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Sawtooth Software TECHNICAL PAPER SERIES Advanced Simulation Module (ASM) for Product Optimization v1.5 Technical Paper Copyright 2003, Sawtooth Software, Inc. 530 W. Fir St. Sequim, WA (360)

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Sawtooth Software TECHNICAL PAPER SERIES Advanced Simulation Module (ASM) for Product Optimization v1.5 Technical Paper Copyright 2003, Sawtooth Software, Inc. 530 W. Fir St. Sequim, WA (360) Advanced Simulation Module for Product Optimization v1.5 Technical Paper October 2003 Copyright 2003, Sawtooth Software, Inc. Introduction Conjoint analysis is used by many marketing organizations to assess the likely degree of success of potential new products. Conjoint analysis assumes that an individual s liking for a product can be approximated as the sum of part worths for its separate attribute levels. A conjoint questionnaire conducts a designed experiment for each individual, providing data from which it is possible to estimate his or her part worths. Those estimated part worths can be used in choice (market) simulations. The simplest simulation specifies several competitive products in terms of their attribute levels, and then predicts which of those products each respondent would prefer. Such results may be used to estimate market share for hypothetical new or modified products, as well as their potential revenue and likely profitability. In the absence of competitive products, conjoint data (calibrated using purchase likelihood data) can also be used to simulate respondents likelihood of purchasing specific products. Conjoint analysis has been enormously successful since its introduction in marketing research more than 30 years ago (Green and Rao, 1971), largely because of its simulation capability. Simulators use part worth data, which can be difficult to understand for many managers, and convert them into product shares of preference resembling market shares that are easy to understand and immensely practical for managers. Simulators represent the best conjoint has to offer in terms of assessing attribute importance and sensitivities, complex interaction or substitution effects, and the likely success of products given certain competitive conditions. Toward Optimization Marketers often turn the question around: rather than ask How good would this product be? they often ask What product would be best? The Advanced Simulator Module (ASM) has been developed to answer such questions. Sawtooth Software is by no means the first to consider how one might search for products that optimize market share or profitability. Green and Krieger (1993) considered the same problem years ago, proposing a method similar in many ways to what we have done. Conjoint simulators provide the best means to date for product optimization. They can take into account the characteristics of currently-available products as well as the desires of a heterogeneous population of potential buyers. Subject to reasonable caveats about the quality of respondent sampling and questionnaire design, conjoint simulations can accurately assess likely product success long before a product is ready for test market. The ASM can optimize based on 1 utility, purchase likelihood, market share, revenue or profitability; however, profitability optimization requires additional user-provided information about feature costs. If you include feature costs, the ASM can also perform cost minimization searches, to search for products that meet some threshold of utility, share, revenue, or profit while minimizing cost. Finding the best product by manually specifying many simulations would be difficult because there can be such a large number of potential products to evaluate. Suppose products are described by 10 attributes, each with 5 levels. Then the number of possible products (ignoring the possibility of interpolation between levels) would be 5 to the 10th power, almost 10 million. Although each of those possible products could be simulated, examining all combinations would take too long to be workable. When we consider that one may wish to optimize multiple products simultaneously, even situations with few attributes would be infeasible for manual search. Another possible approach would be to configure a product with attribute levels that are most desirable on average. But that would fail in two ways. First, it would almost certainly choose an unprofitable product because it would select products with many desirable features and the lowest possible price. The second reason such a method would fail is that it does not recognize heterogeneity in the desires of the market. Marketers know that the most successful products are those that appeal to buyers who are not already satisfied by existing products, and hence existing products must be taken into account. The ASM uses heuristic search strategies to find the optimum (or near-optimum) product or a portfolio of products. It can optimize several kinds of objectives, including estimates of market share, total revenue, profitability, purchase likelihood, and total utility. It does this by exploring the response surface of the objective, such as share, corresponding to attribute levels for the product(s) of interest. Although most response surfaces are multi-dimensional, it is useful to imagine there are only two independent variables. Suppose a product category has two attributes, both continuous, and that we are interested in market share. Then we could represent share estimates from many simulations by a three-dimensional model. The product attributes would be represented by the X and Y axes, and the shares from simulations of each combination of attributes would be represented by the third dimension, the height of a surface. Our task is to find the highest point on that surface. One strategy would be to imagine a grid underlying the surface and to measure its height at every grid point. This is a reasonable approach if there are few dimensions, but quickly becomes unworkable as the number of dimensions increases and the number of grid points multiplies. If the surface has a single peak, another strategy would be to pick a point on the surface, find the direction in which the surface rises most rapidly, and move in that direction to find a higher point, repeating the process until the highest point is found. Such steepest ascent hill-climbing methods are efficient with surfaces having single peaks, but can be misled if there are multiple peaks. Because different optimization strategies are more effective with different kinds of response surfaces, the ASM provides several from which to choose. The ASM can be used to analyze conjoint data from any of Sawtooth Software s conjoint systems (ACA, CBC, or CVA). It can be used for full-profile, partial-profile, and alternative-specific designs. Estimation can include linear terms and interaction terms. It can also be used to analyze conjoint or preference data provided by the researcher that was not necessarily generated by Sawtooth Software s systems. The ASM can also be used with aggregate conjoint data, though it is most effective with individual data. 2 The paragraphs above have provided a general introduction without details; but several topics require closer examination. These include the types of product simulations available, the specific optimization methods provided, and the ways cost information is used in the calculation of profitability. Simulation Methods The Advanced Simulation Module provides several methods for simulating preferences. With the exception of Utility search which requires no additional description, these are all available in the regular Sawtooth Software SMRT simulation software, and are fully described elsewhere. Here we shall provide just a brief description of each, ranging from simplest and fastest to slowest but most useful. First Choice or Maximum Utility: This is the simplest simulation method. Each respondent s utility for each product is estimated by summing the appropriate part worths. The utilities for all products are compared, and the respondent is assumed to choose the product with maximum utility. Another way to say this is that we assume all of a respondent s choice likelihood accrues to his first choice product, regardless of the magnitude of difference in utility between that product and the others. The estimate of a product s share of market is simply the percentage of respondents for whom it has highest utility. This method has some desirable characteristics. It is simple and easy to understand. Also it is fast, so optimizations done with First Choice simulations proceed quickly. Most important, First Choice simulations are not vulnerable to difficulties caused by the inclusion of similar products, such as when evaluating portfolios of similarly branded alternatives. We ll describe this problem shortly. However, first choice simulations also have some undesirable properties. They tend to exaggerate the shares of popular products and underestimate the shares of unpopular products. Further, unlike other methods, there is no way to tune them to compensate for this characteristic. A second shortcoming is that since all of a respondent s choice likelihood is allocated to a single product, the standard errors of the resulting shares are larger than with other methods that distribute a respondent s choice likelihood across several products. At the current stage of simulation technology, the First Choice method is mainly of historical interest, and we would not advocate using it in optimizations unless there are special circumstances, such as a compelling need for computational speed, the benefit of exceptionally large sample sizes, and confirmation that the relative scaling of share results is appropriate. Share of Preference: This method is only slightly more complicated than the First Choice method. As with that method, each respondent s utility is computed for each product. However, rather than assigning all of a respondent s choice likelihood to the product with maximum utility, we allocate choice likelihood among products by first exponentiating all products utilities (converting them to positive numbers) and then percentaging the results so that they sum to 100. (An example appears below.) This is equivalent to employing a logit model for product choice. The Share of Preference method is nearly as fast as the First Choice method, and has the additional benefit that the results can be tuned so the ratio of maximum to minimum estimated product shares can be adjusted as desired. This is accomplished by multiplying the part worths 3 by a positive constant (the exponent ). A large constant causes more extreme share predictions, and in the limit the Share of Preference method approaches the First Choice method. A small constant causes shares to be more nearly equal, and with a very small constant the predicted shares will all become nearly equal. However, as with all logit models, the Share of Preference method is vulnerable to what are known as IIA problems. (IIA is short for independence from irrelevant alternatives ). A simple example can demonstrate this. Suppose there are two quite different products (A and B) for which a respondent has utilities of 0 and 1.0. Then Share of Preference estimates of the respondent s choice likelihoods would be as below: Product Utility Exponentiated Share Utility Estimate A B Now suppose we introduce another product, A, which has characteristics identical to those of product A. Then in a three-way simulation we obtain the following estimates: Product Utility Exponentiated Share Utility Estimate A A B We have nearly doubled the total estimated share of the A products merely by including a second copy. We could drive the estimated total share of the A products as high as we like simply by including many of them. But we know this is not a realistic simulation of real world conditions, where a respondent who prefers traveling via car to a bus is likely to choose the car no matter how many buses are available. By contrast, the First Choice method assigns the respondent to product B no matter how many copies of A are included, demonstrating much more reasonable behavior. With logit models, a newly introduced product takes share from existing products in proportion to their current shares. (The ratio of original shares 26.9 / 73.1 = is the same as the ratio of new shares 21.2 / 57.6 = ) This property is useful in some circumstances, but presents problems in our context because a newly introduced product will probably not take share from others proportionally to their shares. For example, an additional package size for a soft drink may be expected to take more business from other sizes of its own brand than from other brands. We refer to this important property as differential substitution. This IIA property of logit models is troubling, because we may wish to estimate the total market share for a portfolio of products that are somewhat similar to one another. We may wish to know how many more units of a make of car will be purchased if we offer a convertible in addition to a sedan, or how many more ounces of cereal will be purchased if we offer a jumbo package in 4 addition to a regular sized one. In the case of aggregate models, such as a main effects logit model, the Share of Preference method is obviously inappropriate for questions like these. IIA problems are substantially reduced when dealing with individual rather than aggregate simulations. Individual simulations often allocate nearly all of a respondent s preference to a single product, so they become more like First Choice simulations. Thus, Share of Preference simulations are likely to be less misleading when used at the individual level. The Share of Preference method should provide good results when all of the products in a simulation are equally similar to one another. However this is a hard condition to ensure, so it is more prudent to use a method that is not vulnerable to this difficulty. Share of Preference with Correction for Similarity: This simulation method was implemented by Sawtooth Software many years ago. It corrects for product similarity by decreasing estimated shares of products in proportion to their similarity to others. At the time of its introduction it provided an improvement, compared to unadjusted Share of Preference simulations. However, though in the right direction, the corrections are somewhat arbitrary. Technological advances in the last few years have provided another method which is superior. Randomized First Choice (RFC): This is the preferred method for simulations involving choices among competing products. It is slower than other methods, but overcomes the previously described shortcomings. Results for each respondent are simulated many times in sampling iterations. The part worths are perturbed randomly for each iteration. The perturbations are of two types. First, the part worths themselves are perturbed (by adding attribute error ), and the modified part worths are used to sum utilities for each product. Then the utility sums themselves may be further perturbed (by adding product error ). For each iteration the respondent is allocated to the product with highest (perturbed) utility. The results for all iterations are averaged to produce the final estimate of choice share for each respondent. It is clear that real respondents are somewhat inconsistent when making choices. This suggests that the values they ascribe to product features actually vary from moment to moment, and the RFC procedure is an attempt to mimic that variability. This method is much slower than the preceding ones, because each respondent s choices are simulated many times rather than just once. However the method has compensating advantages. The default for the RFC method is to add only attribute rather than product error. In that case IIA problems are avoided and similar products do not receive inflated shares. This means that RFC simulations are appropriate for a wide range of occasions, including estimation of the value of line extensions and portfolios of similar products. Also, unlike simple First Choice simulations, Randomized First Choice simulations can be tuned to provide differing ratios of extremity between shares for popular and unpopular products. The magnitudes of perturbations of part worths and utilities can be adjusted. In general, as magnitude of perturbations is increased, predicted shares become more similar. In the limit, with very large perturbations and many sampling iterations, all products shares would become equal. It is commonly found that First Choice simulation results are too extreme. One reason is that in the real world not every product is always available, and occasionally a buyer must accept a product that would not otherwise be his or her first choice. Like Share of Preference simulations, and 5 unlike First Choice simulations, Randomized First Choice simulations can be tuned (by adjusting the magnitude of perturbations) to more closely mimic actual market shares. Purchase Likelihood Simulations: Sometimes a product category is so new that there are no competitive products to which it may be compared. At such times it is useful to model purchase likelihood rather than share of market. Some conjoint methods produce part worths that are scaled so that utility sums can easily be converted to estimates of purchase likelihood. In that case a simulation could involve a single product, and if there are multiple products, their results are unaffected by one another (for example, all products could have high likelihoods, or low likelihoods). When simulating multiple products with Purchase Likelihood simulations the researcher may be less interested in the sum of the purchase likelihoods than in their maximum for a given respondent. The researcher may seek a portfolio that has something for everyone, and may not care how attractive each respondent finds his/her second-and-third-choice products. For this reason the option is provided of averaging only the likelihoods for highest-likelihood products in a portfolio. Purchase Likelihood simulations can be very fast. But we caution the user not to interpret the results literally. Respondents are notoriously unable to estimate likelihoods of any kind, and likelihoods of purchase of new products are no exception. Purchase Likelihood estimates should never be interpreted as more than directional indicators of buyer preference. Their absolute levels are probably meaningless. Recommendation: We recommend Randomized First Choice as the preferred method in nearly all circumstances. If a much faster method is required, the First Choice method has the advantage of not inflating shares for similar products, but its estimated market shares will probably be too extreme and their standard errors will be relatively large. The Share of Preference method is also fast, and can be tuned to provide the desired amount of variation in product shares, but may inflate the shares of products that are similar to others. This difficulty can be partially ameliorated by using Share of Preference with Correction for Similarity, but the correction is less accurate than that provided by Randomized First Choice. If the product of interest is unique or too new for there to be a competitive product category, then Purchase Likelihood simulations may be appropriate, but only to provide a relative ranking of products rather than to provide accurate estimates of actual purchase likelihoods. All simulation methods can be run either with respondents weighted equally or with respondents weighted by a variable selected by the user. Furthermore, external effects can be included, and the Exponent (scale factor) may be tuned, when appropriate. 6 Optimization Methods To conduct product searches in the ASM, the user specifies several items: One or more products for which optimal attribute levels are to be discovered. Competitive products that will be held constant throughout the analysis (unless searches are to maximize utility or purchase likelihood for a single offering). The objective to be optimized (estimated mark

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