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Optimizing a single-product production-inventory system under constant absolute risk aversion

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Abstract

This paper considers a single-product production-inventory system managed by a base-stock policy where the factory inventory manager with cost concerns over a short time horizon can be modeled with the constant absolute risk aversion (CARA) utility function. We consider both backordering cost and stockout cost scenarios and investigate the roles of capacity utilization level and CARA coefficient on the optimal base-stock level. We derive closed-form solutions for the optimal inventory decisions, present related numerical experiments, and discuss their managerial implications. It is discovered that both scenarios share certain common structure in their optimal inventory decisions. Specifically, in the backordering cost scenario, if the backordering cost is high or the holding cost is low, the optimal base-stock level is high. In the stockout cost scenario, if the stockout cost is high or the holding cost is low, the optimal base-stock level is high. For both scenarios, inventory levels are high with tight capacity, and optimal base-stock level generally increases if the manager becomes more risk averse.

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Acknowledgements

The authors would like to thank the two anonymous reviewers and the editors-in-chief for their constructive comments, which have undoubtedly improved this work. The work of Bo Li and Sen Lin is supported by the National Natural Science Foundation of China [Grant 72271133] and the NISCI-TDH Line-haul Road Transportation Lab.

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Authors and Affiliations

  1. Ningbo China Institute for Supply Chain Innovation, Ningbo, Zhejiang, 315832, China

    Sen Lin & Bo Li

  2. Ningbo University, Ningbo, 315832, Zhejiang, China

    Bo Li

  3. Texas A&M University, College Station, TX, 77843, USA

    Antonio Arreola-Risa

  4. Penn State Shenango, Sharon, PA, 16146, USA

    Yiwei Huang

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  1. Sen Lin
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Correspondence to Bo Li.

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Lin, S., Li, B., Arreola-Risa, A. et al. Optimizing a single-product production-inventory system under constant absolute risk aversion. TOP 31, 510–537 (2023). https://doi.org/10.1007/s11750-022-00650-4

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