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A dynamic programming approach for quickly estimating large network-based MEV models

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  • Mai, Tien
  • Frejinger, Emma
  • Fosgerau, Mogens
  • Bastin, Fabian

Abstract

We propose a way to estimate a family of static Multivariate Extreme Value (MEV) models with large choice sets in short computational time. The resulting model is also straightforward and fast to use for prediction. Following Daly and Bierlaire (2006), the correlation structure is defined by a rooted, directed graph where each node without successor is an alternative. We formulate a family of MEV models as dynamic discrete choice models on graphs of correlation structures and show that the dynamic models are consistent with MEV theory and generalize the network MEV model (Daly and Bierlaire, 2006). Moreover, we show that these models can be estimated quickly using the concept of network flows and the nested fixed point algorithm (Rust, 1987). The main reason for the short computational time is that the new formulation allows to benefit from existing efficient solution algorithms for sparse linear systems of equations.

Suggested Citation

  • Mai, Tien & Frejinger, Emma & Fosgerau, Mogens & Bastin, Fabian, 2017. "A dynamic programming approach for quickly estimating large network-based MEV models," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 179-197.
    • Handle: RePEc:eee:transb:v:98:y:2017:i:c:p:179-197
    DOI: 10.1016/j.trb.2016.12.017
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    References listed on IDEAS

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    Cited by:

    1. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    2. Song, Yuchen & Li, Dawei & Liu, Dongjie & Cao, Qi & Chen, Junlan & Ren, Gang & Tang, Xiaoyong, 2022. "Modeling activity-travel behavior under a dynamic discrete choice framework with unobserved heterogeneity," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(C).
    3. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2023. "Robust maximum capture facility location under random utility maximization models," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1128-1150.
    4. Tien Mai & Patrick Jaillet, 2019. "Robust Product-line Pricing under Generalized Extreme Value Models," Papers 1912.09552, arXiv.org, revised Oct 2021.
    5. Shiva Habibi & Emma Frejinger & Marcus Sundberg, 2019. "An empirical study on aggregation of alternatives and its influence on prediction in car type choice models," Transportation, Springer, vol. 46(3), pages 563-582, June.
    6. Anna Fernández-Antolín & Matthieu Lapparent & Michel Bierlaire, 2018. "Modeling purchases of new cars: an analysis of the 2014 French market," Theory and Decision, Springer, vol. 84(2), pages 277-303, March.
    7. Hung Tran & Tien Mai, 2023. "Network-based Representations and Dynamic Discrete Choice Models for Multiple Discrete Choice Analysis," Papers 2306.04606, arXiv.org.

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