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Optimal Policies and Approximations for a Bayesian Linear Regression Inventory Model

Author

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  • Katy S. Azoury

    (Department of Decision Sciences, College of Business, San Francisco State University, San Francisco, California 94132)

  • Julia Miyaoka

    (Department of Decision Sciences, College of Business, San Francisco State University, San Francisco, California 94132)

Abstract

In this paper, we consider a periodic review inventory problem where demand in each period is modeled by linear regression. We use a Bayesian formulation to update the regression parameters as new information becomes available. We find that a state-dependent base-stock policy is optimal and we give structural results. One interesting finding is that our structural results are not analogous to classical results in Bayesian inventory research. This departure from classical results is due to the role that the independent variables play in the Bayesian regression formulation. Because of the computational complexity of the optimal policy, we propose a combination of two heuristics that simplifies the Bayesian inventory problem. Through analytical and numerical evaluation, we find that the heuristics provide near-optimal results.

Suggested Citation

  • Katy S. Azoury & Julia Miyaoka, 2009. "Optimal Policies and Approximations for a Bayesian Linear Regression Inventory Model," Management Science, INFORMS, vol. 55(5), pages 813-826, May.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:5:p:813-826
    DOI: 10.1287/mnsc.1080.0980
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    References listed on IDEAS

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    3. Zhang, Jian & Zhang, Juliang & Hua, Guowei, 2016. "Multi-period inventory games with information update," International Journal of Production Economics, Elsevier, vol. 174(C), pages 119-127.
    4. Lee, Yun Shin, 2014. "Management of a periodic-review inventory system using Bayesian model averaging when new marketing efforts are made," International Journal of Production Economics, Elsevier, vol. 158(C), pages 278-289.
    5. Prak, Dennis & Teunter, Ruud, 2019. "A general method for addressing forecasting uncertainty in inventory models," International Journal of Forecasting, Elsevier, vol. 35(1), pages 224-238.
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    7. Li, Tianyun & Fang, Weiguo & Baykal-Gürsoy, Melike, 2021. "Two-stage inventory management with financing under demand updates," International Journal of Production Economics, Elsevier, vol. 232(C).

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