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Analysis of the ( Q , r ) Inventory Model for Perishables with Positive Lead Times and Lost Sales

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  • Emre Berk

    (Faculty of Business Administration, Bilkent University, Bilkent 06800, Ankara, Turkey)

  • Ülkü Gürler

    (Faculty of Engineering, Department of Industrial Engineering, Bilkent University, Bilkent 06800, Ankara, Turkey)

Abstract

We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review ( Q , r ) policy, where r Q . The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the ( Q , r ) policy with respect to a time-based benchmark policy and find that the ( Q , r ) policy might be impractical for rare events, but overall appears to be a good heuristic policy.

Suggested Citation

  • Emre Berk & Ülkü Gürler, 2008. "Analysis of the ( Q , r ) Inventory Model for Perishables with Positive Lead Times and Lost Sales," Operations Research, INFORMS, vol. 56(5), pages 1238-1246, October.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:5:p:1238-1246
    DOI: 10.1287/opre.1080.0582
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    References listed on IDEAS

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    1. Chiu, Huan Neng, 1995. "An approximation to the continuous review inventory model with perishable items and lead times," European Journal of Operational Research, Elsevier, vol. 87(1), pages 93-108, November.
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    1. Kouki, Chaaben & Babai, M. Zied & Minner, Stefan, 2018. "On the benefit of dual-sourcing in managing perishable inventory," International Journal of Production Economics, Elsevier, vol. 204(C), pages 1-17.
    2. Elena Belavina & Karan Girotra & Ashish Kabra, 2017. "Online Grocery Retail: Revenue Models and Environmental Impact," Management Science, INFORMS, vol. 63(6), pages 1781-1799, June.
    3. Dehghani, Maryam & Abbasi, Babak, 2018. "An age-based lateral-transshipment policy for perishable items," International Journal of Production Economics, Elsevier, vol. 198(C), pages 93-103.
    4. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    5. Emre Berk & Ülkü Gürler & Saeed Poormoaied, 2020. "On the $$\varvec{(Q,r)}$$(Q,r) policy for perishables with positive lead times and multiple outstanding orders," Annals of Operations Research, Springer, vol. 284(1), pages 81-98, January.
    6. Hansen, Ole & Transchel, Sandra & Friedrich, Hanno, 2023. "Replenishment strategies for lost sales inventory systems of perishables under demand and lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 308(2), pages 661-675.
    7. Yeu-Shiang Huang & Hau-Wen Lo & Jyh-Wen Ho, 2021. "Effects of component commonality and perishability on inventory control in assemble-to-order systems," Operational Research, Springer, vol. 21(1), pages 205-229, March.
    8. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    9. Fredrik Olsson, 2014. "Analysis of inventory policies for perishable items with fixed leadtimes and lifetimes," Annals of Operations Research, Springer, vol. 217(1), pages 399-423, June.
    10. Xiong‐zhi Wang & Guo‐qing Wang, 2019. "Integrating dynamic pricing and inventory control for fresh‐agri product under consumer choice," Australian Economic Papers, Wiley Blackwell, vol. 58(1), pages 96-111, March.
    11. Yonit Barron & Opher Baron, 2020. "The residual time approach for (Q, r) model under perishability, general lead times, and lost sales," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 601-648, December.
    12. Mahmut Parlar & David Perry & Wolfgang Stadje, 2011. "FIFO Versus LIFO Issuing Policies for Stochastic Perishable Inventory Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 405-417, June.
    13. Kouki, Chaaben & Sahin, Evren & Jemaï, Zied & Dallery, Yves, 2013. "Assessing the impact of perishability and the use of time temperature technologies on inventory management," International Journal of Production Economics, Elsevier, vol. 143(1), pages 72-85.
    14. Xiang Li & Guohua Sun & Yongjian Li, 2016. "A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products," Annals of Operations Research, Springer, vol. 242(2), pages 207-221, July.
    15. 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.
    16. Onno Boxma & David Perry & Wolfgang Stadje & Shelley Zacks, 2022. "A compound Poisson EOQ model for perishable items with intermittent high and low demand periods," Annals of Operations Research, Springer, vol. 317(2), pages 439-459, October.
    17. Poormoaied, Saeed & Atan, Zümbül, 2020. "A multi-attribute utility theory approach to ordering policy for perishable items," International Journal of Production Economics, Elsevier, vol. 225(C).
    18. Onno Boxma & David Perry & Shelley Zacks, 2015. "A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 390-402, February.

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