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Approximation Algorithms for Dynamic Assortment Optimization Models

Author

Listed:
  • Ali Aouad

    (London Business School, London NW1 4SA, United Kingdom)

  • Retsef Levi

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Danny Segev

    (Department of Statistics, University of Haifa, Haifa 31905, Israel)

Abstract

We consider the single-period joint assortment and inventory planning problem with stochastic demand and dynamic substitution across products, motivated by applications in highly differentiated markets, such as online retailing and airlines. This class of problems is known to be notoriously hard to deal with from a computational standpoint. In fact, prior to the present paper, only a handful of modeling approaches were shown to admit provably good algorithms, at the cost of strong restrictions on customers’ choice outcomes. Our main contribution is to provide the first efficient algorithms with provable performance guarantees for a broad class of dynamic assortment optimization models. Under general rank-based choice models, our approximation algorithm is best possible with respect to the price parameters, up to lower-order terms. In particular, we obtain a constant-factor approximation under horizontal differentiation, where product prices are uniform. In more structured settings, where the customers’ ranking behavior is motivated by price and quality cues, we derive improved guarantees through tailor-made algorithms. In extensive computational experiments, our approach dominates existing heuristics in terms of revenue performance, as well as in terms of speed, given the myopic nature of our methods. From a technical perspective, we introduce a number of novel algorithmic ideas of independent interest, and unravel hidden relations to submodular maximization.

Suggested Citation

  • Ali Aouad & Retsef Levi & Danny Segev, 2019. "Approximation Algorithms for Dynamic Assortment Optimization Models," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 487-511, May.
  • Handle: RePEc:inm:ormoor:v:44:y:2019:i:2:p:487-511
    DOI: 10.1287/moor.2018.0933
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    References listed on IDEAS

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    1. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    2. Vineet Goyal & Retsef Levi & Danny Segev, 2016. "Near-Optimal Algorithms for the Assortment Planning Problem Under Dynamic Substitution and Stochastic Demand," Operations Research, INFORMS, vol. 64(1), pages 219-235, February.
    3. Garrett van Ryzin & Siddharth Mahajan, 1999. "On the Relationship Between Inventory Costs and Variety Benefits in Retail Assortments," Management Science, INFORMS, vol. 45(11), pages 1496-1509, November.
    4. Dorothée Honhon & Vishal Gaur & Sridhar Seshadri, 2010. "Assortment Planning and Inventory Decisions Under Stockout-Based Substitution," Operations Research, INFORMS, vol. 58(5), pages 1364-1379, October.
    5. Dorothee Honhon & Sreelata Jonnalagedda & Xiajun Amy Pan, 2012. "Optimal Algorithms for Assortment Selection Under Ranking-Based Consumer Choice Models," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 279-289, April.
    6. Jose Blanchet & Guillermo Gallego & Vineet Goyal, 2016. "A Markov Chain Approximation to Choice Modeling," Operations Research, INFORMS, vol. 64(4), pages 886-905, August.
    7. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Mahesh Nagarajan & S. Rajagopalan, 2008. "Inventory Models for Substitutable Products: Optimal Policies and Heuristics," Management Science, INFORMS, vol. 54(8), pages 1453-1466, August.
    10. Paat Rusmevichientong & Huseyin Topaloglu, 2012. "Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model," Operations Research, INFORMS, vol. 60(4), pages 865-882, August.
    11. Vivek F. Farias & Srikanth Jagabathula & Devavrat Shah, 2013. "A Nonparametric Approach to Modeling Choice with Limited Data," Management Science, INFORMS, vol. 59(2), pages 305-322, December.
    12. James M. Davis & Guillermo Gallego & Huseyin Topaloglu, 2014. "Assortment Optimization Under Variants of the Nested Logit Model," Operations Research, INFORMS, vol. 62(2), pages 250-273, April.
    13. Paat Rusmevichientong & Benjamin Van Roy & Peter W. Glynn, 2006. "A Nonparametric Approach to Multiproduct Pricing," Operations Research, INFORMS, vol. 54(1), pages 82-98, February.
    14. Vishal Gaur & Dorothée Honhon, 2006. "Assortment Planning and Inventory Decisions Under a Locational Choice Model," Management Science, INFORMS, vol. 52(10), pages 1528-1543, October.
    15. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    16. Guang Li & Paat Rusmevichientong & Huseyin Topaloglu, 2015. "The d -Level Nested Logit Model: Assortment and Price Optimization Problems," Operations Research, INFORMS, vol. 63(2), pages 325-342, April.
    17. Jacob B. Feldman & Huseyin Topaloglu, 2017. "Revenue Management Under the Markov Chain Choice Model," Operations Research, INFORMS, vol. 65(5), pages 1322-1342, October.
    18. A. Gürhan Kök & Marshall L. Fisher, 2007. "Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application," Operations Research, INFORMS, vol. 55(6), pages 1001-1021, December.
    19. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
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    3. Paat Rusmevichientong & Mika Sumida & Huseyin Topaloglu, 2020. "Dynamic Assortment Optimization for Reusable Products with Random Usage Durations," Management Science, INFORMS, vol. 66(7), pages 2820-2844, July.

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