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Article Excerpt
The main objective of this paper is to provide a decision-support system of micro-level customized promotions, primarily for use in online stores. Our proposed approach utilizes the one-on-one and interactive nature of the Internet shopping environment and provides recommendations on when to promote how much to whom. We address the issue by first constructing a joint purchase incidence-brand choice-purchase quantity model that incorporates how variety-seeking/inertia tendency differs among households and change over time for the same household. Based on the model, we develop an optimization procedure to derive the optimal amount of price discount for each household on each shopping trip. We demonstrate that the proposed customization method could greatly improve the effectiveness of current promotion practices, and discuss the implications for retailers and consumer packaged goods companies in the age of Internet technology.
Key words: customized promotions; profit optimization; Internet marketing; decision support system; personalized marketing; econometric models; purchase incidence; brand choice; purchase quantity; variety-seeking; inertia
History: This paper was received June 7, 2000, and was with the authors 21 months for 4 revisions, processed by Scott Neslin.
1. Introduction
Customized promotions have been gaining popularity in the retail industry as more companies come to realize the potential of customer-centric strategies over mass-market strategies (Global Cosmetic Industry December 2001). So far, industry practices and marketing academic research have mainly focused on the issue of how to target certain consumers for a given promotion, but the depth and timing of promotions are not tailored toward individuals nor adjusted by updated information on their purchases. On the other hand, technological development, especially the rapid growth of the Internet, has provided the potential to deliver promotions that are customized for each individual household on each shopping trip. This would represent micro-marketing at the finest level. The main objective of this research is to develop a decision-support system that provides recommendations on when to promote how much to whom, primarily for use in online stores.
Previous research on promotion decision-support systems has derived promotion calendars for brick-and-mortar retailers (Tellis and Zufryden 1995) or manufacturers (Silva-Risso et al. 1999) which are not differentiated at the individual household level. On the other hand, research addressing individual level customization topics has focused on targeting but not timing (e.g., Shaffer and Zhang 1995, Rossi et al. 1996). The emphasis of our research is on the timing of promotions. We believe that timing could make targeting more efficient and help achieve the full potential of micro-marketing, and that the Internet has provided an opportunity to realize such potential.
A distinctive feature of our proposed promotion customization system is that it utilizes the interactive and one-on-one nature of the Internet shopping environment. It derives the optimal price promotion for each household on each shopping trip by taking into account the time-varying pattern of purchase behavior and the impact of current promotion on future purchases. The promotion decision is updated on each subsequent shopping trip for a household.
We approach the problem by first constructing a joint purchase incidence-brand choice-purchase quantity model that incorporates how variety-seeking/inertia tendency may differ among households and change over time within the same household. Based on the proposed consumer response model, we develop a decision-support system to optimize the depth of promotion for each household on each shopping trip. Time-varying patterns of variety-seeking/inertia have a direct implication on how promotions should be timed. Most previous studies on variety-seeking and/or inertia assumed that these properties remain constant over time for the same individual/household (for some exceptions see Kahn et al. 1986, Bawa 1990, Trivedi et al. 1994). Timing would play a more important role in promotion decisions if the variety-seeking/inertia tendency varies over time for a substantial proportion of consumers in a market. For example, a promotion aimed at a consumer who did not buy the target brand on the previous occasion may not be profitable if she is in a high inertia state, while a promotion aimed at a consumer who bought the target brand on the previous occasion may not be profitable if she is in a high variety-seeking state. Our empirical analysis shows that the variety-seeking/inertia tendency does vary over time for the majority of households in the data. Therefore, we believe that a decision-support system designed to offer customized promotions should take into account such behavioral changes.
The rest of this paper is organized as follows. In [section] 2, we describe the formulation of our consumer response model. In [section] 3, we develop an optimization procedure for customized promotions. In [section] 4, we present model estimation results and demonstrate the application and effectiveness of the proposed customization method. In [section] 5, we discuss the limitations of this research and managerial implications for retailers and consumer packaged goods manufacturers.
2. Model Formulation
Previous research has demonstrated that it is important to take into account the interdependence in purchase incidence, brand choice, and purchase quantity decisions (e.g., Chiang 1991, Chintagunta 1993, Arora et al. 1998, Bell et al. 1999). We develop a new formulation to model the three components simultaneously. Our model shares similarities with those in the studies cited above, yet has unique features in certain aspects. Define
[I.sub.it] = 1 if household i makes a category purchase at shopping trip t; otherwise,
[B.sub.ikt] = 1 if household i purchases alternative k at shopping trip t; otherwise,
[Q.sub.ikt] = household i's purchase quantity of alternative k at shopping trip t.
We derive the joint probability Pr([I.sub.it] = 1, [B.sub.ikt] = 1, [Q.sub.ikt] = q) as follows.
2.1. Purchase Incidence and Brand Choice
The utility function of alternative k at shopping trip t for household i is given by
(1) [U.sub.ikt] = [V.sub.ikt] + [[epsilon].sub.ikt] = [X.sub.kt][[beta].sub.i] + [[epsilon].sub.ikt], k = 1, ..., K,
where [V.sub.ikt], the systematic component of brand utilities, is a function of brand-specific constants, marketing-mix variables such as regular price and price discount, and a time-varying purchase event feedback effect component. The specification of [V.sub.ikt] will be elaborated later.
At each shopping trip t, the shopper decides whether to make a category purchase and will do so only if the utilities of the alternatives under consideration exceed a threshold. We formulate the threshold as
(2) [U.sub.i0t] = [V.sub.i0t] + [[epsilon].sub.i0t] = [[lambda].sub.0i] + [[lambda].sub.1i]FRE[Q.sub.i] + [[lambda].sub.2i]L[Q.sub.it] + [[epsilon].sub.i0t],
where [[lambda].sub.0i] is a constant, FREQ, is household i's purchase frequency in the initialization period, and L[Q.sub.it] is the household's mean-centered last purchase quantity before shopping trip t. L[Q.sub.it] is used to capture inventory effects on purchase incidence decisions. To control for difference in purchase quantity across households, L[Q.sub.it] is computed as the last purchase quantity minus the household's average purchase quantity in the initialization period. This operationalization has been used by Jain and Vilcassim (1991) and Chintagunta and Haldar (1998). Note that it would not be appropriate to include an inventory variable in our model because it requires the use of the interpurchase duration which is endogenous to purchase incidence decisions (Chintagunta and Haldar 1998).
Assume that [[epsilon].sub.ikt], k = 0, 1, ..., K, follows i.i.d. Type I extreme value distribution with location parameter and scale parameter 1. It can be shown that the category purchase incidence probability and conditional brand choice probability are
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
(4) = Pr ([B.sub.ikt]) = 1 | [I.sub.it] = 1) = exp ([V.sub.ikt])/[[summation of].sup.K.sub.j=1] exp ([V.sub.ijt]),
respectively. (1) Note that because [V.sub.ikt] is a function of price and promotion, among other variables, a promotion for any brand will increase the category purchase incidence probability. The joint probability of purchase incidence and choice is
(5) Pr([I.sub.it] = 1, [B.sub.ikt] = 1) = exp([V.sub.i0t]) + [[summation of].sup.K.sub.j] exp([V.sub.ijt]).
2.2. Purchase Quantity
Let [Q.sup.*.sub.ikt] be a latent variable that determines how much household i wants to buy alternative k at shopping trip t, and [Q.sub.ikt] be the observed purchase quantity. Then,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
Specify
(6) [Q.sup.*.sub.ikt] = [Z.sub.ikt][[phi].sub.i] + [[xi].sub.ikt] = [[phi].sub.0i] + [[phi].sub.1i]A[Q.sub.i] + [[phi].sub.2i]FRE[Q.sub.i] + [[phi].sub.3i]R[P.sub.kt] + [[phi].sub.4i]P[C.sub.kt] + [[xi].sub.ikt],
where A[Q.sub.i] is household i's average purchase quantity and FRE[Q.sub.i] is its purchase frequency in the initialization period, R[P.sub.kt] and P[C.sub.kt] are alternative k's regular price and price cut, and [[xi].sub.ikt] is the unobserved random term. (2)
The interdependence between purchase incidence and choice and quantity decisions is formulated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
Let [[epsilon].sup.*.sub.ikt] = [max.sub.j=0, 1, ... K and [not equal to] k] {[V.sub.ijt] + [[epsilon].sub.ijt]} - [[epsilon].sub.ikt]. By properties of the extreme value distribution (see Ben-Akiva and Lerman, 1985, p. 105), [max.sub.j=0, 1, ... K and [not equal to] k] {[V.sub.ijt] + [[epsilon].sub.ijt]} follows a Type I extreme value distribution with location parameter ln[[summation of].sub.j=0, 1, ... K and j [not equal to] k] exp([V.sub.ijt])] and scale parameter 1, and [[epsilon].sup.*.sub.ikt] follows a logistic distribution with cumulative distribution function (CDF):
F([[epsilon].sup.*.sub.ikt]) = 1/1 + exp{ln[[summation of].sub.j=0, 1, ... K and j [not equal to] k] exp([V.sub.ijt])] - [epsilon].sup.*.sub.ikt]}.
Assume that the quantity random term, [[xi].sub.ikt], follows a logistic distribution with mean and scale parameter [[delta].sub.[xi]]. Its CDF is given by
F([[xi].sub.ikt]) = 1/1 + exp(-[[delta].sub.[xi]][[xi].sub.ikt]),
and its variance is [[sigma].sup.2.sub.[xi]] = [[pi].sup.2]/3[[delta].sub.[xi]]. We adopt a flexible bivariate logistic distribution proposed by Gumbel (1961) for the joint distribution of [[epsilon].sup.*.sub.ikt] and [[xi].sub.ikt]. Unlike the standard bivariate logistic distribution in which the correlation between the two variables is fixed to 0.5, this formulation allows the correlation coefficient to be estimated from the data. The joint CDF is given by (Gumbel 1961, p. 347)
(7) F([[epsilon].sup.*.sub.ikt], [[xi].sub.ikt] = F([[epsilon].sup.*.sub.ikt])F([[xi].sub.ikt])
x [1 + [theta](1 - F([[epsilon].sup.*.sub.ikt]))(1 - F([[xi].sub.ikt]))],
- 1 [less than or equal to] [theta] [less than or equal to] 1,
where [theta] is to be estimated from the data. The correlation coefficient of [[epsilon].sup.*.sub.ikt] and [[xi].sub.ikt] is [rho] = 3[theta]/[[pi].sup.2]. To ensure that the estimate of [theta] falls between [-1, 1], we use [theta] = sin([tau]) in the estimation procedure.
The probability of observing [Q.sub.ikt] > is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],
where f(*,*) is the joint density function of [[epsilon].sup.*.sub.ikt] and [[xi].sub.ikt]. The bivariate logistic distribution enables us to get a closed-form expression of the above integral. We present the result here and show the derivation in Appendix C:
(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
In Equation (8), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is the joint probability Pr([I.sub.it] = 1, [B.sub.ikt] = 1), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is the marginal probability Pr([Q.sub.ikt] = [q.sub.ikt]), and [theta] captures the interdependence of [[epsilon].sup.*.sub.ikt] and [[xi].sub.ikt]. When [theta] = 0, Equation (8) reduces to Pr([I.sub.it] = 1, [B.sub.ikt] = 1, [Q.sub.ikt] = [q.sub.ikt]) = Pr([I.sub.it] = 1, [B.sub.ikt] = 1)Pr([Q.sub.ikt] = [q.sub.ikt]). In other words, Pr([Q.sub.ikt] = [q.sub.ikt] | [I.sub.it] = 1, [B.sub.ikt] = 1) = Pr([Q.sub.ikt] = [q.sub.ikt]). Because the choice probability Pr([I.sub.it] = 1, [B.sub.ikt] = 1) decreases with [[epsilon].sup.*.sub.ikt] by the definition of [[epsilon].sup.*.sub.ikt], [theta] > indicates that unobserved factors in the quantity and choice components for alternative k are negatively correlated, and [theta] < indicates that unobserved factors in the two components are positively correlated. In the extreme case where Pr([I.sub.it] = 1, [B.sub.ikt] = 1) = 1, i.e., if alternative k is always purchased, Equation (8) reduces to Pr([I.sub.it] = 1, [B.sub.ikt] = 1, [Q.sub.ikt] = [q.sub.ikt]) = Pr([Q.sub.ikt] = [q.sub.ikt]), regardless of whether [[epsilon].sup.*.sub.ikt] and [[xi].sub.ikt] are correlated.
2.3. Brand Utility Functions
We now explain the brand utility functions in detail with an emphasis on the purchase event feedback effect, which is defined as the impact of past purchases on current brand preference (cf., Gedenk and Neslin 1999). We distinguish between two types of purchase event feedback effects. The first type is attributed to a consumer's intentional tendency to stick to or switch away from an item bought on the previous category purchase occasion, which is not caused by external influences such as...
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