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Direct marketing is a type of advertising campaign that allows businesses and nonprofit organizations to communicate directly to a selected group of consumers. The communication methods include postal mail, telemarketing, email marketing, cell phone text messaging, interactive consumer websites, fliers, catalog distribution, and promotional letters. Direct marketing is practiced by businesses of all sizes and types—from the smallest startup companies to the leading Fortune 500 companies.

A key factor in direct marketing is a “call to action.” Each customer is asked to take a specific action, such as returning a questionnaire, placing a catalog order, mailing a prepaid postcard, calling a toll-free telephone number, clicking a link to a specific website, redeeming a discount coupon, or ordering a product online with a promotional code (Bose and Chen 2009). With a call to action, the customers’ responses are directly traceable and easily measured by the direct marketer. Using the data of customer responses over time, we can predict the customer response rate and speed, and we can use that information in making important marketing decisions.

Suppose, for example, that a direct marketer mailed a catalog simultaneously to all customers in a target population. After the launch of a direct marketing campaign, the marketer has recorded the number of orders that have been placed each day. Based on the daily sales record, the marketer needs to estimate the total number of catalog items that will eventually be ordered. If the marketer underestimates the total demand, the catalog item in stock will run out, and the marketer may suffer the loss of customer good will or extra ordering and expedite shipping costs. On the other hand, overstocking the catalog item may result in higher inventory, maintenance, and salvage costs.

A similar prediction problem was evident when we mailed out a questionnaire to individuals in a target population and recorded the number of individuals who responded to the questionnaire each day. The same type of prediction problem is applicable with solicitation letters for fundraising, credit card applications, discount coupons in the Sunday newspaper, and email advertisements with promotional codes.

In this paper, we propose a geometric response model with three parameters to predict the customers’ response patterns in a direct marketing campaign. One of the key parameters is a delivery time that describes the delivery time of a direct marketer’s request and the delivery time of customers’ responses. With the use of mail survey data, we demonstrate the superior performance of our response model over other conventional curve-fitting models.

The remainder of the paper is structured as follows. The following section is a brief review of various response methods that have been proposed in marketing literature. We then develop a geometric response model with three parameters and demonstrate how to estimate these parameters via the maximum likelihood method. We consider three types of probability distributions of the delivery time. We use the weekly response data collected by Huxley (1980) to demonstrate how to estimate the parameter values and compare three different delivery time models. Some concluding remarks are given in the last section.

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