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a Department of Marketing, University of Iowa, W376 Pappajohn Business Building, Iowa City, IA 52242-1000, USA b Department of ... Keywords: Genetic algorithms; Marketing; Product positioning. 1. ...... analytic derivatives. Operations ...
European Journal of Operational Research 146 (2003) 621–633 www.elsevier.com/locate/dsw

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Optimal new product positioning: A genetic algorithm approach Thomas S. Gruca a

a,1

, Bruce R. Klemz

b,*

Department of Marketing, University of Iowa, W376 Pappajohn Business Building, Iowa City, IA 52242-1000, USA b Department of Marketing, Winona State University, 101 Somsen, Winona, MN 55987, USA Received 23 March 1999; accepted 24 October 2001

Abstract Identifying an optimal positioning strategy for new products is a critical and difficult strategic decision. In this research, we develop a genetic algorithm based procedure called GA SEARCH that identifies optimal new product positions. In two simulation comparisons and an empirical study, we compare the results from GA SEARCH to those obtained from the best currently available algorithm (PRODSRCH). We find that GA SEARCH performs better regardless of the number of ideal points, existing products, number of attributes or choice set size. Furthermore, GA SEARCH can account for choice set size heterogeneity. Results show that GA SEARCH outperformed the best current algorithm when choice set size varied at the individual level, an important source of consumer heterogeneity that has been ignored in current algorithms formulated to solve this optimization problem.  2003 Elsevier Science B.V. All rights reserved. Keywords: Genetic algorithms; Marketing; Product positioning

1. Introduction For the brand manager, optimizing a new productÕs positioning is a critical and difficult decision. Addressing this issue, Shocker and Srinivasan (1979) developed a framework for identifying optimal new product concepts using joint space models of consumer perceptions and preferences. Joint space analysis entails mapping the *

Corresponding author. Tel.: +1-507-457-2662; fax: +1-507457-5001. E-mail addresses: [email protected] (T.S. Gruca), [email protected] (B.R. Klemz). 1 Tel.: +1-319-335-0946; fax: +1-319-335-1956.

locations of existing products and ideal points for each individual (or market segment) using multidimensional scaling (MDS) of consumer perceptions via factor analysis, discriminant analysis or similarity scaling. Using this joint mapping of ideal points and product locations, a manager can model consumersÕ choices of existing products, predict their responses to new products, and identify optimal new product concepts. In the ensuing time period, there have been a number of algorithms developed to identify optimal new product positions from MDS-based maps of consumer perceptions and preferences. Thorough reviews of the MDS-based product positioning literature can be found in Sudharshan

0377-2217/03/$ - see front matter  2003 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 2 2 1 7 ( 0 2 ) 0 0 3 4 9 - 1

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et al. (1987, hereafter SMS), Green and Krieger (1989) and Kaul and Rao (1995). Each step in this evolution was motivated, in part, by attempts to improve the realism of the consumer choice setting. For example, the algorithms that account for a probabilistic choice model tend to provide better solutions, larger share projections, for new product positions (Sudharshan et al., 1987). We continue this evolution of improving the description of the consumerÕs decision setting by showing that variations in the size of the individualÕs choice set (choice set size heterogeneity) have a significant effect on the optimal positioning solutions obtained. The optimal positioning algorithm presented in this research, GA SEARCH, accounts for this heterogeneity condition and we found that it dramatically outperforms the best existing optimal positioning algorithm. In this paper, we report the results of two simulation studies and an empirical comparison study. We found that GA SEARCH outperforms the best of the existing optimal positioning algorithms as identified in Sudharshan et al. (1987). In fact, GA SEARCH performs better regardless of the number of ideal points, existing products, number of attributes or choice set size. Furthermore, GA SEARCH performed better when choice set size varied by ideal point (individual), an important source of consumer heterogeneity that has been ignored in current algorithms formulated to solve this optimal positioning problem. 2 The organization of this paper is as follows. In the next section, we briefly discuss previous research on MDS-based optimal product positioning and building the ÔperfectÕ product. This is followed by a description of GA SEARCH. The designs and results of our two simulation comparison studies and empirical study are presented next. We conclude the paper with a discussion of the implications of this research.

2

While Sudharshan et al. (1987, p. 186) mention the possibility of individual choice set sizes, this option has never been implemented.

2. Optimal positioning literature review In their review, Shocker and Srinivasan (1979) formalized the process of identifying optimal new product concepts using input from consumers at every stage from defining the market to predicting the success of a new product. Since then, a number of algorithms have been developed for MDS-based product positioning. The early approaches (e.g., Albers, 1979; Albers and Brockhoff, 1977; Gavish et al., 1983) had two limitations in common. First, the search methods for these procedures were dependent on the number of ideal points (individuals or segments) in the joint space. Consequently, as the number of ideal points rose, so did the complexity of the optimization problem. Second, these algorithms were formulated for the single choice problem in which the demand from each ideal point is assumed to be completely captured by the closest product to it. In essence, this model suggests a consumer always chooses the product nearest to their ideal. While the first limitation simply slowed down the convergence to a suitable solution, the second limitation ignored empirical evidence about the nature of consumersÕ choices in many consumer markets. It has been shown in studies of panel data (beginning with Massy et al., 1970) that consumers often choose probabilistically from a small set of products in the market. One might attribute this behavior to the effects of promotions or availability. However, it has been observed that even if all brands are equally available at no cost, most (53 out of 77) consumers do not choose only their most preferred brand (Best, 1976). This indicates that the probabilistic choice behavior may be a product of variety seeking or factors other than environmental effects (McAlister and Pessemier, 1982). In 1987, SMS presented a new product positioning algorithm called PRODSRCH which incorporated a probabilistic model of consumer choice. In their formulation, demand from an ideal point is distributed to a product in inverse proportion its relative distance from the ideal point so long as the product is within the fixed size choice set of the ideal point. Otherwise, the product captures no demand share from that ideal point.

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To illustrate the differences between the single choice model and the probabilistic choice model, we will use the Shocker and Srinivasan (1974) spatial choice model for finite ideal points. This notation will be used throughout the balance of the paper. • xi;p is the location ith ideal point on the pth dimension, 3 • yj;p is the modal perception of the jth product on the pth dimension, • wi;p is the relative importance of the pth dimension to the ith ideal point, • Si is the sales potential for ideal point i. The weighted Euclidean distance (di;j ) between the ith ideal point and jth product position is given by Eq. (1). !1=2 X 2 di;j ¼ wi;p ðxi;p  yj;p Þ : ð1Þ p

In the single choice model, the demand captured by product j is Si if di;j < di;J for all j 6¼ J . In the probabilistic choice model, the share of an ideal pointÕs demand captured by a given product j is determined by the size of the choice set (k) and the relative distances of all available products. It is assumed that due to self interest, consumers are more likely to choose products closest to their ideal points (Aaker and Meyer, 1974). The brand share for product j from the ith ideal point (pi;j ) is based on Eq. (2): , X pi;j ¼ ð1=di;j Þ ð1=di;k Þ k

for the k closest products;

ð2Þ

¼ 0 otherwise: To determine the demand for product j, the share from the ideal point (pi;j ) is multiplied by the sales potential of the ith ideal point (Si ). In an extensive simulation comparison, SMS showed that PRODSRCH performs better than

3 The ideal point location need not lie within the feasible product space.

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the earlier algorithms of Albers and Brockhoff (1977) and Gavish et al. (1983) in situations where consumers allocate their demand probabilistically. In the single choice situation, one version of the Gavish et al. (1983) algorithm performs very well. Another advantage of PRODSRCH is that it relies on a well tested general purpose non-linear programming algorithm known as QRMNEW (May, 1979). Consequently, the complexity of the problem is determined by the number of dimensions of the search space (product dimensions) rather than the number of ideal points and product positions. For MDS-based product positioning, PRODSRCH is currently considered to be best approach for the single product location problem (Green and Krieger, 1989, p. 132). Recent research shows that the size of the choice set varies whether choice is modeled at the segment (Grover and Srinivasan, 1987) or individual (Gruca, 1989) level. The formulation of PRODSRCH incorporates a parameter k that indicates the size of the choice set for all ideal points in the market. While the formal statement of the PRODSRCH model suggests that k might vary by individual, the PRODSRCH program does not incorporate this source of consumer heterogeneity. In the next section, we formally state the MDS-based product positioning problem. 2.1. The MDS-based product positioning problem Using the choice model described above, the problem of finding a single optimal new product position can be formulated as the following mixed integer nonlinear program 4 (Albers, 1979; Gavish et al., 1983; Sudharshan et al., 1987): X ðpi;new Þðui;new ÞSi over X p ð3Þ Maximize: i

4 Note that this formulation does not include self products, i.e. existing products from the company entering a new product. The self product option is included in SMS paper but the simulation does not involve this situation. We follow their example here. However, the self product situation can be easily incorporated in the GA SEARCH procedure.

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subject to i

d ðki Þð1  ui;new Þ 6

X

!1=2 wi;p ðxi;p  ynew;p Þ

2

p

6 d i ðki Þðui;new Þ

ð4Þ

where X p is the space of p product dimensions, ui;new ¼ 1 if the new product is within the ki closest products to the ith ideal point and 0 otherwise, and d i (ki ) is the distance from the ith ideal point to the ki th closest product. This optimization problem is considered np-hard. In this formulation, we pursue the same goal as in the current MDS-based product positioning literature, i.e. maximize the overall preference share for the new product concept. 5 This is a key consideration for all new products given the role of channel members in controlling access to consumers. Flescher et al. (1984) found that channel members required that a product have a minimum market share of 5% before it would be carried at the retail level. In the ready-to-eat cereal market, Schmalensee (1978, p. 317) suggests that new entrants need a market share of at least 3% to succeed. With the increased attention by retailers to slotting fees and performance guarantees, preference share maximization seems to be a logical starting point for identifying new product concepts using MDS-based models. Once a promising new product location is identified, the problem of transforming this concept into an actual product (or service depending on the application) arises. For example, the

5

If data on costs at different product locations were available along with a competitive pricing model for all brands, then we could solve for the profit maximizing location using GA SEARCH. However, as pointed out by SMS, while many authors call for this increased realism in product positioning (e.g. Bachem and Simon, 1981; Schmalensee and Thisse, 1985), there are significant barriers to such an implementation including cost measurement challenges. In the past few years, there has been significant progress on the issue of the existence of price equilibria in spatial location models (Choi et al., 1990, 1992). A recent review again called for this increased complexity without offering any new insights into these key problems (Kaul and Rao, 1995).

translation between the perceptual dimensions of the joint space and the physical product dimensions is aided by previous research that suggests a logarithmic relationship between actual flavor concentration and its perceived level (Huber, 1975). In such fortuitous circumstances, the results from an MDS-based positioning algorithm can be easily translated into a testable product. However, in most product categories, this translation can be more elaborate. For example, the consulting firm Arthur D. Little has been exploring the relationships between the perceptions of consumers and professional sensory panels for soft drinks (Beverage World, 1983). Using canonical correlation and other methods, relationships between the attributes used by professional ‘‘tasters’’ to evaluate products (smell, basic tastes, mouthfeel) can be related to consumersÕ perceptions of sweetness, smoothness, citrus flavor or even ‘‘cola-ness.’’ Using this information, product positions generated in the consumersÕ perceptual space can be interpreted by professional sensory panels and translated into physical products by mapping their evaluations to product attributes.

2.2. The product positioning search domain The identification of optimal new product positions in a joint space of consumer ideal points and existing product locations is a difficult (nphard) optimization problem. To better illustrate the complexity of this optimization problem, the objective function (maximized preference share) for a simple three ideal point market consisting of two existing brands and each ideal point having a two product choice set will results in the search domain reflected in Fig. 1. The search domains typically found in consumer choice settings are far more complicated than that presented in this comparatively simple figure. Clearly, complexity increases dramatically with increases in the number of brands, number of segments (customers), attribute levels, etc. Genetic algorithms, the optimization algorithm used in GA SEARCH, have been shown to be useful in such complex search and optimization domains (Holland, 1975).

T.S. Gruca, B.R. Klemz / European Journal of Operational Research 146 (2003) 621–633

Fig. 1. Objective function for three ideal point, two existing brands, two product choice set.

3. The GA SEARCH optimal positioning procedure The GA SEARCH procedure is based on a genetic algorithm that is an optimization method inspired by the theory of natural selection (Holland, 1975). It differs from traditional calculusbased optimization that requires continuous and differentiable objective functions. The computation of the derivatives of the objective function in traditional optimization routines are important since many optimization routines use a direction indicated by the first derivative of the objective function (or some proxy) to improve the current solution. In addition, the termination of the calculus-based algorithm may be based on characteristics of the objective function including the first or second derivatives. In problems with high dimensionality, discontinuities or multiple local optima, traditional calculus-based optimization methods are expensive in terms of computation time or they may terminate prematurely leading to a sub-optimal solution. Genetic algorithms are based on a very different approach to the problem of finding an optimal or near optimal solution. A genetic algorithm works directly with the solution space to generate new and better solutions through processes modeled on how organisms adapt to their environment: reproduction, mating and mutation. The only use of the objective function is to determine the fitness of any proposed solution with the ‘‘environment’’ of the

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problem domain. For example, in the optimal positioning problem discussed here, the objective function is based on the preference share estimate for the product position. The stopping criteria are usually based on a degree of improvement over past solutions rather than the evaluation of a derivative of the objective function. This approach to generating new solutions gives genetic algorithms an advantage in very challenging optimization situations. Examples include optimal control (Nachtigall and Vogel, 1996), decision support systems (Pakath and Zaveri, 1995), assembly line balancing (Leu and Matheson, 1994) and scheduling problems (Chen et al., 1995). GA optimization routines have been used recently in marketing applications as well. For example, Balakrishnan and Jacob (1996) use genetic algorithms as a core element in the development of decision support systems for new product design using conjoint preference data. In the specific area of competitive strategy, Midgley et al. (1997) use GAs to ‘‘breed’’ artificial managers (‘‘agents’’) in a competitive market and then compare the actions of these artificial agents to those of real managers. They demonstrate that GAs can indeed be used to build strategies that outperform actual brand managers. GAs have also been used to build timing rules to assess the impact that the timing of marketing mix activity has on oneÕs own market share (Klemz, 1999). Klemz (1999) further demonstrates how these timing rules can be combined with elasticity analysis to provide a richer model of market structure. 3.1. Using GAs to estimate optimal product positions The optimal product positioning problem addressed in this research is described by three types of input information and incorporates both preference and perception data, rather than preference only data (e.g. Balakrishnan and Jacob, 1996). The first data used is the number of attribute dimensions and their boundaries. The second data used is the locations of existing products with respect to these dimensions. The final data includes the locations of ideal points, the dimension weights,

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their sales potentials, and the sizes of the choice sets. Formulating this problem for genetic algorithm optimization is accomplished as follows and is detailed in Fig. 2. Every possible new product position in the p-dimensional joint space can be represented as a decimal p-tuple. This location is encoded into a binary string (known as a chromosome in the genetic algorithm literature) based on the range of possible solutions and the degree of precision required. For example, a string of 8

bits (known as genes) can represent 28 ¼ 256 different locations. Therefore, if a single product dimension is bounded in a decimal space of (5.0, 5.0), then each bit positions represents 0.0391 or 1/256th of the range. A position with the coding 00100100 would be decoded as 3.5924  (36  0:0391  5:00, where 36 is the decimal value of the binary string, 0.0391 is the increment value and )5.00 is the beginning of the bounded search space). With such a coding system, any range of continuous numbers can be represented to any

Fig. 2. Overview of GA SEARCH procedure.

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level of precision required. To improve precision, in this application, a 32 bit coding scheme was used to represent each dimension in the positioning search space. To begin the genetic algorithm optimization process, a population of binary strings (chromosomes) is chosen and randomly generated (Goldberg, 1989). In order to evaluate these solutions, they must be converted to decimal p-tuple representation in the joint space model. In other words, the binary chromosome must be converted into a product position which can be evaluated by an objective function that is based on the locations of existing product and the ideal point locations, dimension weights, sales potentials and choice set sizes. This process is known as evaluating the fitness of the chromosomes. This process is based on the concept of the fitness of the organism (with a given chromosome structure) to compete in the natural selection process. After the initial solutions (new product locations) are evaluated, they are converted back to their binary representations. A number of operations modeled on genetic selection are used to create the next generation of chromosomes. These include reproduction, mating and mutation. The selection of the next generation of chromosomes is a random process that assigns higher probabilities of being selected to those chromosomes with higher fitness values. Therefore, solutions with higher objective function values are more likely to be chosen for reproduction in the next generation. The method we use is Roulette Wheel selection in which the probability of a chromosomeÕs being selected for reproduction is proportionate to its fitness value (Goldberg, 1989, p. 63). This method was selected based on its extensive use in the GA literature. Once chromosomes with high fitness values are selected, they may be recombined into new chromosomes in a process called mating or cross-over. The probability with which this recombination will occur is referred to as the cross-over rate. The mating/cross-over process capitalizes on the binary coding of solutions by randomly choosing a cut point that is used to combine portions of two ‘‘parent’’ binary strings into two next generation binary strings. The part of one parent string before

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the cut point is combined with the latter section (past the cut point) of the other parent to create one off spring. The order of combination is reversed for the other off spring. In this research, we used a cross-over rate of 0.90, and this value was selected based on trial examples using cross-over rates that ranged from 0.80 to 1.00. In addition to mating, genetic algorithms also create mutations of good solutions by randomly changing a single bit of the binary representation. The probability with which this mutation will occur is referred to as the mutation rate. This process ensures that the genetic algorithm will not quickly converge on a local optimum. This is traditionally set to a very small value. Based on Goldberg (1989), we used a mutation rate of 0.01 in GA SEARCH that was selected based on trial examples using mutation rates ranging from 0.001 to 0.01. This next generation of solutions is then converted into the decimal representation for evaluation using the objective function. Generations continue until a stopping rule is met. The stopping rule used in our research was based on no improvement in projected market share for 100 generations. Otherwise the same reproduction, mating and mutation operations are applied to the current solution population until the stopping criterion is satisfied. As with any algorithm formulated to solve an np-hard problem, GA SEARCH cannot guarantee that it will produce a globally optimal solution. Therefore, we must evaluate its ability to produce better solutions than the currently available methods like PRODSRCH. We discuss our simulation comparison studies in the next section.

4. Methodology and comparison results This research contains two simulations and an empirical study. Each category of analysis is detailed separately. 4.1. Simulation studies To improve the validity of methods comparisons, we followed the simulation methodology

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utilized in SMS. Namely, we simulated the positions of ideal points at the individual level within a finite product space. The locations ranged between 0.0 and 10.0 for each dimension. The distribution of ideal points came from a normal distribution with mean 5.5 and standard deviation 3.5. Any ideal points generated outside of the problem boundaries were regenerated. Attribute weights were generated to be positive and sum to one over all product dimensions. The positions for existing products were determined using a grid search procedure. For each problem posed, both PRODSRCH and GA SEARCH were set to search within the same tolerance to identify the best possible new product position. For each market size, there is a fixed level of preference share available to all brands, existing as well as new. The preference share that may be obtained by a new product is determined by the relative positions of the ideal points and existing products as well as the product dimension weights (SMS, pp. 191–192). 4.1.1. Simulation study 1: Homogenous choice set size For the first comparison, we generated 300 problems using the technique previously detailed where each individual in a given market had the same choice set size. Each replication used a random starting condition for the GA estimation. This represents five sets of 60 scenarios (for a total of 300 replications) of the number of ideal points (100 or 300), number of existing products (5 or 15), number of product dimensions (2, 3 or 5) and choice set size (1 through 5). Attribute weights were simulated as well. In every problem, the attribute weights were positive and summed to one. In addition, sales potentials for all ideal points were set to be equal with a value of one. We compared the preference share attained by each algorithm using a paired comparison t-test. The new product locations identified by GA SEARCH were significantly larger than those identified by PRODSRCH. The difference was significant at the 0.00 level (t statistic ¼ 10:12). In addition to this overall comparison, we are also interested in how the relative advantage of GA SEARCH over PRODSRCH varies across the

Table 1 Simulation results for homogeneous choice set size problems Market parameter

Level

Performance index (GA SEARCH result/ PRODSRCH result)100

Number of ideal points

100

109

300 5

108 107

15 2

111 106

3 5 1 2 3 4 5

110 110 114 108 109 109 103

Number of existing products Number of product dimensions

Choice set size

*

Significant difference at the 0.05 level. Significant difference at the 0.01 level.

**

number of ideal points, number of existing products, number of product dimensions and choice set sizes. We constructed a performance index by dividing the preference share from GA SEARCH by the PRODSRCH solution and multiplying by 100. If GA SEARCH identified a better new product location, the index would be greater than 100 or vice versa. We report the average results below in Table 1. We used the performance index as the dependent variable in an ANOVA with the study parameters as the independent variables. The overall ANOVA was significant (F ¼ 3:10, p < 0:00). Two of the study parameters were also significant. The number of existing products was significant at the 0.03 level (F ¼ 4:77). GA SEARCH performed relatively better (about 4%) when the number of existing products is higher (15 compared to 5). In addition, the size of the choice set was significant at the 0.00 level (F ¼ 3:83). GA SEARCH performed relatively better when the choice set was smaller. The average performance index for a choice set of one was 114 compared to 103 for a choice set of 5. This was the only significant difference across choice set size (Tukey test at 0.05 level).

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4.1.2. Simulation study 2: Heterogeneous choice set size For our second study we allowed for individual choice set size heterogeneity. As in study 1, we generated 12 sets of simulated markets: two levels of market size (100 and 300 ideal points), two levels of existing products (5 and 15) and three levels of product dimensions (2, 3 and 5). Dimension weights were set to be positive and sum to one. Sales potentials were set to one as well. This yields 12 different combinations of market parameters. For the individualÕs choice set size, we generated a random integer from a uniform distribution bounded by 1 and 5. The existing products were generated using an assumed choice set size of one, based on the SMS finding that an algorithm designed for the single choice situation (GHS-IV) performed well even in the presence of probabilistic choice. We generated five sets of markets for each of the 12 market combination for a total of 60 replications of the problem setting. The PRODSRCH algorithm was used to find the best position under the single choice model (k ¼ 1) and the probabilistic choice model for k values (choice set size) of 2 through 5. For our comparison, we used the best result of the five positions identified by PRODSRCH. As in the first study, we first tested the overall performance of GA SEARCH and PRODSRCH. Overall, GA SEARCH performed better than PRODSRCH for 59 of the 60 simulated heterogeneous choice set size market situations. A paired comparisons t-test shows that the preference share of the new product location identified by GA SEARCH was significantly higher than the PRODSRCH results (t-statistic ¼ 10:82, p < 0:00). Again we computed a performance index by dividing the preference share from GA SEARCH by the PRODSRCH solution and multiplying by 100. The results are presented in Table 2. The ANOVA is significant at the 0.00 level (F ¼ 5:66). Two of the study parameters were significant. As in Simulation Study 1, GA SEARCH performed relatively better when there are more existing products (F ¼ 4:14, p < 0:05). The average performance index for 15 existing products was 114 compared to 110 for 5 existing products.

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Table 2 Simulation study results for heterogeneous choice set size problems Market parameter

Level

Performance index (GA SEARCH result/ PRODSRCH result)100

Number of ideal points

100

113

300 5

110 110

15 2

114 109

3 5

109 118

Number of existing products Number of product dimensions

*

Significant difference at the 0.05 level Significant difference at the 0.01 level.

**

In addition, the relative performance of GA SEARCH varied significantly by the dimensionality of the product space (F ¼ 8:17, p < 0:00). The performance index was significantly higher for 5D spaces (average ¼ 118) compared to 2D or 3D spaces (averages of 109 and 109 respectively). From our results, it is clear that when choice set size is not constant within a population of decision makers, GA SEARCH performs much better than PRODSRCH. Since this condition is probably present in many consumer markets, the ability of an algorithm to accommodate these variations is important. Overall, from the results of these two simulation comparisons, we conclude that GA SEARCH is superior to PRODSRCH in a wide range of product positioning situations. 4.2. Empirical comparison study In addition to the two simulations, and to further illustrate the impact of consumer choice set size heterogeneity on product positioning, we modeled a US retail coffee market using the wellknown IRI coffee scanner data. Using a year of purchases (March 1980 to February 1981) from the Marion, IN market, we developed a joint space map of the branded ground coffee market. As in Fraser and Bradford (1983), we retained only those brands that accounted for at least 1%

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Table 3 Regular coffee brands in Marion, IN market Brand name

Market share in study period, % (based on lbs or lb equivalents)

Folgers Folgers Flaked Chase and Sandborn Maxwell House Brim Sanka

32 23 4 28 6 7

of the purchases of the panel. 6 These six brands (listed in Table 3) accounted for more than 95% of the branded coffee purchases. There were 210 continually reporting households in the sample. To construct the joint space of product locations and household ideal points, we used the pickany data procedure developed by Levine (1979). The pick-any procedure has been used in several past marketing applications (Green and DeSarbo, 1981; Holbrook et al., 1982; Moore and Winer, 1987). Of available alternative procedures that utilize choice data to create joint space maps, this procedure offers the best balance of ease of use, face validity and predictive ability (Elrod and Winer, 1988). Input for the pick any procedure consisted of purchase vectors for each household. Each element of the vector reflected the number of pounds (or pound equivalents for flaked brands) purchased by the household during the study period. Following Moore and Winer (1987), a three dimensional solution was used. The product positions are shown in Figs. 3 and 4. As expected, the decaffeinated brands are clustered together away from the other brands. Folgers Flaked brand is also positioned away from the core of brands. This may be due to its designation as a flaked brand.

Fig. 3. Marion ground coffee market.

Fig. 4. Marion ground coffee market.

6

House and generic brands were excluded since previous research suggests that there is a vertical structure of the grocery markets based on price. Specifically, lower priced brands tend to compete more with each other and not as much with premium brands (Blattberg and Winisieski, 1989).

We cross-validated the product positions using a map developed by using brand switching data (Lehmann, 1972). A brand switching matrix is used as input to a nonmetric, MDS program

T.S. Gruca, B.R. Klemz / European Journal of Operational Research 146 (2003) 621–633 Table 4 The number of different brands purchased by each household Choice set size, k

Proportion of sample (%)

Proportion of volume (%)

1 2 3 4 5

27 30 26 15 1

26 31 25 16 1

(KYST by Kruskal et al., 1973). The output is a perceptual map with the product locations. 7 The inter-point correlation between the distances obtained using the pick any scaling and the Lehmann procedure was 0.87. These results compare favorably with the 0.69 obtained using KYST to cross validate the results of the pick any scaling procedure (Holbrook et al., 1982). The Shocker and Srinivasan (1974) model for finite ideal points was used to determine the share for any given product position (Eqs. (1) and (2)). In this application, we assumed that the attribute weights (wi;p ) were all equal (1.0). Examining the number of different brands purchased by each household, we find the following distribution, illustrated in Table 4. The choice set size for this sample ranges from k ¼ 1 to 5 with a mean k of 2.33 and standard deviation of 1.08. Households with a choice set of one brand account for 26% of total purchase volume. This compares with 35% of the households in Grover and Srinivasan (1987) in their examination of a 12 brand instant coffee market. Since PRODSRCH cannot handle individual level choice set size (choice set size heterogeneity), using this joint space configuration, we employed PRODSRCH to find the optimal product position under the assumption that the choice set size for all ideal points was the same. We rounded the average k value to 2 (k ¼ 2). The resulting location is indicated in Figs. 3 and 4 as ‘‘Prodsrch k ¼ 2’’. The PRODSRCH solution for k ¼ 2 is a clone of the Folgers Flaked brand. Evaluating this solution, we

7

The relative positions in the product map generated from brand switching data was similarly configured. These maps are available to interested readers.

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find that the position identified by PRODSRCH achieves a preference share of 13%. When we employed GA SEARCH, which accounts for choice set size heterogeneity, (described in the previous section) to this same problem, we found a different and better solution. This new product concept is located closer to the larger regular ground brands of Maxwell House and Folgers as well as the minor brand Chase and Sandborn. The expected sales potential for this GA SEARCH location is 17% (recall that the PRODSRCH solution is a 13% preference share product solution). From a practical standpoint, it is worth noting that a 4 point difference in preference share can be quite substantial, namely, each share point in the US coffee market is worth approximately $50 million at retail. As stated previously, SMS suggest that ‘‘algorithm performance under erroneous specification of k (choice set size) remains a question for future research’’ (page 199). Addressing this issue, GA SEARCH directly models consumer level choice set size. We find that the product position identified using a single (average) choice set size for the population (those identified by PRODSRCH) is different and less desirable (smaller preference share estimate) than that identified using GA SEARCH, an algorithm which can incorporates an individual choice set value for each ideal point.

5. Discussion The two simulation comparisons and empirical study reported in this research demonstrate the power and flexibility of using genetic algorithms to estimate optimal new product positioning. In the first comparison, the relative performance advantage of GA SEARCH over PRODSRCH is as large as the gap between PRODSRCH and the single choice algorithms it replaced. Note that the design of this first study should have favored PRODSRCH since 80% of the situations used a probabilistic choice model with a fixed size choice set, the situation for which PRODSRCH was designed. In the second simulation comparison, the choice set size was varied and overall performance

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advantage of GA SEARCH over PRODSRCH was larger. Making this change to the basic algorithm was quite minimal. It mainly involved replacing a constant with a vector in the fitness evaluation section of the algorithm. This simple change dramatically increased both the performance of the algorithm and improved the realistic nature of the market description. The practical result of modeling choice set size heterogeneity can best be illustrated by looking at the coffee study reported in this research. Namely, the product position specified by GA SEARCH is both higher in projected preference share and is located at a noticeably different product position than that reported using PRODSRCH (Figs. 3 and 4). This research also illustrates how flexible the genetic algorithm approach can be in complex product positioning problems. If required, choice can be modeled with an idiosyncratic mix of ideal points, anti-ideal points, or vectors depending on the individual ideal point. The only requirements are that a common set of dimensions be used for product positions and locations on these dimensions can be used to compute preference shares from each ideal point in the market. The basic optimization engine does not change. The only alterations come in the fitness function evaluation procedure.

6. Conclusions GA SEARCH meets the Caroll and Green (1997) criteria for an MDS-based new product positioning algorithm: powerful and flexible. First, our research clearly indicates that GA SEARCH outperforms the best available algorithms designed to solve this optimal positioning problem. Second, GA SEARCH is flexible and it easily incorporates an important but ignored source of consumer heterogeneity choice set size to provide superior product positions. Having illustrated such a powerful and flexible optimal product positioning tool, we hope more progress can be made in making analytical product positioning a useful and valuable managerial tool.

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