based on the 105 pairwise preference judgments 
 obtained, ideal point coordinates and the corresponding attribute 
 weights were estimated. The goodness of the estimated decision model 
 for each subject was determined based on a Kendall's tau statistic 
 reported by LINMAP for the match between observed pairwise preferences 
 and those predicted using the estimated model. If the estimated deci- 
 sion model for a subject did not lead to a significant match between 
 observed and predicted preferences, it meant that almost any random 
 model could have done just as well. This could happen if the subjects 
 did not like the products considered or provided nonsense preference 
 judgments. Care was taken to ensure that subjects understood the 
 seriousness of the study (as part of scholarly research). The calibra- 
 tions very closely corresponded with the verbal debriefings obtained 
 from subjects at the end of the second phase of this study. 
 
 The next step was the creation of a market of existing products 
 based on the consumer decision models thus obtained, and then to 
 generate optimal new product concepts for such a market. 
 
 Market Generation 
 
 We generated existing products in the same manner as in the computer 
 simulation comparison of May, Shocker, and Sudharshan (1982). This 
 step avoided any bias due to subject familiarity with products used in 
 the calibration stage. Existing products were thus generated using 
 ideal points and attribute weights estimated earlier. A value of one 
 for k was chosen, as all the methods compared in simulation could work 
 
-11- 
 
 with this model. This could also be treated as a base model (e.g., 
 Pessemier (1971); Braun and Srinivasan (1975)). We wanted to generate 
 a set of existing products such that sufficient choice would be avail- 
 able for the subjects. We introduced the existing products using our 
 sequential entry strategy with a check, the criterion being that each 
 existing product was to be the closest product to at least one ideal 
 point (as in the simulation) of May, Shocker and Sudharshan (1982). 
 Five existing products were introduced using a crude grid search. To 
 ensure validity, three more existing products were located by inspec- 
 tion to satisfy unfilled "demand." Subjects were, therefore, presented 
 with ten stimuli for the second phase of measurement. Exhibit 2 is a 
 graphical representation of the existing products, the new products, 
 and the ideal points. As can be seen from this figure, the existing 
 products provide a fairly wide variety of alternatives, requiring 
 tradeoffs by subjects in- their preference judgments. 
 
 Optimal new products were then generated using PRODSRCH and GHS. 
 At this stage, the preference shares of both the new products under both 
 k = 1 and k = k (the estimated value) conditions were predicted. 
 
 Product Formulation 
 
 The existing and new products generated in the previous stage had 
 to be formulated into physical products. The product coordinates were 
 generated in a joint space of preferences and perception. This space 
 was described by two perceptual dimensions corresponding to flavor 
 intensities. Each was operationalized as the natural logarithm of the 
 concentration of a flavor. 
 
-12- 
 
 : i 
 
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 KEY 
 
 Ideal Points 
 Existing Products 
 using GRID SEARCH 
 Additional existing 
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-13- 
 
 Thus , to create a product we computed the concentrations of rasp- 
 berry and lemon flavors that were to constitute it. This was done 
 by obtaining inverse natural logarithms of the coordinates generated 
 earlier. This procedure was carried out for the eight existing and the 
 two new products. These products were then formulated as in the first 
 stage of stimulus creation. 
 
 Observations 
 
 Preferences for these ten stimuli were obtained by two different 
 methods from each subject. First, the ten stimuli were arranged pair- 
 wise (45 pairs). Each subject (following the same procedure as in 
 phase one) recorded the stimulus out of each pair that he preferred. 
 The order of presentation of the stimuli was randomized to avoid order 
 bias. After a break of 15 minutes, subjects then ranked the ten sti- 
 muli in order of preference. The procedure used follows Green and Tull 
 (1978, p. 480). Each subject tasted each beverage in turn and put it 
 in one of three groups (with instructions that it was not necessary for 
 them to place an equal number in each group) labeled: 
 
 Definitely like 
 
 Neither definitely like nor dislike 
 
 Definitely dislike 
 Following this, the subjects took the first group and ranked the bever- 
 ages in it from most liked to least liked, and similarly for the second 
 and third groups. (Each taste of a beverage was followed by a water 
 rinse. The procedure for tasting was the same as that used in phase 
 one.) By means of this two stage procedure for the second method, the 
 
-14- 
 
 full set of ten beverages (stimuli) was eventually ranked from most 
 liked to least liked by each subject. 
 
 Verbal Report 
 
 Following the final preference measurement, subjects were asked 
 several questions regarding their preferences for Kool-Aid, lemon and 
 raspberry flavors. These questions were aimed at obtaining responses 
 which could be used to provide face validity ("does it make sense") for 
 the ideal points and attribute weights estimated by LINMAP (Srinivasan 
 and Shocker (1973)). Subjects were provided with a description of the 
 study they participated in and gratitude was expressed. 
 
 Analysis 
 
 In Exhibit 3 we have provided a schematic representation of the 
 plan of analysis followed. 
 
 FACE VALIDITY (l) 1 
 
 The standardized attribute weights estimated for each subject were 
 compared with his verbalizations regarding the relative importance he 
 would place on the concentrations of the two flavors (lemon and rasp- 
 berry) in deciding between beverages with different combination of the 
 two flavors. The estimated standardized attribute weights are shown in 
 columns 2 and 3 of Table 1 for each subject. The first sixteen subjects 
 in Table 1 were those for whom models could be estimated with significant 
 internal validity and finite ideal points. For subjects with serial 
 numbers 20, 21 and 23 in Table 1, preference orderings predicted on the 
 
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-16- 
 
 Table 1 
 
 Face Validity Tabulation 
 
 Subject Att. Wt. 
 Number Lem. Rasn 
 
 2 
 3 
 4 
 
 5 
 6 
 7 
 
 0.68 0.32 
 0.69 0.31 
 0.81 0.19 
 
 0.85 0.15 
 0.83 0.17 
 0.67 0.33 
 
 0.94 0.06 
 
 0.82 0.18 
 
 10 
 
 0.5 
 
 0.5 
 
 11 
 
 0.95 
 
 0.05 
 
 12 
 
 0.67 
 
 0.33 
 
 13 
 
 0.95 
 
 0.05 
 
 14 
 
 0.68 
 
 0.32 
 
 15 
 
 0.48 
 
 0.52 
 
 16 
 
 0.57 
 
 0.43 
 
 17 
 
 0.66 
 
 0.34 
 
 18 
 
 
 
 19 
 
 - 
 
 1,0 
 
 20 
 
 0.4 
 
 0.6 
 
 21 
 
 0.15 
 
 0.85 
 
 22 
 
 0.5 
 
 0.5 
 
 Comments 
 
 Ideal Point 
 
 Attribute Weight Lem. RasD 
 
 0.25 0.75 Rasp. impt. 
 
 Lemon more impt. 
 Lemon more impt. 
 Lemon more impt. 
 
 Rasp, more impt. 
 Lemon more impt. 
 Lemon more impt. 
 
 4.3 5.1 
 
 5.7 4.7 
 2.02 0.0 
 
 3.8 0.0 
 
 5.05 0.0 
 
 5.6 ■ 5.3 
 3.8 2.9 
 
 Strongly prefers 5.7 5.65 
 
 lemon (doesn't 
 
 like sweets) 
 
 Lemon more impt. 4.7 0.0 
 
 Rasp, over lemon 
 
 Lemon much more 
 
 impt. 
 
 Lemon more impt. 
 
 Lemon (but likes 
 
 sweets) 
 
 Lemon more impt. 
 
 Greater weight to 5.5 
 
 raspberry 
 
 Rasp, more impt. 
 
 Rasp, preferred 
 
 Like lemon a lot 100.0 10.8 
 
 Rasp. impt. IRR 4.93 
 
 Lemon more impt. 5.7 5.7 
 
 0.0 
 
 1.3 
 
 5.3 
 
 0.0 
 
 5.6 
 
 5.02 
 
 5.5 
 
 0.0 
 
 5.7 
 
 5.1 
 
 5.5 
 
 5.1 
 
 3.4 
 
 2.5 
 
 0.0 
 
 0.0 
 
 23 
 
 Lemon more impt. 
 Doesn't like 
 
 0.42 0.58 Not available 
 
 0.0 
 0.0 
 
 5.3 
 0.0 
 
 6.6 5.3 
 
 Comments on 
 
 Concentration 
 Desired 
 
 Rasp, on stronger 
 side 
 
 More sweetness 
 More rasp. 
 Lot of lemon 
 Hardly any rasp. 
 Mod. cone. 
 Mod. More Rasp. 
 More rasp, 
 than L 
 Strong beverage 
 
 A little rasp. 
 
 Mod. lemon 
 
 Light cone. 
 
 Stronger lemon 
 
 cone. 
 
 Mod. amount of both 
 
 Strong cone. 
 
 Mod. and More rasp. 
 Strong cone. 
 
 Mod. , and More rasp. 
 
 Weaker tne better 
 
 Like lemon a lot 
 
 Doesn't like Kool 
 
 Aid 
 
 Mod . , and 
 
 More R the 
 
 Doesn't like R or 
 L 
 
 Not available 
 
 i 
 
 L - Lemon 
 
 R, Rasp. - Raspberry 
 
 Cone. - Concentration 
 
 Mod. - Moderate 
 
 IRR - Irrelevant 
 
 Impt. - Important 
 
-17- 
 
 basis of estimated models showed a poor (insignificant) fit with the 
 corresponding preference orderings on which the estimates were based. 
 For subjects 17, 18, 19, and 22, it was not possible to fit signifi- 
 cantly good models with "finite" ideal points. 
 
 In general, there is a good correspondence between respondents' 
 claimed and estimated relative importances for the two flavors, as can 
 be seen from the summary chart, Table 2. There were only two mis- 
 matches (out of 16) between the estimates and the verbalizations of 
 which attribute was the more important one. A closer examination of 
 columns 2, 3 and 4 of Table 1 shows, in general, a good correspondence 
 between the estimated magnitudes of the attribute weights and the 
 qualifications used in verbalizations. 
 
 For example, subject (#8) eight's estimated attribute weights for 
 lemon and raspberry are 0.94 and 0.06 respectively and he "strongly 
 prefers lemon"; subject (#11) eleven's estimated weights are 0.95 and 
 0.05 for lemon and raspberry respectively, and he considers "lemon much 
 more important." 
 
 Examination of the estimated ideal points and corresponding verbal- 
 ization for subjects (#17-22) seventeen through twenty-two (columns 5, 
 6, and 7; Table 1) indicates, in general, a good match between the two. 
 In the instances of infinite ideal points, the verbalization suggested 
 the same. For instance, subject seventeen claimed to like very weak 
 concentrations ("the weaker the better") and the ideal estimated for her 
 was 0.0, 0.0); for subject (//19) nineteen, one of the attributes (lemon) 
 was estimated to be irrelevant. She claimed not to like Kool-Aid. 
 
-18- 
 
 Table 2 
 Attribute Weight Face Validity Summary 
 
 Number of Subjects Claiming 
 to Consider This Attribute as 
 the More ImDortant One 
 
 Lemon 
 
 Raspberry 
 
 Number of 
 
 Subjects Lemon 
 
 estimated to 
 
 consider this 
 
 attribute as 
 
 the more Raspberry 
 
 important one 
 
 11 
 
 
 
 2 
 
 2 
 
 Total 16* subjects 
 
 *Importance weights were tied for one subject. 
 
-19- 
 
 INTERNAL VALIDITY OF ESTIMATION 
 
 Table 3 shows the value of Kendall's tau corresponding to the model 
 fitted for each subject. This statistic reflects the correlation 
 between the preference orderings of the calibration stimuli provided 
 by a subject and the preference ordering of the same stimuli predicted 
 using the model fitted for the same subject. For sixteen subjects, 
 (with finite estimated ideal points) this statistic was significant at 
 the 5% level of significance (a = 0.05). In other words, for 88.9% 
 of the subjects finite ideal points models with significant fits were 
 estimated. So as not to confound our results with poor preference model 
 estimation fit, it was decided to use internal validity as a requirement 
 for including a subject's model for further comparisons. 
 
 CONSISTENCY OF AGGREGATE PREFERENCE MEASURED 
 
 Since the study was concerned with comparing the methods based on 
 the preference shares observed, the concern was with the consistency of 
 the aggregate preference measured. In other words, the stability of 
 the aggregate preference obtained from the subjects was to be examined. 
 Therefore, two measures of preference for the ten products (stimuli 
 used in the second phase of measurement) were obtained for each subject. 
 The first set of preferences was obtained using the method of "pairwise 
 comparisons," and the second, using the method of "rank-ordering." For 
 each pair of products (a,b) (45 pairs in all) the number of subjects 
 preferring product "a" over "b" in "paired comparisons," and also the 
 number of subjects preferring "a" to "b" in "rank orderings" was 
 observed. 
 
-20- 
 
 Table 3 
 
 Internal Validity Tabulation 
 of LINMAP Models 
 
 Subject 
 
 St. # Kendall's 7* for model fitted 
 
 1 0.61 
 
 2 0.35 
 
 3 0.39 < 
 
 4 0.39 
 
 5 0.72 
 
 6 0.37 
 
 7 0.54 
 
 8 0.32 
 
 9 0.58 
 
 10 0.79 
 
 11 0.53 
 
 12 0.72 
 
 13 0.68 
 
 14 0.28 
 
 15 0.63 
 
 16 0.81 
 
 17 0.28 (both co) a 
 
 18 0.4 6 (lemon &) a 
 
 19 0.11 (lemon irrelevant) 3 
 
 20 0.03 (both finite) a 
 
 21 0.2 (lemon co ) a 
 
 22 0.52 (both at co ) a 
 
 23 0.29 (both finite) a 
 
 a - Paranthetical comments refer to the ideal levels o: 
 the two attributes - lemon and raspberry. 
 
-21- 
 
 An indication of the consistency of the preference share measure is 
 provided by the discrepancies observed between the number of subjects 
 preferring product "a" to "b" in one set of preference measurements to 
 the number preferring "a" to "b" in the other set of preference measure- 
 ments. 
 
 The mean discrepancy over the 45 pairs was 1.35, with the mode 
 being 0, standard deviation being 3.83 and the coefficient of variation 
 was 0.26. Thus indicating, in general, satisfactory consistency of the 
 measure of preference share. 
 
 CHOICE OF THE MORE APPROPRIATE MODEL 
 
 To study the importance of the value of the parameter, "k," the 
 fits between the observed ranking of the products and that predicted 
 using each of the two models with k = 1, and k = k respectively were 
 compared. Before comparing the relative performance of the new products 
 of PRODSRCH and GHS with their relative predicted performance, estab- 
 lishment of the appropriate measure of relative predicted performance 
 was required. Some search methods cannot utilize all the information 
 available about a particular market, in their search for an "optimal" 
 new product concept. For instance, PROPOSAS, ZIPMAP, and GHS cannot 
 utilize information regarding the value(s) of "k." As shown in the 
 analysis of the computer simulation data, by Shocker, May, and Sudharshan 
 (1982), the non-utilization of this information, regarding the value of 
 "k," could prove quite costly. For example, if k = 1 was actually the 
 case, GHS would, in general, locate the product with the highest prefer- 
 ence share (in the case of markets with equal segment sales potentials). 
 
-22- 
 
 However, if in fact the value of k was other than 1, PRODSRCH would, 
 in general, find a better new product concept than was found by GHS. 
 
 k was estimated by obtaining the mean of the number of different 
 fruit flavored beverages consumed (in the last few months) by the sub- 
 jects. k was thus estimated to be 4. 
 
 In this study, k = 1 was used in locating a new product with GHS, 
 and k = 4 for generating an "optimal" new product concept for our 
 market with PRODSRCH. (Reminder: these two methods were chosen as 
 they were found by May, Shocker, and Sudharshan (1982) to be the best 
 under these respective assumptions of the value of k.) 
 
 In the analysis of the laboratory data, therefore, the predicted 
 preference shares for the new product concepts with which to compare 
 their relative observed preference shares must first be established by 
 evaluating the accuracy of both the k = 1 and the k = 4 predicted pre- 
 ference shares. 
 
 Evaluation of "k = I" Model 
 
 Since the focus is on the relative performance of different products 
 we examined the relationship between the predicted relative performance 
 of all the 10 products using the k = 1 model (in the second phase of 
 measurement) with their relative performances. The ten products we 
 ranked on the basis of the number of subjects they were predicted to 
 "capture" (were closest to). In Table 4, this ranking is referred to 
 as "Predicted Ranking." 
 
 The same ten products were ranked on the basis of the information 
 obtained from the subjects. Each subject had provided a ranking of all 
 
-23- 
 
 Table 4 
 
 Observed Ranking of Products 
 (Based on Preference) 
 
 Consideration Sets bv Subject 
 
 Subject 
 
 1 
 2 
 3 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 Products 
 (left to right in order 
 of decreasing preference) 
 
 3,8 
 
 4,1,5,2,3 
 
 1 
 
 9 
 
 2 
 
 4,6,3,9 
 
 3,6,5,7 
 
 6 
 
 1 
 
 5,2,6,7 
 
 8,9,10 
 
 3,9 
 
 7,5,4,6 
 
 1,6 
 
 7,5,4,6 
 
 6,2 
 
 II. Ranks by Product 
 (within consideration sets) 
 
 Product Rank 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 
 12 3 4 5 
 
 1 
 2 
 1 
 
 2 
 
 3 
 
 1 
 
 1 
 
 - 1 - 
 
 - 1 
 
 - 1 - 
 
 
 III. Consideration Set Size 
 
 Size 
 
 
 
 Fre 
 
 ouencv 
 
 1 
 
 
 
 
 5 
 
 2 
 
 
 
 
 4 
 
 3 
 
 
 
 
 1 
 
 4 
 
 
 
 
 5 
 
 5 
 
 
 
 
 1 
 
 Mean = 
 
 2 
 
 .6 
 
 
 
 Modes 
 
 = 
 
 1, 
 
 5 
 
 
 IV. Pairvise Product Comparisons 
 
 (a >b product 'a' performs better than T b') 
 
 (a <b product 'b T performs better than 'a') 
 (a = b cannot rank) 
 
 1 >2 
 1 >3 
 1 >4 
 1 =5 
 1 >6 
 1 >7 
 1 >8 
 1 >9 
 1 >10 
 
 2 <3 
 
 2 =4 
 2 <5 
 
 2 <6 
 2 <7 
 >8 
 = 9 
 
 3 >4 
 3 <5 
 
 3 <6 
 3 =7 
 3 >8 
 3 >9 
 
 4 <5 
 
 4 <6 
 4 >7 
 4 >8 
 4 =9 
 
 5< 6 
 
 5> 7 
 
 5> 8 
 
 5> 9 
 
 6 >7 
 6> 8 
 6> 9 
 
 7> 8 
 7> 9 
 
 8< 9 
 
 >10 3 >10 4 >10 5> 10 6> 10 7> 10 8> 10 9> 10 
 
 V. Ranking of Products 
 
 Ran k 
 
 ]_ 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 Product 
 
 1 5 6 
 
 7 3 
 
 9 
 
 4 
 
 2 
 
 8 10 J 
 
-24- 
 
 10 products. Further, each subject indicated the subset of these 10 
 products that he would consider consuming. The development of this 
 ranking is shown in Table 4. The ranking was derived by comparing 
 each pair of products, based on the rankings received by each product. 
 Subtable V of Table 4 shows the ranking of all ten products derived by 
 studying these pairwise comparisons. Note that we could not rank pro- 
 ducts 9, 4 and 2. However, as is evident from subtable IV, they, as a 
 group, fit between products 3 and 10. 
 
 This observed preference based ranking of the ten products was com- 
 pared with the predicted ranking. The statistic used for testing the 
 match between the two is the Spearman's rank correlation coefficient. 
 
 The value of "r " obtained was 0.43. Thus, the null hypotheses that 
 s 
 
 the match between the two sets of ranking is no better than chance can- 
 not be rejected at the 0.05 level (using Siegel's (1965, p. 212) sugges- 
 tion for sample sizes of 10 and above) • 
 
 Evaluation of "k =4" Model 
 
 In the case of the k = 4 model also we wanted to test the null 
 hypothesis: That, "the match between predicted and observed rankings 
 of all the products is as expected by chance;" versus the alternative, 
 "the match between the predicted and the observed rankings of all the 
 products is significantly (statistically) higher than can be obtained 
 by chance." The Spearman's rank correlation coefficient was again cal- 
 culated, for the ranking of the 10 products based on the k = 4 Model, 
 and the observed ranking (as derived in Table 4). 
 
-25- 
 
 The value of r calculated is 0.625, which using Siegel's (1956, 
 
 s 
 
 p. 212) suggestion leads to a t statistic corresponding to r calcu- 
 
 D 
 
 lated of 2.265. This suggests the rejection of the null hypothesis at 
 the 5% level of significance implying that the match obtained using the 
 k = 4 model between the observed and predicted rank ordering is better 
 than can be obtained by chance alone. 
 
 Comparison of "Optimal New Products" 
 
 The Sign Test 
 
 The predicted preference share of the PRODSRCH product relative to 
 that of the GHS product was 4.33. In other words, the PRODSRCH product 
 is expected to be the "better" optimal new product. From Table II, 
 Table 4 it can be seen that the PRODSRCH product was ranked first by 
 two subjects, ranked second by one and ranked fourth by one whereas, 
 the GHS product was included in the consideration set of only one sub- 
 ject, as the third ranked product (this subject's consideration set 
 size was three). This seems to indicate that the PRODSRCH product per- 
 forms better than the GHS product. 
 
 The two products (PRODSRCH f s and GHS's) were compared using "The 
 Sign Test" (Siegel, 1956, pp. 68-75). A test was carried to determine 
 if a significant number of subjects preferred the PRODSRCH new product 
 to the one from GHS. In both sets of preference judgments obtained in 
 the second phase, we found thirteen subjects (out of sixteen) preferring 
 the PRODSRCH new product to that of GHS. The sign test leads to rejec- 
 tion of the null hypotheses at the 0.05 level of significance (calculated 
 probability = 0.011). 
 
-26- 
 
 The Performance of a k = 1 Model in a k > 1 World 
 
 The k = 4 model seems to provide a better fit to the observed pre- 
 ferences Chan does the k = 1 model, thus indicating the importance of 
 using the right value of k, and suggesting that values of k other than 
 1 should be incorporated in models of optimal product concept genera- 
 tion. This same result also indicates that the ranking of the different 
 new products in the computer simulation obtained by May, Shocker, and 
 Sudharshan (1982) seems to be valid. That is, the ranking that would 
 be indicated by the computer simulation is not significantly different 
 from that observed. Generalizability to an external population would 
 require a different design with a much larger sample size (about 200, 
 based on sample size requirements using a chi-squared comparison of pro- 
 portions design) for the testing stage. But, what should be the sample 
 size for calibration? This size would, perhaps, be dependent on product 
 class and the number of segments in that market. This question is itself 
 worth an empirical investigation. 
 
 Summary of Study 
 
 In this study, we developed models of preference (ideal-point 
 models) for a set of subjects for different combinations of raspberry- 
 lemon flavored beverages. Using an estimated value of k, PRODSRCH 
 located its "optimal" new product position (assuming a set of existing 
 products). Using a value of 1 for k, GHS located its "optimal" new 
 product position. Numerically, these positions were quite different. 
 Also, the predicted preference shares for these two "new products" were 
 different, with PRODSRCH producing the "better" product. In comparisons 
 
-27- 
 
 of the new products created corresponding to the generated "optimal" 
 position, we found that subjects could distinguish between the two pro- 
 ducts. Further, the PRODSRCH new product performed (in terms of rela- 
 tive preference) better than the GHS new product, giving us more confi- 
 dence in using the preference measures, computed as here, in evaluating 
 alternative new product concepts. 
 
 IMPLICATIONS FOR MANAGEMENT DECISION MAKING 
 
 The results of the research have some significant implications for 
 marketing planners (and strategists). In general, the research findings 
 are important to marketing planners because, to the extent that their 
 understanding of the factors of consideration in the generation of new 
 product concepts is improved, they may be able to better assess the 
 quality of the solutions obtained for their situation. The multiattri- 
 bute framework used permits an understanding of not only the specific 
 optimal new product concept generated, but also permits comprehension 
 of the product's expected competitive environment — which segments (con- 
 sumers) are expected to include this product in their consideration set; 
 and the products with which it would specifically compete with for con- 
 sumer preferences. 
 
 The influence that some of the simplifying assumptions (made by 
 modellers) have on the "quality" of new products generated indicates 
 that it would be appropriate for managers to give these factors more 
 explicit consideration in the choice of a decision aid system for opti- 
 mal new product concept generation. Most of the optimal new product 
 concept generation methods currently available do not allow for values 
 
-28- 
 
 of the consideration set parameter being other than one. Given the 
 sensitivity of solutions to this parameter, such a facility is to be 
 desired. New product concepts generated using the k = 1 model might 
 result in missed opportunities. Further, marketing researchers must 
 pay increasing attention to obtaining better measures of k. Wrong 
 measures could again lead to new product concepts that are suboptimal. 
 
 While management already knows the importance of market segmenta- 
 tion, the results of this research reinforce this importance. By demon- 
 strating the sensitivity of solution quality to a combination of "k" 
 and segment sales potentials, these results led us to believe that 
 while market segmentation is being performed, marketing researchers may 
 want to incorporate the "consideration set" as an important segmenta- 
 tion variable. Misspecif ication of segments in terms of both k and/or 
 segment sales potentials could lead to false understanding of the oppor- 
 tunities and threats available for new product concepts — opportunities 
 in the form of the expected preference shares, and threats in the in- 
 correct identification of the intensity of competition from particular 
 existing products. 
 
 The new product concept gathering methods not only generate the 
 optimal position, but also provide information as to the extent to 
 which existing products would be affected by the introduction of the 
 new product. Such measures (after proper validation) would provide 
 valuable information for management upon which to base decisions. 
 
 Finally, given the possibility of errors in measurement of key 
 variables such as "k" and segment sales potentials, management may 
 wish to view results of sensitivity analysis with respect to these 
 
-29- 
 key variables for their specific decision context. Such analyses can 
 only be performed by using the more "generalizable" methods. In our 
 framework, PRODSRCH seems to be the method that permits such a flexi- 
 bility while still providing superior results. 
 
 While the laboratory study demonstrated, in a limited fashion, the 
 possibilities of creating products from (numerical) product concepts, 
 such a demonstration was limited to products which involved the sensory 
 perceptions of product attributes (some examples of such products are 
 food, cosmetics and beverages). This issue of realizing actual products 
 from concepts is important for further research. 
 
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 D/79 
 
APPENDIX A 
 
 Following Pessemier, et al . (1971), choice is modelled probabilisti- 
 cally as a function of this measure of preference where the individual 
 or segment is presumed to choose from among the lc-closest competitors, 
 where k is an integer-valued parameter which can vary between 1 and the 
 number of available brands. We operationalize this framework in terms 
 of the following notation. Let: 
 
 B = the set of ru existing brands which constitutes the 
 product-market of interest, j = 1, 2, ..., n • 
 
 M = the set of n individuals and/or market segments which 
 
 represent demand for the products in B, i = 1, 2, ..., il . 
 
 (n ) = the n -dimensional space spanned by determinant product 
 attributes, i.e., p = 1, 2, ..., n . 
 
 (n ) = a major subspace of A in which existing and new products 
 K. A 
 
 may feasibly be located. R is determined by technological, 
 economic, and managerial constraints. R * A, in general. 
 
 Y- = {y- } = the modal perception (over all segments in M) of the j 
 product on the p dimension in A. 
 
 W. = {w. } = the set of attribute weights for the i segment, reflect- 
 ing the relative effect of the p attribute in the i 
 segments' preference decision-making. 
 
 I. = II. } = the most desired attribute levels ("ideal point") of the 
 l l ip J r / 
 
 attributes for the i market segment. This ideal point 
 will be assumed finite, but it need not lie in R. 
 
d . = the evaluation of the j product alternative by the i 
 
 market segment. This evaluation may be in the form of a 
 preference rating, intention to buy, etc. Several alter- 
 native definitions of d. . (also interpretable as a measure 
 
 I* Vi t" Vi 
 
 of proximity of the j product to the i segments' ideal 
 point) have been proposed in the literature. The alterna- 
 tive models are generally special cases of the weighted 
 Euclidean model (1) and are examples of what Green and 
 Srinivasan (1978) have termed conjoint analysis models. 
 
 d.. = [ E A (I. - y. ) 2 w. ] 1/2 (1) 
 
 iJ „_, iP JP iP 
 p-1 
 
 S. = the i ' segments' demand (in $ or units) for all products 
 
 in B over the period. S. will be presumed constant. 
 
 II.. = the share if the i segments' demand allocated to the j 
 product alternative. II.. ■ f(d..) and 
 
 E n. . = 1 for all i = 1, 2, ..., n 
 j=l 1J 
 
 Following Bachem and Simon (1981) and Shocker and Srinivasan (1974), 
 
 several forms for II.. (decision rules) can be considered: 
 
 Case 1 . Every available alternative could have some non-zero like- 
 
 b n B b 
 
 lihood of purchase, e.g., II.. = a./d.. where a. = 1/ E (1/d..) and b 
 
 is a parameter which varies with the product class (Pessemier, et al . 
 
 1971). Since producers would tend to locate their products at or near 
 
 concentrations of demand; if ideal points are distributed throughout 
 
 the space and/or attribute weights vary substantially across segments, 
 
this decision rule should lead to relatively high likelihoods of selec- 
 tion for some products and low ones for others (with some arbitrary 
 assignment of segment demand to any product located precisely at the 
 segment's ideal point (if this occurred)). This rule says that whether 
 or not a segment purchases a brand, there is always the potential to do 
 so, particularly if the time period over which predictions are expected 
 to hold is long. As a model of segment behavior, it is more credible 
 than as a model of individual behavior, where individuals often are 
 observed to restrict their purchases to many fewer than all available 
 brands (Silk and Urban 1978). 
 
 Case 2 . Those who argue individuals would rarely purchase brands 
 they did not like (or judged unsuitable for their intended usage or 
 with which they were unfamiliar) , might prefer a rule which limited 
 positive probabilities of purchase to a subset of alternatives. Indi- 
 viduals are also more likely to become familiar with products which 
 better meet their objectives, due to self-interest (Aaker and Myers 
 1974), therefore a parameter k (possibly k. which varies with each 
 individual), which restricts choice to the k "closest" alternatives, 
 
 b - A , ,00 ...._ ,(k) 
 _.. for a.. 
 
 would lead to a definition of II.. = a./d". for d. . < d)^ / , where d^ 
 
 in i iJ iii» l 
 
 is the distance from the i segment's ideal point to its k closest 
 
 product, and II. . = otherwise. 
 
 Case 3 . A third rule assumes that individuals purchase only their 
 
 most preferred brand, i.e., k = 1, so that H. . = 1 for that i for which 
 
 ij J 
 
 d. . = d and II. . = otherwise. The logic for this would be compelling 
 if choice was deterministic, and all product alternatives were equally 
 available and familiar (that is, why should individuals purchase other 
 
than their first choice under such circumstances?). However, since 
 likelihood of choice will typically depend upon other factors besides 
 product characteristics (such as convenience, availability, salesperson 
 recommendations, brand last purchased, and special situations) one would 
 expect some variance in actual behavior. Surprisingly, then, Pessemier, 
 et al . (1971) found that this first choice model gave good predictions 
 in the aggregate even though it was inferior to Case 1 (above) in pre- 
 dicting individual- level choice. Whether analysis at the level of market 
 segments, rather than individuals, would affect this result is not known, 
 and should depend upon the basis for segmentation used. Additional sup- 
 port for a first choice model was found by Parker and Srinivasan (1976). 
 The conditional logit model has also been used to model frequency of 
 first choice among groups of customers (Hauser and Koppelman 1979, Punj 
 and Staelin 1978) with good predictive results, and represents yet another 
 alternative to those already discussed. 
 
 The form of the objective function for optimal location of a single 
 new product concept changes with the different forms for II... Assume 
 that the firm's single objective is to maximize total incremental demand, 
 or preference share, from the new product introduction. This means that 
 we must account for any demand for the new product which is cannibalized 
 from the firm's existing brands. Let 
 
 f. = the set of k out of the ri existing products closest to 
 the i segments ideal point, 
 
 Y* 
 
 = the set of k out of the il + 1 products, existing and new , 
 closest to that point, 
 
X. = a subset of ¥ . consisting of existing products marketed 
 by the introducing firm, i.e., self-products, 
 
 X* = a subset of f* consisting of all brands (existing and new) 
 
 marketed by the introducing firm, 
 
 II.. = the set of product likelihoods of purchase before new 
 ij 
 
 product introduction, 
 
 II*. = the set of product likelihoods of purchase after new 
 ij 
 
 product introduction, 
 
 = {x } = the new product location, 
 
 and 
 
 = an arbitrarily large number. 
 
 Then we wish to 
 
 . I n*.. .E H.. 
 °M J e xj ij J e Xjl ij 
 
 Maximize Z u. = rrr = f? S. 
 
 i=l j e ¥* ij j e f. ij 
 
 subject to: 
 
 n 
 
 d M (1 - u.) < [ Z A (1.. - x ) 2 w..] 1/2 < d (k) + L(l - u.) 
 i i , ij p ij i i 
 
 p=l 
 
 for all x e R, and i e M where u, is zero or one depending on whether 
 (1) or not (0) the new product is among the k closest for the i seg- 
 ment. 
 
This formulation results in a nonlinear, mixed integer programming 
 problem, involving the location of the new product and indicators as to 
 whether it lies within the k-closest set of products for a market seg- 
 ment. 
 
 If we assume that every brand alternative has non-zero probability 
 of purchase, then the quadratic constraints never become binding (i.e., 
 we have u. = 1 for all i e M) , and the problem reduces to an unconstrained 
 maximization of the objective function over R. If 1 < k < il + 1, then 
 we must consider the quadratic constraints, but the H.. f s will be con- 
 tinuous, except when x» changes for a segment. This means that the 
 derivatives of the objective function will be well-behaved almost every- 
 where, so that gradient-based techniques may be of value. Finally, when 
 k = 1, H . . will be non-zero for only one product, so that the objective 
 function simplifies considerably. 
 
 The major complication in this formulation is the nonlinear con- 
 straints which serve as a linkage between the location variables and the 
 X? sets. With a weighted Euclidean distance measure, even for k - 1, 
 the problem reduces to an integer programming problem with quadratic con- 
 straints, which is a difficult problem to solve in a reasonable amount 
 of time. (Technically it is NP-complete. See Garey and Johnson (1979) 
 for a thorough discussion of this topic.)