Journal of Global Optimization

, Volume 66, Issue 2, pp 291–309 | Cite as

Optimizing assortment and pricing of multiple retail categories with cross-selling

  • Ahmed Ghoniem
  • Bacel Maddah
  • Ameera Ibrahim


This paper investigates the joint optimization of assortment and pricing decisions for complementary retail categories. Each category comprises substitutable items (e.g., different coffee brands) and the categories are related by cross-selling considerations that are empirically observed in marketing studies to be asymmetric in nature. That is, a subset of customers who purchase a product from a primary category (e.g., coffee) can opt to also buy from one or several complementary categories (e.g., sugar and/or coffee creamer). We propose a mixed-integer nonlinear program that maximizes the retailer’s profit by jointly optimizing assortment and pricing decisions for multiple categories under a classical deterministic maximum-surplus consumer choice model. A linear mixed-integer reformulation is developed which effectively enables an exact solution to relatively large problem instances using commercial optimization solvers. This is encouraging, because simpler product line optimization problems in the literature have posed significant computational challenges over the last decades and have been mostly tackled via heuristics. Moreover, our computational study indicates that overlooking cross-selling between retail categories can result in substantial profit losses, suboptimal (narrower) assortments, and inadequate prices.


Cross-selling Assortment planning Pricing Retail Mathematical programming 



This research was supported by Qatar National Research Fund, National Priorities Research Program under Grant NPRP 5-591-5-082.


  1. 1.
    Agrawal, N., Smith, S.A.: Optimal retail assortments for substitutable items purchased in sets. Nav. Res. Logist. 50(7), 793–822 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Anupindi, R., Gupta, S., Venkataramanan, M.: Managing variety on the retail shelf: using household scanner panel data to rationalize assortments. In: Retail Supply Chain Management, International Series in Operations Research Management Science, Springer, US 122, pp. 155–182 (2009)Google Scholar
  3. 3.
    Aydin, G., Ziya, S.: Pricing promotional products under upselling. Manuf. Serv. Oper. Manag. 10(3), 360–376 (2008)Google Scholar
  4. 4.
    Basuroy, S., Mantrala, M., Walters, R.: The impact of category management on retail prices and performance: theory and evidence. J. Mark. 65, 16–32 (2001)CrossRefGoogle Scholar
  5. 5.
    Best, R.J.: The predictive aspects of a joint-space theory of stochastic choice. J. Mark. Res. 13, 198–206 (1976)CrossRefGoogle Scholar
  6. 6.
    Braun, M.A., Srinivasan, V.: Amount of information as a determinant of consumer behavior toward new products. In: Proceedings of the American Marketing Association, pp. 373–378 (1975)Google Scholar
  7. 7.
    Burkart, W.R., Klein, R., Mayer, S.: Product line pricing for services with capacity constraints and dynamic substitution. Eur. J. Oper. Res. 219, 347–359 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Cachon, G.P., Kök, A.G.: Category management and coordination in retail assortment planning in the presence of basket shopping consumers. Manag. Sci. 53(6), 934–951 (2007)CrossRefzbMATHGoogle Scholar
  9. 9.
    Chen, K., Hausman, W.H.: Mathematical properties of the optimal product line selection problem using choice-based conjoint analysis. Manag. Sci. 46(2), 327–332 (2000)CrossRefzbMATHGoogle Scholar
  10. 10.
    Dean, J.: Pricing policies for new products. Harv. Bus. Rev. 28, 45–53 (1950)Google Scholar
  11. 11.
    DeGraba, P.: Volume discounts, loss leaders, and competition for more profitable customers. Working paper # 260—Federal Trade Commission, Bureau of Economics (2003)Google Scholar
  12. 12.
    Dobson, G., Kalish, S.: Positioning and pricing of a product-line: formulation and heuristics. Mark. Sci. 7, 107–125 (1988)CrossRefGoogle Scholar
  13. 13.
    Dobson, G., Kalish, S.: Heuristics for pricing and positioning a product-line using conjoint and cost data. Manag. Sci. 39(2), 160–175 (1993)CrossRefGoogle Scholar
  14. 14.
    Ghoniem, A., Maddah, B.: Integrated retail decisions with multiple selling periods and customer segments: optimization and insights. Working paper, University of Massachusetts, Amherst (2013)Google Scholar
  15. 15.
    Green, P.E., Krieger, A.M.: Models and heuristics for product line selection. Mark. Sci. 4(1), 1–19 (1985)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Green, P.E., Srinivasan, V.: Conjoint analysis in consumer research: issues and outlook. J. Consum. Res. 5, 103–123 (1978)CrossRefGoogle Scholar
  17. 17.
    Green, P.E., Srinivasan, V.: Conjoint analysis in marketing: new developments with implications for research and practice. J. Mark. 54(4), 3–19 (1990)CrossRefGoogle Scholar
  18. 18.
    Hall, J.M., Kopalle, P.K., Krishna, A.: Retailer dynamic pricing and ordering decisions: category management versus brand-by-brand approaches. J. Retail. 86(2), 172–183 (2010)CrossRefGoogle Scholar
  19. 19.
    Hanson, W., Martin, R.K.: Optimal bundle pricing. Manag. Sci. 36, 155–174 (1990)CrossRefzbMATHGoogle Scholar
  20. 20.
    Hess, J.D., Gerstner, D.: Loss leader pricing and rain check policy. Mark. Sci. 6(4), 358–374 (1987)CrossRefGoogle Scholar
  21. 21.
    Johnson, R.M.: Trade-off analysis of consumer values. J. Mark. Res. 11, 121–127 (1976)CrossRefGoogle Scholar
  22. 22.
    Keller, P.W., Levi, R., Perakis, G.: Efficient formulations for pricing under attraction demand models. Math. Program. 145(1–2), 223–261 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Kraus, U.G., Yano, C.A.: Product line selection and pricing under a share-of-surplus choice model. Eur. J. Oper. Res. 150, 653–671 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Maddah, B., Bish, E.K.: Locational tying of complementary retail items. Nav. Res. Logist. 56, 421–438 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Maddah, B., Bish, E.K., Munreo, B.: Pricing, variety, and inventory decisions for categories of substitutable items. In: Kemph, K., Keskinocak, P., Uzsoy, R. (eds.) Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook. Kluwer Academic Publishers, Dordrecht (2011)Google Scholar
  26. 26.
    Manchanda, P., Ansari, A., Gupta, S.: The shopping basket: a model for multicategory purchase incidence decisions. Mark. Sci. 18(2), 95–114 (1999)CrossRefGoogle Scholar
  27. 27.
    McBride, R.D., Zufryden, F.S.: An integer programming approach to the optimal product line selection problem. Mark. Sci. 7(2), 126–140 (1988)CrossRefGoogle Scholar
  28. 28.
    Mild, A., Reutterer, T.: An improved collaborative filtering approach for predicting cross-category purchase based on binary market basket data. J. Retail Consum. Serv. 10, 123–133 (2003)CrossRefGoogle Scholar
  29. 29.
    Mulhern, F.J., Leone, R.P.: Implicit price bundling of retail products: a multiproduct approach to maximizing store profitability. J. Mark. 55(4), 63–76 (1991)CrossRefGoogle Scholar
  30. 30.
    Pessemier, E.A., Burger, P., Teach, R., Tigert, D.: Using laboratory brand preference scales to predict consumer brand purchases. Manag. Sci. 17, 371–385 (1971)CrossRefGoogle Scholar
  31. 31.
    Rodríguez, B., Aydin, G.: Assortment selection and pricing for configurable products under demand uncertainty. Eur. J. Oper. Res. 210(3), 635–646 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Russel, G.J., Petersen, A.: Analysis of cross category dependence in market basket selection. J. Retail. 76, 367–392 (2000)CrossRefGoogle Scholar
  33. 33.
    Shankar, V., Kannan, P.K.: An across-store analysis of intrinsic and extrinsic cross-category effects. Cust. Needs Solut. J. 1(2), 143–153 (2014)CrossRefGoogle Scholar
  34. 34.
    Shioda, R., Tuncel, L., Myklebust, T.G.J.: Maximum utility product pricing models and algorithms based on reservation price. Comput. Optim. Appl. 48, 157–198 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Smith, J.C., Lim, C., Alptekinoğlu, A.: New product introduction against a predator: a bilevel mixed-integer programming approach. Nav. Res. Logist. 56, 714–729 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Subramanian, S., Sherali, H.: A fractional programming approach for retail category price optimization. J. Glob. Optim. 48(2), 263–277 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Walras, L.: Elements of Pure Economics or the Theory of Social Wealth. Allen and Unwin, London (Sydney) (1954)Google Scholar
  38. 38.
    Walters, R.G.: Retail promotions and retail store performance: a test of some key hypotheses. J. Retail. 64, 153–180 (1988)Google Scholar
  39. 39.
    Walters, R.G.: Assessing the impact of retail price promotions on product substitution, complementary purchase, and interstore sales displacement. J. Mark. 55, 16–28 (1991)CrossRefGoogle Scholar
  40. 40.
    Zenor, M.J.: The profit benefits of category management. J. Mark. Res. 31, 202–213 (1994)CrossRefGoogle Scholar
  41. 41.
    Zhang, R., Kaku, I., Xiao, Y.: Deterministic EOQ with partial backordering and correlated demand caused by cross-selling. Eur. J. Oper. Res. 210(3), 537–551 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Zufryden, F.S.: A conjoint measurement-based approach for optimal new product design and market segmentation. In: Shocker, A.D. (ed.) Analytic Approaches to Product and Marketing Planning. Cambridge, MA, pp. 100–114 (1977)Google Scholar
  43. 43.
    Zufryden, F.S.: Product line optimization by integer programming. In: Proceedings of the Annual Meeting of ORSA/TIMS, San Diego, CA (1982)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Operations and Information Management Department, Isenberg School of ManagementUniversity of Massachusetts AmherstAmherstUSA
  2. 2.Engineering Management Program, Faculty of Engineering and ArchitectureAmerican University of BeirutBeirutLebanon

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