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Research Note: A Dynamic Programming Approach to Customer Relationship Pricing


  • Michael Lewis

    () (Department of Marketing, University of Florida, Bryan Hall, Gainesville, Florida 32611)


The practice of offering discounts to prospective customers represents a rudimentary form of using transaction history measures to customize the marketing mix. Furthermore, the proliferation of powerful customer relationship management (CRM) systems is providing the data and the communications channels necessary to extend this type of pricing strategy into true dynamic marketing policies that adjust pricing as customer relationships evolve. In this paper, we describe a dynamic programming--based approach to creating optimal relationship pricing policies. The methodology has two main components. The first component is a latent class logit model that is used to model customer buying behavior. The second component is a dynamic optimization procedure that computes profit-maximizing price paths. The methodology is illustrated using subscriber data provided by a large metropolitan newspaper. The empirical results provide support for the common managerial practice of offering discounts to new customers. However, in contrast to current practice, the results suggest the use of a series of decreasing discounts based on the length of customer tenure rather than a single steep discount for first-time purchasers. The dynamic programming (DP) methodology also represents an important approach to calculating customer value (CV). Specifically, the DP framework allows the calculation of CV to be an explicit function of marketing policies and customer status. As such, this method for calculating CV accounts for the value of managerial flexibility and improves upon existing methods that do not model revenue and attrition rates as functions of marketing variables.

Suggested Citation

  • Michael Lewis, 2005. "Research Note: A Dynamic Programming Approach to Customer Relationship Pricing," Management Science, INFORMS, vol. 51(6), pages 986-994, June.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:6:p:986-994

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    Cited by:

    1. repec:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9536-1 is not listed on IDEAS
    2. Ricardo Montoya & Oded Netzer & Kamel Jedidi, 2010. "Dynamic Allocation of Pharmaceutical Detailing and Sampling for Long-Term Profitability," Marketing Science, INFORMS, vol. 29(5), pages 909-924, 09-10.
    3. Baohong Sun, 2006. "—Technology Innovation and Implications for Customer Relationship Management," Marketing Science, INFORMS, vol. 25(6), pages 594-597, 11-12.
    4. repec:eee:jouret:v:89:y:2013:i:3:p:231-245 is not listed on IDEAS
    5. repec:eee:jouret:v:89:y:2013:i:3:p:263-280 is not listed on IDEAS
    6. Andrés Musalem & Yogesh V. Joshi, 2009. "—How Much Should You Invest in Each Customer Relationship? A Competitive Strategic Approach," Marketing Science, INFORMS, vol. 28(3), pages 555-565, 05-06.
    7. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.
    8. Mark Tanya & Niraj Rakesh & Dawar Niraj, 2007. "Using Customer Relationship Trajectories to Segment Customers and Predict Profitability," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. repec:pal:jorsoc:v:60:y:2009:i:5:d:10.1057_palgrave.jors.2602609 is not listed on IDEAS
    10. Romana Khan & Michael Lewis & Vishal Singh, 2009. "Dynamic Customer Management and the Value of One-to-One Marketing," Marketing Science, INFORMS, vol. 28(6), pages 1063-1079, 11-12.
    11. repec:eee:joinma:v:23:y:2009:i:2:p:169-178 is not listed on IDEAS
    12. Sunil Gupta & Valarie Zeithaml, 2006. "Customer Metrics and Their Impact on Financial Performance," Marketing Science, INFORMS, vol. 25(6), pages 718-739, 11-12.
    13. Fruchter, Gila E. & Sigué, Simon P., 2013. "Dynamic pricing for subscription services," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2180-2194.


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