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On the Optimal Product Line Selection Problem with Price Discrimination


  • Cornelia Schön

    () (GISMA Business School, Leibniz University Hannover, 30167 Hannover, Germany)


Product line design decisions are determinant for a firm's market success and, simultaneously, very costly to implement and change. To evaluate the profitability of a design, a number of mathematical programming approaches have been proposed in the last three decades--typically nonlinear integer optimization problems that can only be tackled heuristically for real-world instances. Recently, Chen and Hausman (2000) efficiently exploited the fractional programming properties of a stylized model for product line and price selection with the objective to maximize contribution given homogeneous customer behavior by an aggregate multinomial logit choice model. We extend the approach of Chen and Hausman (Chen, K. D., W. H. Hausman. 2000. Technical note: Mathematical properties of the optimal product line selection problem using choice-based conjoint analysis. Management Sci. 46(2) 327-332) to determine an optimal product line under a personalized or group pricing strategy in markets with multiple heterogeneous consumers such that total profit (including fixed costs) is maximized. Personalized/group pricing is a growing discrimination strategy that more and more businesses are realizing is not only very profitable, but also often implementable in the era of e-business. Our problem formulation allows to incorporate commonly applied attraction choice models including the multinomial logit, the Bradley-Terry-Luce, and approximately the first choice model. Though the problem is generally nonlinear, we show that the fractional substructure resulting from attraction choice models can still be exploited to globally solve real-world instances in reasonable time.

Suggested Citation

  • Cornelia Schön, 2010. "On the Optimal Product Line Selection Problem with Price Discrimination," Management Science, INFORMS, vol. 56(5), pages 896-902, May.
  • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:5:p:896-902

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    References listed on IDEAS

    1. Winfried Steiner & Harald Hruschka, 2002. "A Probabilistic One-Step Approach to the Optimal Product Line Design Problem Using Conjoint and Cost Data," Review of Marketing Science Working Papers 1-4-1003, Berkeley Electronic Press.
    2. Xinfang (Jocelyn) Wang & Jeffrey D. Camm & David J. Curry, 2009. "A Branch-and-Price Approach to the Share-of-Choice Product Line Design Problem," Management Science, INFORMS, vol. 55(10), pages 1718-1728, October.
    3. Day, Jamison M. & Venkataramanan, M.A., 2006. "Profitability in product line pricing and composition with manufacturing commonalities," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1782-1797, December.
    4. Yuxin Chen & Ganesh Iyer, 2002. "Research Note Consumer Addressability and Customized Pricing," Marketing Science, INFORMS, vol. 21(2), pages 197-208, November.
    5. Kyle D. Chen & Warren H. Hausman, 2000. "Technical Note: Mathematical Properties of the Optimal Product Line Selection Problem Using Choice-Based Conjoint Analysis," Management Science, INFORMS, vol. 46(2), pages 327-332, February.
    6. Thisse, Jacques-Francois & Vives, Xavier, 1988. "On the Strategic Choice of Spatial Price Policy," American Economic Review, American Economic Association, vol. 78(1), pages 122-137, March.
    7. Kohli, Rajeev & Krishnamurti, Ramesh, 1989. "Optimal product design using conjoint analysis: Computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 40(2), pages 186-195, May.
    8. Paul E. Green & Abba M. Krieger, 1985. "Models and Heuristics for Product Line Selection," Marketing Science, INFORMS, vol. 4(1), pages 1-19.
    9. Varian, Hal R., 1989. "Price discrimination," Handbook of Industrial Organization,in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 10, pages 597-654 Elsevier.
    10. Kraus, Ursula G. & Yano, Candace Arai, 2003. "Product line selection and pricing under a share-of-surplus choice model," European Journal of Operational Research, Elsevier, vol. 150(3), pages 653-671, November.
    11. Neeraj Arora & Xavier Dreze & Anindya Ghose & James Hess & Raghuram Iyengar & Bing Jing & Yogesh Joshi & V. Kumar & Nicholas Lurie & Scott Neslin & S. Sajeesh & Meng Su & Niladri Syam & Jacquelyn Thom, 2008. "Putting one-to-one marketing to work: Personalization, customization, and choice," Marketing Letters, Springer, vol. 19(3), pages 305-321, December.
    12. Alexandre Belloni & Robert Freund & Matthew Selove & Duncan Simester, 2008. "Optimizing Product Line Designs: Efficient Methods and Comparisons," Management Science, INFORMS, vol. 54(9), pages 1544-1552, September.
    13. Vidyanand Choudhary & Anindya Ghose & Tridas Mukhopadhyay & Uday Rajan, 2005. "Personalized Pricing and Quality Differentiation," Management Science, INFORMS, vol. 51(7), pages 1120-1130, July.
    14. Paul E. Green & Abba M. Krieger, 1992. "An Application of a Product Positioning Model to Pharmaceutical Products," Marketing Science, INFORMS, vol. 11(2), pages 117-132.
    15. Gregory Dobson & Shlomo Kalish, 1993. "Heuristics for Pricing and Positioning a Product-Line Using Conjoint and Cost Data," Management Science, INFORMS, vol. 39(2), pages 160-175, February.
    16. Anindya Ghose & Vidyanand Choudhary & Tridas Mukhopadhyay & Uday Rajan, 2002. "Personalized Pricing and Quality Differentiation on the Internet," Review of Marketing Science Working Papers 2-1-1005, Berkeley Electronic Press.
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