Revenue Management and Pricing Analytics pp 129-160 | Cite as

# Assortment Optimization

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## Abstract

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.

## References

- 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 - 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
- A. Aouad, V.F. Farias, R. Levi, Assortment optimization under consider-then-choose choice models. Technical report, MIT, Cambridge, MA (2016)Google Scholar
- 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 - 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
- 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 - F. Bernstein, V. Martinez-de-Albeniz, Dynamic product rotation in the presence of strategic customers. Manag. Sci.
**63**(7), 2092–2107 (2017)CrossRefGoogle Scholar - D. Bertsimas, V. Misic, Robust product line design. Oper. Res.
**65**(1), 19–37 (2017)CrossRefGoogle Scholar - D. Bertsimas, V. Misic, Exact first-choice product line optimization. Oper. Res.
**67**(3), 651–670 (2019)CrossRefGoogle Scholar - J. Blanchet, G. Gallego, V. Goyal, A Markov chain approximation to choice modeling. Oper. Res.
**64**(4), 886–905 (2016)CrossRefGoogle Scholar - 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 - 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 - F. Caro, J. Gallien, Dynamic assortment with demand learning for seasonal consumer goods. Manag. Sci.
**53**(2), 276–292 (2007)CrossRefGoogle Scholar - F. Caro, J. Gallien, Inventory management of a fast-fashion retail network. Oper. Res.
**58**(2), 257–273 (2010)CrossRefGoogle Scholar - 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 - 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 - 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 - 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 - 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 - 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 - 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 - E. Cinar, V. Martinez-de-Albeniz, A closed-loop approach to dynamic assortment planning. Technical report, University of Navarra, Barcelona (2014)Google Scholar
- 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
- 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
- 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 - A. Desir, V. Goyal, An FPTAS for capacity constrained assortment optimization. Technical report, Columbia University, New York, NY (2013)Google Scholar
- 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
- 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
- D. Dzyabura, S. Jagabathula, Offline assortment optimization in the presence of an online channel. Manag. Sci.
**64**(6), 2767–2786 (2018)CrossRefGoogle Scholar - 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 - 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
- J. Feldman, Space constrained assortment optimization under the paired combinatorial model. Technical report, Washington University, St. Louis, MO (2018)Google Scholar
- 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 - 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 - 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 - J.B. Feldman, H. Topaloglu, Revenue management under the Markov chain choice model. Oper. Res.
**65**(5), 1322–1342 (2017)CrossRefGoogle Scholar - 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 - 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
- J. Feldman, A. Paul, H. Topaloglu, Technical note – assortment optimization with small consideration sets. Oper. Res. (2019, forthcoming)Google Scholar
- K. Ferreira, J. Goh, Assortment rotation and the value of concealment. Technical report, Harvard Business School, Cambridge, MA (2018)Google Scholar
- G. Gallego, A. Li, Attention, consideration then selection choice model. Technical report, Hong Kong University of Science and Technology, Hong Kong (2016)Google Scholar
- G. Gallego, H. Topaloglu, Constrained assortment optimization for the nested logit model. Manag. Sci.
**60**(10), 2583–2601 (2014)CrossRefGoogle Scholar - 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
- 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 - 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
- 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 - S. Jagabathula, Assortment optimization under general choice. Technical report, New York University, New York, NY (2016)Google Scholar
- S. Jagabathula, P. Rusmevichientong, A nonparametric joint assortment and price choice model. Manag. Sci.
**63**(9), 3128–3145 (2017)CrossRefGoogle Scholar - 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 - 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 - S. Kunnumkal, V. Martinez-de-Albeniz, Tractable approximations for assortment planning with product costs. Oper. Res.
**67**(2), 436–452 (2019)Google Scholar - 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 - 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 - X.A. Pan, D. Honhon, Assortment planning for vertically differentiated products. Prod. Oper. Manag.
**21**(2), 253–275 (2012)CrossRefGoogle Scholar - 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 - P. Rusmevichientong, H. Topaloglu, Robust assortment optimization under the multinomial logit choice model. Oper. Res.
**60**(4), 865–882 (2012)CrossRefGoogle Scholar - 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 - 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 - 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 - 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 - V.-A. Truong, Optimal selection of medical formularies. J. Revenue Pricing Manag.
**13**(2), 113–132 (2014)CrossRefGoogle Scholar - C. Ulu, D. Honhon, A. Alptekinoglu, Learning consumer tastes through dynamic assortments. Oper. Res.
**60**(4), 833–849 (2012)CrossRefGoogle Scholar - 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 - R. Wang, Capacitated assortment and price optimization under the multinomial logit choice model. Oper. Res. Lett.
**40**(6), 492–497 (2012)CrossRefGoogle Scholar - R. Wang, Assortment management under the generalized attraction model with a capacity constraint. J. Revenue Pricing Manag.
**12**(3), 254–270 (2013)CrossRefGoogle Scholar - R. Wang, O. Sahin, The impact of consumer search cost on assortment planning and pricing. Manag. Sci.
**64**(8), 3649–3666 (2018)CrossRefGoogle Scholar - 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
- R. Wang, Z. Wang, Consumer choice models with endogenous network effects. Manag. Sci.
**63**(11), 3944–3960 (2017)CrossRefGoogle Scholar - H. Zhang, P. Rusmevichientong, H. Topaloglu, Assortment optimization under the paired combinatorial logit model. Technical report, Cornell University, Ithaca, NY (2017)CrossRefGoogle Scholar