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Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment

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  • Yonit Barron

    (Industrial Engineering and Management, Ariel University, Ariel 40700, Israel)

Abstract

We study a continuous-review stock management of a retailer for a single item in a limited storage (buffer) in a random environment. The stock level fluctuates according to two independent compound Poisson processes with discrete amounts of items (batches) that enter and leave the storage facility. The storage facility is controlled by a three-parameter base-stock replenishment policy. All items exceeding the storage capacity are transferred to an unlimited foreign facility. In addition, a restricted backlogging possibility is permitted; additional demands for items are lost sales. We further assume a random shelf life, the possibility of total inventory collapse, and a random lead time. Applying Markov theory, we derive the optimal control parameters minimizing the long-run expected total cost. A sensitivity analysis is conducted focusing on the comparison between the pure lost-sales policy and a partial backordering policy. Accordingly, we identify cases where one policy is cost effective compared to the other, particularly with respect to the batch patterns (sign, rate, average, and variability), and the associated costs.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1341-:d:1384967
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    References listed on IDEAS

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    1. Kouki, Chaaben & Legros, Benjamin & Zied Babai, M. & Jouini, Oualid, 2020. "Analysis of base-stock perishable inventory systems with general lifetime and lead-time," European Journal of Operational Research, Elsevier, vol. 287(3), pages 901-915.
    2. Kebing Chen & Jing‐Sheng Song & Jennifer Shang & Tiaojun Xiao, 2022. "Managing hospital platelet inventory with mid‐cycle expedited replenishments and returns," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2015-2037, May.
    3. Wang, Daqin & Tang, Ou, 2014. "Dynamic inventory rationing with mixed backorders and lost sales," International Journal of Production Economics, Elsevier, vol. 149(C), pages 56-67.
    4. David A. Schrady, 1967. "A deterministic inventory model for reparable items," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(3), pages 391-398.
    5. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    6. Douglas C. Montgomery & M. S. Bazaraa & Ajit K. Keswani, 1973. "Inventory models with a mixture of backorders and lost sales," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 255-263, June.
    7. Kebing Chen & Tiaojun Xiao & Shengbin Wang & Dong Lei, 2021. "Inventory strategies for perishable products with two-period shelf-life and lost sales," International Journal of Production Research, Taylor & Francis Journals, vol. 59(17), pages 5301-5320, September.
    8. Ernesto Armando Pacheco-Velázquez & Manuel Robles-Cárdenas & Saúl Juárez Ordóñez & Abelardo Ernesto Damy Solís & Leopoldo Eduardo Cárdenas-Barrón, 2023. "A Heuristic Model for Spare Parts Stocking Based on Markov Chains," Mathematics, MDPI, vol. 11(16), pages 1-21, August.
    9. Daniel P. Heyman, 1978. "Return policies for an inventory system with positive and negative demands," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(4), pages 581-596, December.
    10. Mrudul Y. Jani & Heta A. Patel & Amrita Bhadoriya & Urmila Chaudhari & Mohamed Abbas & Malak S. Alqahtani, 2023. "Deterioration Control Decision Support System for the Retailer during Availability of Trade Credit and Shortages," Mathematics, MDPI, vol. 11(3), pages 1-27, January.
    11. 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.
    12. Hsien-Jen Lin, 2017. "Two-critical-number control policy for a stochastic production inventory system with partial backlogging," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 4123-4135, July.
    13. David Rosenberg, 1979. "A new analysis of a lot‐size model with partial backlogging," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(2), pages 349-353, June.
    14. Kamran Moinzadeh, 1989. "Operating Characteristics of the (S - 1, S) Inventory System with Partial Backorders and Constant Resupply Times," Management Science, INFORMS, vol. 35(4), pages 472-477, April.
    15. Saeed Poormoaied & Zümbül Atan & Ton de Kok & Tom Van Woensel, 2020. "Optimal inventory and timing decisions for emergency shipments," IISE Transactions, Taylor & Francis Journals, vol. 52(8), pages 904-925, August.
    16. Fleischmann, Moritz & Kuik, Roelof, 2003. "On optimal inventory control with independent stochastic item returns," European Journal of Operational Research, Elsevier, vol. 151(1), pages 25-37, November.
    17. Goedhart, Joost & Haijema, René & Akkerman, Renzo, 2023. "Modelling the influence of returns for an omni-channel retailer," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1248-1263.
    18. Cui, Hailong & Rajagopalan, Sampath & Ward, Amy R., 2020. "Predicting product return volume using machine learning methods," European Journal of Operational Research, Elsevier, vol. 281(3), pages 612-627.
    19. Joaquín Sicilia & Luis San-José & Juan García-Laguna, 2012. "An inventory model where backordered demand ratio is exponentially decreasing with the waiting time," Annals of Operations Research, Springer, vol. 199(1), pages 137-155, October.
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