Assortment Optimization

  • Guillermo Gallego
  • Huseyin Topaloglu
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 279)


A fundamental question in revenue management involves deciding which fares to offer in response to a request from an origin to a destination. The solution depends on available capacity, the time of departure, and how consumers make choices. This problem needs to be solved in real time as travel requests arrive. The assortment optimization problem is crucial in other RM applications such as hotels and car rentals, and is becoming more important in retailing and e-commerce. The fundamental tradeoff in assortment optimization is that broad assortments result in demand cannibalization and spoilage, while narrow assortments result in disappointed consumers that may walk away without purchasing. The formulation can be interpreted broadly to include more strategic decisions such as the location of stores within a city. The profitability of an assortment can be best captured through a choice model that provides sale probabilities as a function of the set of products contained in the assortment. In this chapter, we formulate and solve assortment optimization problems for many of the choice models presented in the previous chapter.


  1. A. Alptekinoglu, A. Grasas, When to carry eccentric products? Optimal retail assortment under consumer returns. Prod. Oper. Manag. 23 (5), 877–892 (2014)Google Scholar
  2. A. Aouad, D. Segev, Display optimization for vertically differentiated locations under multinomial logit preferences. Technical report, London School of Business, London, UK (2018)Google Scholar
  3. A. Aouad, V.F. Farias, R. Levi, Assortment optimization under consider-then-choose choice models. Technical report, MIT, Cambridge, MA (2016)Google Scholar
  4. A. Aouad, V.F. Farias, R. Levi, D. Segev, The approximability of assortment planning under ranking preferences. Oper. Res. 66 (6), 1661–1669 (2018a)CrossRefGoogle Scholar
  5. A. Aouad, J.B. Feldman, D. Segev, The exponomial choice model: assortment optimization and application to public transit choice prediction in San Francisco. Technical report, Washington University, St. Louis, MO (2018b)Google Scholar
  6. G. Berbeglia, G. Joret, Assortment optimisation under a general discrete choice model: a tight analysis of revenue-ordered assortments, in Proceedings of the 2017 ACM Conference on Economics and Computation, Cambridge, MA (2017), pp. 345–346Google Scholar
  7. F. Bernstein, V. Martinez-de-Albeniz, Dynamic product rotation in the presence of strategic customers. Manag. Sci. 63 (7), 2092–2107 (2017)CrossRefGoogle Scholar
  8. D. Bertsimas, V. Misic, Robust product line design. Oper. Res. 65 (1), 19–37 (2017)CrossRefGoogle Scholar
  9. D. Bertsimas, V. Misic, Exact first-choice product line optimization. Oper. Res. 67(3), 651–670 (2019)CrossRefGoogle Scholar
  10. J. Blanchet, G. Gallego, V. Goyal, A Markov chain approximation to choice modeling. Oper. Res. 64 (4), 886–905 (2016)CrossRefGoogle Scholar
  11. J.J.M. Bront, I. Mendez Diaz, G. Vulcano, A column generation algorithm for choice-based network revenue management. Oper. Res. 57 (3), 769–784 (2009)CrossRefGoogle Scholar
  12. G. Cachon, C. Terwiesch, Y. Xu, Retail assortment planning in the presence of consumer search. Manuf. Serv. Oper. Manag. 7 (4), 330–346 (2005)CrossRefGoogle Scholar
  13. F. Caro, J. Gallien, Dynamic assortment with demand learning for seasonal consumer goods. Manag. Sci. 53 (2), 276–292 (2007)CrossRefGoogle Scholar
  14. F. Caro, J. Gallien, Inventory management of a fast-fashion retail network. Oper. Res. 58 (2), 257–273 (2010)CrossRefGoogle Scholar
  15. F. Caro, V. Martinez-de-Albeniz, The effect of assortment rotation on consumer choice, and its impact on competition, in Operations Management Models with Consumer-Driven Demand, ed. by S. Netessine, C. Tang (Springer, New York, 2009)Google Scholar
  16. F. Caro, V. Martinez-de-Albeniz, How fast fashion works: can it work for you, too? IESE Insight Rev. 21, 58–65 (2014)CrossRefGoogle Scholar
  17. F. Caro, V. Martinez-de-Albeniz, Fast fashion: business model overview and research opportunities, in Retail Supply Chain Management: Quantitative Models and Empirical Studies, ed. by N. Agrawal, S.A. Smith (Springer, New York, 2015)Google Scholar
  18. F. Caro, J. Gallien, M. Diaz, J. Garcia, J.M. Corredoira, M. Montes, J.A. Ramos, J. Correa, Zara uses operations research to reengineer its global distribution process. Interfaces 40 (1), 71–84 (2010)CrossRefGoogle Scholar
  19. F. Caro, V. Martinez-de-Albeniz, P. Rusmevichientong, The assortment packing problem: multiperiod assortment planning for short-lived products. Manag. Sci. 60 (11), 2701–2721 (2014)CrossRefGoogle Scholar
  20. J.-K. Chong, T.-H. Ho, C.S. Tang, A modeling framework for category assortment planning. Manuf. Serv. Oper. Manag. 3 (3), 191–210 (2001)CrossRefGoogle Scholar
  21. H. Chung, H.-S. Ahn, S. Jasin, (Rescaled) multi-attempt approximation of choice model and its application to assortment optimization. Prod. Oper. Manag. 8(2), 341–353 (2019)CrossRefGoogle Scholar
  22. E. Cinar, V. Martinez-de-Albeniz, A closed-loop approach to dynamic assortment planning. Technical report, University of Navarra, Barcelona (2014)Google Scholar
  23. P.B. Collado, V. Martinez-de-Albeniz, Estimating and optimizing the impact of inventory on consumer choices in a fashion retail setting. Technical report, University of Navarra, Barcelona (2017)Google Scholar
  24. J. Davis, G. Gallego, H. Topaloglu, Assortment planning under the multinomial logit model with totally unimodular constraint structures. Technical report, Cornell University, School of Operations Research and Information Engineering (2013)Google Scholar
  25. J.M. Davis, G. Gallego, H. Topaloglu, Assortment optimization under variants of the nested logit model. Oper. Res. 62 (2), 250–273 (2014)CrossRefGoogle Scholar
  26. A. Desir, V. Goyal, An FPTAS for capacity constrained assortment optimization. Technical report, Columbia University, New York, NY (2013)Google Scholar
  27. A. Desir, V. Goyal, D. Segev, C. Ye, Capacity constrained assortment optimization under the Markov chain based choice model. Technical report, Columbia University, New York, NY (2015)CrossRefGoogle Scholar
  28. A. Desir, V. Goyal, S. Jagabathula, D. Segev, A Mallows-smoothed distribution over rankings approach for modeling choice. Technical report, Columbia University, New York, NY (2018)CrossRefGoogle Scholar
  29. D. Dzyabura, S. Jagabathula, Offline assortment optimization in the presence of an online channel. Manag. Sci. 64 (6), 2767–2786 (2018)CrossRefGoogle Scholar
  30. V.F. Farias, S. Jagabathula, D. Shah, A non-parametric approach to modeling choice with limited data. Manag. Sci. 59 (2), 305–322 (2013)CrossRefGoogle Scholar
  31. V.F. Farias, S. Jagabathula, D. Shah, Building optimized and hyperlocal product assortments: a nonparametric choice approach. Technical report, MIT, Cambridge, MA (2016)Google Scholar
  32. J. Feldman, Space constrained assortment optimization under the paired combinatorial model. Technical report, Washington University, St. Louis, MO (2018)Google Scholar
  33. J. Feldman, A. Paul, Relating the approximability of the fixed cost and space constrained assortment problems. Prod. Oper. Manag. 8(5), 1238–1255 (2019)CrossRefGoogle Scholar
  34. J. Feldman, H. Topaloglu, Bounding optimal expected revenues for assortment optimization under mixtures of multinomial logits. Prod. Oper. Manag. 24 (10), 1598–1620 (2015a)CrossRefGoogle Scholar
  35. J.B. Feldman, H. Topaloglu, Technical note – capacity constraints across nests in assortment optimization under the nested logit model. Oper. Res. 63 (4), 812–822 (2015b)CrossRefGoogle Scholar
  36. J.B. Feldman, H. Topaloglu, Revenue management under the Markov chain choice model. Oper. Res. 65 (5), 1322–1342 (2017)CrossRefGoogle Scholar
  37. J. Feldman, H. Topaloglu, Technical note – capacitated assortment optimization under the multinomial logit model with nested consideration sets. Oper. Res. 66 (2), 380–391 (2018)CrossRefGoogle Scholar
  38. J. Feldman, D. Zhang, X. Liu, N. Zhang, Taking assortment optimization from theory to practice: evidence from large field experiments on alibaba. Technical report, Washington University, St. Louis, MO (2018)Google Scholar
  39. J. Feldman, A. Paul, H. Topaloglu, Technical note – assortment optimization with small consideration sets. Oper. Res. (2019, forthcoming)Google Scholar
  40. K. Ferreira, J. Goh, Assortment rotation and the value of concealment. Technical report, Harvard Business School, Cambridge, MA (2018)Google Scholar
  41. G. Gallego, A. Li, Attention, consideration then selection choice model. Technical report, Hong Kong University of Science and Technology, Hong Kong (2016)Google Scholar
  42. G. Gallego, H. Topaloglu, Constrained assortment optimization for the nested logit model. Manag. Sci. 60 (10), 2583–2601 (2014)CrossRefGoogle Scholar
  43. G. Gallego, G. Iyengar, R. Phillips, A. Dubey, Managing flexible products on a network. Computational Optimization Research Center Technical Report TR-2004-01, Columbia University (2004)Google Scholar
  44. G. Gallego, R. Ratliff, S. Shebalov, A general attraction model and sales-based linear program for network revenue management under consumer choice. Oper. Res. 63 (1), 212–232 (2015)CrossRefGoogle Scholar
  45. G. Gallego, A. Li, V.A. Truong, X. Wang, Approximation algorithms for product framing and pricing. Technical report, Columbia University, New York, NY (2016a)Google Scholar
  46. D. Honhon, S. Jonnalagedda, X.A. Pan, Optimal algorithms for assortment selection under ranking-based consumer choice models. Manuf. Serv. Oper. Manag. 14 (2), 279–289 (2012)CrossRefGoogle Scholar
  47. S. Jagabathula, Assortment optimization under general choice. Technical report, New York University, New York, NY (2016)Google Scholar
  48. S. Jagabathula, P. Rusmevichientong, A nonparametric joint assortment and price choice model. Manag. Sci. 63 (9), 3128–3145 (2017)CrossRefGoogle Scholar
  49. A.G. Kok, M. Fisher, R. Vaidyanathan, Assortment planning: review of literature and industry practice, in Retail Supply Chain Management, ed. by N. Agrawal, S.A. Smith (Springer, New York, 2008)Google Scholar
  50. S. Kunnumkal, On upper bounds for assortment optimization under the mixture of multinomial logit models. Oper. Res. Lett. 43 (2), 189–194 (2015)CrossRefGoogle Scholar
  51. S. Kunnumkal, V. Martinez-de-Albeniz, Tractable approximations for assortment planning with product costs. Oper. Res. 67(2), 436–452 (2019)Google Scholar
  52. G. Li, P. Rusmevichientong, H. Topaloglu, The d-level nested logit model: assortment and price optimization problems. Oper. Res. 62 (2), 325–342 (2015)CrossRefGoogle Scholar
  53. I. Mendez-Diaz, J.M. Bront, G. Vulcano, P. Zabala, A branch-and-cut algorithm for the latent-class logit assortment problem. Discrete Appl. Math. 164 (1), 246–263 (2014)CrossRefGoogle Scholar
  54. X.A. Pan, D. Honhon, Assortment planning for vertically differentiated products. Prod. Oper. Manag. 21 (2), 253–275 (2012)CrossRefGoogle Scholar
  55. A. Paul, J. Feldman, J.M. Davis, Assortment optimization and pricing under a nonparametric tree choice model. Manuf. Serv. Oper. Manag. 20 (3), 550–565 (2018)CrossRefGoogle Scholar
  56. P. Rusmevichientong, H. Topaloglu, Robust assortment optimization under the multinomial logit choice model. Oper. Res. 60 (4), 865–882 (2012)CrossRefGoogle Scholar
  57. P. Rusmevichientong, Z.-J.M. Shen, D.B. Shmoys, A PTAS for capacitated sum-of-ratios optimization. Oper. Res. Lett. 37 (4), 230–238 (2009)CrossRefGoogle Scholar
  58. P. Rusmevichientong, Z.-J.M. Shen, D.B. Shmoys, Dynamic assortment optimization with a multinomial logit choice model and capacity constraint. Oper. Res. 58 (6), 1666–1680 (2010)CrossRefGoogle Scholar
  59. P. Rusmevichientong, D.B. Shmoys, C. Tong, H. Topaloglu, Assortment optimization under the multinomial logit model with random choice parameters. Prod. Oper. Manag. 23 (11), 2023–2039 (2014)CrossRefGoogle Scholar
  60. K. Talluri, G. van Ryzin, Revenue management under a general discrete choice model of consumer behavior. Manag. Sci. 50 (1), 15–33 (2004a)CrossRefGoogle Scholar
  61. V.-A. Truong, Optimal selection of medical formularies. J. Revenue Pricing Manag. 13 (2), 113–132 (2014)CrossRefGoogle Scholar
  62. C. Ulu, D. Honhon, A. Alptekinoglu, Learning consumer tastes through dynamic assortments. Oper. Res. 60 (4), 833–849 (2012)CrossRefGoogle Scholar
  63. G.J. van Ryzin, S. Mahajan, On the relationship between inventory costs and variety benefits in retailassortments. Manag. Sci. 45 (11), 1496–1509 (1999)CrossRefGoogle Scholar
  64. R. Wang, Capacitated assortment and price optimization under the multinomial logit choice model. Oper. Res. Lett. 40 (6), 492–497 (2012)CrossRefGoogle Scholar
  65. R. Wang, Assortment management under the generalized attraction model with a capacity constraint. J. Revenue Pricing Manag. 12 (3), 254–270 (2013)CrossRefGoogle Scholar
  66. R. Wang, O. Sahin, The impact of consumer search cost on assortment planning and pricing. Manag. Sci. 64 (8), 3649–3666 (2018)CrossRefGoogle Scholar
  67. Y. Wang, Z.-J.M. Shen, Joint optimization of capacitated assortment and pricing problem under the tree logit model. Technical report, University of California, Berkeley, CA (2017)Google Scholar
  68. R. Wang, Z. Wang, Consumer choice models with endogenous network effects. Manag. Sci. 63 (11), 3944–3960 (2017)CrossRefGoogle Scholar
  69. H. Zhang, P. Rusmevichientong, H. Topaloglu, Assortment optimization under the paired combinatorial logit model. Technical report, Cornell University, Ithaca, NY (2017)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Guillermo Gallego
    • 1
  • Huseyin Topaloglu
    • 2
  1. 1.Clearwater BayHong Kong
  2. 2.ORIECornell UniversityNew YorkUSA

Personalised recommendations