4OR

, Volume 14, Issue 1, pp 57–75 | Cite as

Assortment optimization under a multinomial logit model with position bias and social influence

  • Andrés Abeliuk
  • Gerardo Berbeglia
  • Manuel Cebrian
  • Pascal Van Hentenryck
Research paper

Abstract

Motivated by applications in retail, online advertising, and cultural markets, this paper studies the problem of finding an optimal assortment and positioning of products subject to a capacity constraint in a setting where consumers preferences can be modeled as a discrete choice under a multinomial logit model that captures the intrinsic product appeal, position biases, and social influence. For the static problem, we prove that the optimal assortment and positioning can be found in polynomial time. This is despite the fact that adding a product to the assortment may increase the probability of selecting the no-choice option, a phenomenon not observed in almost all models studied in the literature. We then consider the dynamics of such a market, where consumers are influenced by the aggregate past purchases. In this dynamic setting, we provide a small example to show that the natural and often used policy known as popularity ranking, that ranks products in decreasing order of the number of purchases, can reduce the expected profit as times goes by. We then prove that a greedy policy that applies the static optimal assortment and positioning at each period, always benefits from the popularity signal and outperforms any policy where consumers cannot observe the number of past purchases (in expectation).

Keywords

Assortment optimization Marketing Social influence 

Mathematics Subject Classification

90B50 

Notes

Acknowledgments

We thank the reviewers for their constructive remarks and suggestions. NICTA is funded by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program.

References

  1. Abeliuk A, Berbeglia G, Cebrian M, Van Hentenryck P (2015) The benefits of social influence in optimized cultural markets. PloS One 10(4):e0121934. doi:10.1371/journal.pone.0121934 CrossRefGoogle Scholar
  2. Berbeglia G, Joret G (2015) Assortment optimisation under a general discrete choice model: a tight analysis of revenue ordered assortments. Available at SSRN 2620165Google Scholar
  3. Block HD, Marschak J (1960) Random orderings and stochastic theories of responses. Contrib probab Stat 2:97–132Google Scholar
  4. Bront JJM, Méndez-Díaz I, Vulcano G (2009) A column generation algorithm for choice-based network revenue management. Oper Res 57(3):769–784CrossRefGoogle Scholar
  5. Buscher G, Cutrell E, Morris MR (2009) What do you see when you’re surfing?: using eye tracking to predict salient regions of web pages. In: Proceedings of the SIGCHI conference on human factors in computing systems, pp 21–30. ACMGoogle Scholar
  6. Craswell N, Zoeter O, Taylor M, Ramsey B (2008) An experimental comparison of click position-bias models. In: Proceedings of the 2008 international conference on web search and data mining, pp 87–94. ACMGoogle Scholar
  7. Daly Andrew, Zachary Stanley (1978) Improved multiple choice models. Determ Travel Choice 335:357Google Scholar
  8. Davis J, Gallego G, Topaloglu H (2013) Assortment planning under the multinomial logit model with totally unimodular constraint structures. Technical report, Department of IEOR, Columbia UniversityGoogle Scholar
  9. Davis JM, Gallego G, Topaloglu H (2014) Assortment optimization under variants of the nested logit model. Oper Res 62(2):250–273CrossRefGoogle Scholar
  10. Dreze Xavier, Hoch Stephen J, Purk Mary E (1995) Shelf management and space elasticity. J Retail 70(4):301–326CrossRefGoogle Scholar
  11. Engstrom P, Forsell E (2014) Demand effects of consumers’ stated and revealed preferences. Available at SSRN 2253859Google Scholar
  12. Gallego G, Iyengar G, Phillips R, Dubey A (2004) Managing flexible products on a network. Technical report, Columbia University, New YorkGoogle Scholar
  13. Hardy GH, Littlewood JE, Polya G (1952) Inequalities. Cambridge University Press, CambridgeGoogle Scholar
  14. Hummel P, McAfee RP (2014) Position auctions with externalities. In: Tie-Yan Liu, Qi Qi, Yinyu Ye (eds) Web and Internet Economics: Proceeding of the 10th International Conference, WINE 2014, Beijing, China, 14–17 December 2014Google Scholar
  15. Joachims T, Granka L, Pan B, Hembrooke H, Gay G (2005) Accurately interpreting clickthrough data as implicit feedback. In: Proceedings of the 28th annual international ACM SIGIR conference on research and development in information retrieval, pp 154–161. ACMGoogle Scholar
  16. Kempe D, Mahdian M (2008) A cascade model for externalities in sponsored search. In: Papadimitriou, Christos, Zhang, Shuzhong (eds) Internet and Network Economics. Proceedings of the 4th International Workshop, WINE 2008, Shanghai, China, 17–20 December 2008Google Scholar
  17. Krumme C, Cebrian M, Pickard G, Pentland S (2012) Quantifying social influence in an online cultural market. PloS One 7(5):e33785. doi:10.1371/journal.pone.0033785 CrossRefGoogle Scholar
  18. L’Ecuyer P, Maillé P, Stier-Moses N, Tuffin B (2015) Revenue-maximizing rankings for online platforms with quality-sensitive consumers. Technical Report: Les Cahiers du Gerad, G-2015-73. University of Montreal, Montreal, CanadaGoogle Scholar
  19. Lerman K, Hogg T (2014) Leveraging position bias to improve peer recommendation. PloS One 9(6):06CrossRefGoogle Scholar
  20. Liu Q, van Ryzin G (2008) On the choice-based linear programming model for network revenue management. Manuf Serv Oper Manag 10(2):288–310Google Scholar
  21. Duncan Luce R (1965) Individual choice behavior. Wiley, New YorkGoogle Scholar
  22. Maillé Patrick, Markakis Evangelos, Naldi Maurizio, Stamoulis George D, Tuffin Bruno (2012) Sponsored search auctions: an overview of research with emphasis on game theoretic aspects. Electron Commer Res 12(3):265–300CrossRefGoogle Scholar
  23. Rusmevichientong P, Shen Z-JM, Shmoys DB (2010a) Dynamic assortment optimization with a multinomial logit choice model and capacity constraint. Oper Res 58(6):1666–1680CrossRefGoogle Scholar
  24. Rusmevichientong P, Shmoys D, Topaloglu H (2010b) Assortment optimization with mixtures of logits. Technical report, School of IEOR, Cornell UniversityGoogle Scholar
  25. Salganik Matthew J, Dodds Peter Sheridan, Watts Duncan J (2006) Experimental study of inequality and unpredictability in an artificial cultural market. Science 311(5762):854–856CrossRefGoogle Scholar
  26. Talluri Kalyan, Van Ryzin Garrett (2004) Revenue management under a general discrete choice model of consumer behavior. Manag Sci 50(1):15–33CrossRefGoogle Scholar
  27. Tucker Catherine, Zhang Juanjuan (2011) How does popularity information affect choices? A field experiment. Manag Sci 57(5):828–842CrossRefGoogle Scholar
  28. Williams HCWL (1977) On the formation of travel demand models and economic evaluation measures of user benefit Environ Plan 9(3):285–344Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Andrés Abeliuk
    • 1
  • Gerardo Berbeglia
    • 2
  • Manuel Cebrian
    • 1
  • Pascal Van Hentenryck
    • 3
  1. 1.The University of Melbourne and National ICT AustraliaMelbourneAustralia
  2. 2.Melbourne Business SchoolThe University of Melbourne and National ICT AustraliaMelbourneAustralia
  3. 3.Department of Industrial and Operations EngineeringThe University of MichiganAnn ArborUSA

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