Optimizing assortment and pricing of multiple retail categories with cross-selling
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.
KeywordsCross-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.
- 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.Aydin, G., Ziya, S.: Pricing promotional products under upselling. Manuf. Serv. Oper. Manag. 10(3), 360–376 (2008)Google Scholar
- 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
- 10.Dean, J.: Pricing policies for new products. Harv. Bus. Rev. 28, 45–53 (1950)Google Scholar
- 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
- 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
- 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
- 37.Walras, L.: Elements of Pure Economics or the Theory of Social Wealth. Allen and Unwin, London (Sydney) (1954)Google Scholar
- 38.Walters, R.G.: Retail promotions and retail store performance: a test of some key hypotheses. J. Retail. 64, 153–180 (1988)Google Scholar
- 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.Zufryden, F.S.: Product line optimization by integer programming. In: Proceedings of the Annual Meeting of ORSA/TIMS, San Diego, CA (1982)Google Scholar