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The Application of Queueing Theory to Continuous Perishable Inventory Systems

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  • Stephen C. Graves

    (Massachusetts Institute of Technology)

Abstract

This paper develops two distinct models for studying inventory systems with continuous production and perishable items. The perishable items have a deterministic usable life after which they must be outdated. For each of the models, analytical expressions derived from queueing theory, are found for the steady-state distribution of system inventory. Knowledge of this steady-state behavior may be used for evaluation of system performance, and for consideration of alternatives for improving system performance. Both models assume that inventory is replenished by a continuous production process. The first model, assuming continuous inventory units, has Poisson demand requests with the size of each request distributed as an exponential random variable. The second model has Poisson demand requests with all demands being for a single unit. The analysis for both models exploits the similarity of the inventory system with a single-server queueing system.

Suggested Citation

  • Stephen C. Graves, 1982. "The Application of Queueing Theory to Continuous Perishable Inventory Systems," Management Science, INFORMS, vol. 28(4), pages 400-406, April.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:4:p:400-406
    DOI: 10.1287/mnsc.28.4.400
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    Cited by:

    1. Kopach, Renata & Balcioglu, Baris & Carter, Michael, 2008. "Tutorial on constructing a red blood cell inventory management system with two demand rates," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1051-1059, March.
    2. Ravichandran, N., 1995. "Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand," European Journal of Operational Research, Elsevier, vol. 84(2), pages 444-457, July.
    3. Liming Liu & Zhaotong Lian, 1999. "(s, S) Continuous Review Models for Products with Fixed Lifetimes," Operations Research, INFORMS, vol. 47(1), pages 150-158, February.
    4. Krishnamoorthy, A. & Babu, S. & Narayanan, Viswanath C., 2009. "The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service," European Journal of Operational Research, Elsevier, vol. 195(1), pages 174-185, May.
    5. Michael N. Katehakis & Benjamin Melamed & Jim Junmin Shi, 2022. "Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost," Annals of Operations Research, Springer, vol. 317(2), pages 665-691, October.
    6. Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.
    7. Kouki, Chaaben & Jouini, Oualid, 2015. "On the effect of lifetime variability on the performance of inventory systems," International Journal of Production Economics, Elsevier, vol. 167(C), pages 23-34.
    8. Opher Baron & Oded Berman & David Perry, 2010. "Continuous review inventory models for perishable items ordered in batches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 217-247, October.
    9. Kim, Bara & Kim, Jeongsim, 2018. "Extension of the loss probability formula to an overloaded queue with impatient customers," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 54-62.
    10. Z Shen & M Dessouky & F Ordonez, 2011. "Perishable inventory management system with a minimum volume constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(12), pages 2063-2082, December.
    11. Kai Li & Yuqian Pan & Bayi Cheng & Bohai Liu, 2018. "The Setting and Optimization of Quick Queue," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 1014-1026, September.
    12. Philipp Afèche & Adam Diamant & Joseph Milner, 2014. "Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks," Operations Research, INFORMS, vol. 62(5), pages 1179-1201, October.
    13. Jim Shi, 2022. "Optimal continuous production-inventory systems subject to stockout risk," Annals of Operations Research, Springer, vol. 317(2), pages 777-804, October.
    14. Babak Abbasi & Golnaz Vakili & Stuart Chesneau, 2017. "Impacts of Reducing the Shelf Life of Red Blood Cells: A View from Down Under," Interfaces, INFORMS, vol. 47(4), pages 336-351, August.
    15. David Perry, 1999. "Analysis of a Sampling Control Scheme for a Perishable Inventory System," Operations Research, INFORMS, vol. 47(6), pages 966-973, December.
    16. Kevin Granville & Steve Drekic, 2019. "On a 2-class polling model with reneging and $$k_i$$ k i -limited service," Annals of Operations Research, Springer, vol. 274(1), pages 267-290, March.
    17. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.
    18. David Perry & M. J. M. Posner, 1998. "AN (S − 1, S) Inventory System with Fixed Shelf Life and Constant Lead Times," Operations Research, INFORMS, vol. 46(3-supplem), pages 65-71, June.
    19. 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.
    20. M. Amirthakodi & V. Radhamani & B. Sivakumar, 2015. "A perishable inventory system with service facility and feedback customers," Annals of Operations Research, Springer, vol. 233(1), pages 25-55, October.
    21. Toraubally, Waseem A., 2023. "Comparative advantage with many goods: New treatment and results," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1188-1201.
    22. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    23. 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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