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Shortage decision policies for a fluid production model with MAP arrivals

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  • Yonit Barron
  • Dror Hermel

Abstract

We consider on a continuous production/inventory process where a single machine produces a certain product into a finite buffer. The demands arrive according to a Markov Additive Process governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. Two shortage policies are considered: the backorder policy, in which any demand that cannot be satisfied immediately is backlogged, and the order policy, in which any demand that cannot be satisfied immediately is supplied (alternatively, the latter policy can be considered as lost sales). We assume that the total cost includes a production loss cost, a penalty cost, a fixed cost for an order and a variable cost for the ordered amount. By applying the regenerative theory, we use tools from the exit-time theorem for fluid processes to obtain the discounted cost functionals under both policies. In addition, the models are extended to include a non-zero safety stock. Numerical examples, sensitivity analysis and comparative study are included.

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  • Yonit Barron & Dror Hermel, 2017. "Shortage decision policies for a fluid production model with MAP arrivals," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 3946-3969, July.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:14:p:3946-3969
    DOI: 10.1080/00207543.2016.1218083
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    References listed on IDEAS

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    Cited by:

    1. (Ai-Chih) Chang, Jasmine & Lu, Haibing & (Junmin) Shi, Jim, 2019. "Stockout risk of production-inventory systems with compound Poisson demands," Omega, Elsevier, vol. 83(C), pages 181-198.
    2. Nethanel Drezner & Yonit Barron, 2024. "An emergency supply policy for an inventory replenishment model with returns and partial backorders," Annals of Operations Research, Springer, vol. 343(1), pages 175-221, December.
    3. Barron, Yonit, 2022. "The continuous (S,s,Se) inventory model with dual sourcing and emergency orders," European Journal of Operational Research, Elsevier, vol. 301(1), pages 18-38.
    4. Yonit Barron & Chananel Benshimol, 2024. "Emergency Supply Alternatives for a Storage Facility of a Repairable Multi-Component System," Mathematics, MDPI, vol. 12(17), pages 1-37, August.
    5. Yonit Barron, 2024. "Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment," Mathematics, MDPI, vol. 12(9), pages 1-30, April.

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