Example Models

Marketing

@RISK Models

Minimum edition: @RISK 6.0 Standard. A Markov chain is a process observed through time where the probability distribution of the next state of the process, given the current state, is independent of the past states. This model illustrates the evolution of prices through time.

This model finds the optimal numbers of ads for a company to place in various media to minimize the mean cost per exposure. There are two sources of uncertainty for each media: the total audience reached and the percentage of this audience that is the target for the company.

Minimum Edition: @RISK Industrial. The goal of this model is to determine the allocation of marketing expenses to retaining current customers and acquiring new prospects. It assumes a nonlinear cost effectiveness functions for the percent obtained (either customers retained or prospects acquired), based on the amount spent per customer or prospect.

This model explores an incentive to increase customer loyalty in a market such as the cell phone market. Each year, each of our customers remains with us with a given probabilit, and each of the competitors' customers switches to us with another given probability. The question is whether it is worth our while to incentivize their customers to switch to us. The model assumes a one-time monetary incentivewhen they make such a switch.

This model is for a company that mails its catalog to a customer every quarter. For each customer, the company keeps track of the recency (the number of catalogs since the customer last purchased) and frequency (the total number of purchases so far). It costs \$1 to mail a catalog. If the customer makes a purchase, the company's profit (not counting the cost of mailing the catalog) is Pert distributed with given parameters. The company keeps mailing catalogs to a customer until 24 catalogs produce no purchases, that is, until recency reaches 24.

Minimum Edition: @RISK Industrial. This model illustrates pricing in a two-channel market, Web and retail. If the price in one channel is set low, it will not only create a higher demand in that channel, but it will tend to cannibalize demand from the other channel. So the pricing decisions are not obvious. RISKOptimizer is used to find the prices that maximize the mean profit from the two channels.

Minimum Edition: @RISK Industrial. This model illustrates why companies lower their prices from time to time, that is, why they have sales. Essentially, it is because different customers have different reservation prices, the most they are willing to pay for a product they want. By reducing the price at key times, companies are able to attract customers with lower reservation prices who would otherwise not purchase.

Evolver Models

This example illustrates two uses of Evolver. In the Parameter Estimation sheet, historical monthly values of sales and advertising are used to estimate the parameters of a sales function. Evolver is used to find the parameters that minimize the sum of squared errors between actual and forecasted sales. Then in the Optimization Model sheet, Evolver is used to maximize the NPV of net profits by choosing monthly advertising levels.

NeuralTools Models

This model uses NeuralTools to classify a large number of email messages as spam or not spam, based on a large number of characteristics of the messages. It also uses the Variable Impact tool in NeuralTools to screen for predictors that might not be useful.

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