# Overcoming the “recency trap” in customer relationship management

## Abstract

Purchase likelihood typically declines as the length of time since the customer’s previous purchase (“recency”) increases. As a result, firms face a “recency trap,” whereby recency increases for customers who do not purchase in a given period, making it even less likely they will purchase in the next period. Eventually the customer is effectively lost to the firm. We develop and illustrate a modeling approach to target a firm’s marketing efforts, keeping in mind the customer’s recency state. This requires an empirical model that predicts purchase likelihood as a function of recency and marketing, and a dynamic optimization that prescribes the most profitable way to target customers. In our application we find that customers’ purchase likelihoods as well as response to marketing depend on recency. These results are used to show that the targeting of email and direct mail should depend on the customer’s recency and that the optimal decision policy enables the average high recency customer, who currently is virtually worthless to the firm, to become profitable.

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## Notes

1. Note that given the definition of recency as time since previous purchase, “higher recency” or “increased recency” means a longer time period has elapsed since the customer last purchased.

2. A customer’s recency state is assigned at the end of the period. As in all CLV models, since we start the calculation from the time the customer makes her or his first purchase, we know the customer is in recency state 1 at the end of period 1. So the probabilities in Table 1 start off with a probability of 1 (the customer buys in period 1) by definition. The customer then has a 0.23 probability of purchase in period 2, because ProbPurchase(1) = 0.23. The subsequent purchase probabilities, and hence the states, are determined by the migration probabilities at the top of Table 1.

3. Note that if as in Table 1, the highest recency state is ≥20, once ≥20 becomes that customer’s current state and he or she does not buy, he or she “migrates” to state ≥20, since we are collapsing states 20, 21, 22, etc. into one state, ≥20. That is, S+1 is state ≥20 if the current state is ≥20.

4. Note the exception that since we have 20 recency states, if the customer is in recency state ≥ 20 and doesn’t purchase, he or she remains in state ≥20.

5. In fact, discussion with the firm’s management suggested that the company was not currently targeting email or direct mail efforts in any way, i.e., they were not using previous purchase, etc., to target marketing. If they had been, this would have created an endogeneity that we would have had to handle in our estimation of the logistic customer response function (see Rhee and McIntyre 2008).

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## Author information

Authors

### Corresponding author

Correspondence to Scott A. Neslin.

The authors are grateful to Brett Gordon for his help and guidance in implementing the value iteration method used in this work. We are also grateful for comments made by Olivier Toubia and students in his marketing models seminar. We are indebted to Rong Guo for preparing the data used in the analysis. We thank an anonymous online food service company for providing the data used in this research. Finally, we thank the three anonymous reviewers for their valuable comments and suggestions.

## Appendix

### Value iteration algorithm used to derive the optimal policy (D*|S)

1. 1.

Let V(S)w = the value function at iteration w for a customer who is in state S.

2. 2.

We have two decision variables—email effort and direct mail effort. These each range from 0 to 3 (3 is the maximum value of these variables in the data, and we wanted to stay within the range of the data). We divide each of these variables into 30 increments of 0.1. Therefore, the policy function (D|S) is a set of two values for each state, consisting of one of 30 possible email decisions and one of 30 possible direct mail decisions.

3. 3.

Find initial values, V(S)0. We did this by computing the short-term profit function, π it (S) for each of the 900 possible email/direct mail combinations, for each state, and taking the maximum as the initial value, V(S)0.

4. 4.

For each state the maximum value of $$V{{(S)}^w} = \mathop{{\max }}\limits_D \left\{ {\pi (S) + \delta (ProbPurch \times V{{{\left( {{{S}^{\prime }}} \right)}}^{{w - 1}}} + \left( {1 - ProbPurch) \times V{{{\left( {{{S}^{{\prime \prime }}}} \right)}}^{{w - 1}}}} \right)} \right\}$$ by trying all 900 possible combinations of email and direct mail. Call the combination that produces this maximum (D *|S).

5. 5.

Test whether V(S)wV(S)w−1 <0.00001 for each state S. If this holds, the process has converged and the current value of V(S)w is the value function for customers in state S, and the most recently used combination of email and dmail is the optimal policy function (D *|S). If the condition does not hold for all states S, set V(S)w−1 = V(S)w and proceed back to step 4 for another iteration. Note that we have updated the value function because now in step 4, the new value functions we created on the left side of the equation will be on the right side of the equation.

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Neslin, S.A., Taylor, G.A., Grantham, K.D. et al. Overcoming the “recency trap” in customer relationship management. J. of the Acad. Mark. Sci. 41, 320–337 (2013). https://doi.org/10.1007/s11747-012-0312-7

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• DOI: https://doi.org/10.1007/s11747-012-0312-7

### Keywords

• Customer relationship management
• Customer lifetime value
• Optimization
• Migration model
• Customer recency