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(s, S) Continuous Review Models for Products with Fixed Lifetimes

Author

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  • Liming Liu

    (Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Zhaotong Lian

    (University of Massachusetts, Amherst, Massachusetts 01003)

Abstract

We analyze an ( s , S ) continuous review perishable inventory system with a general renewal demand process and instantaneous replenishments. Though continuous review systems seem more amenable to optimization analysis than do periodic review systems, the existing literature addressing this type of model is rather limited. This limitation motivated us to seek greater understanding of this important class of inventory models. Using a Markov renewal approach, we obtain closed-form solutions for the steady state probability distribution of the inventory level and system performance measures. We then construct a closed-form expected cost function. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of different parameters. The numerical results illustrate the system behavior and lead to managerial insights into controlling such inventory systems.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:1:p:150-158
    DOI: 10.1287/opre.47.1.150
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    References listed on IDEAS

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    1. William P. Pierskalla & Chris D. Roach, 1972. "Optimal Issuing Policies for Perishable Inventory," Management Science, INFORMS, vol. 18(11), pages 603-614, July.
    2. Morris A. Cohen, 1976. "Analysis of Single Critical Number Ordering Policies for Perishable Inventories," Operations Research, INFORMS, vol. 24(4), pages 726-741, August.
    3. Dan Chazan & Shmuel Gal, 1977. "A Markovian Model for a Perishable Product Inventory," Management Science, INFORMS, vol. 23(5), pages 512-521, January.
    4. Purushottaman Nandakumar & Thomas E. Morton, 1993. "Near Myopic Heuristics for the Fixed-Life Perishability Problem," Management Science, INFORMS, vol. 39(12), pages 1490-1498, December.
    5. Steven Nahmias, 1975. "Optimal Ordering Policies for Perishable Inventory—II," Operations Research, INFORMS, vol. 23(4), pages 735-749, August.
    6. Morris A. Cohen & Dov Pekelman, 1978. "LIFO Inventory Systems," Management Science, INFORMS, vol. 24(11), pages 1150-1162, July.
    7. Stephen C. Graves, 1982. "The Application of Queueing Theory to Continuous Perishable Inventory Systems," Management Science, INFORMS, vol. 28(4), pages 400-406, April.
    8. Howard J. Weiss, 1980. "Optimal Ordering Policies for Continuous Review Perishable Inventory Models," Operations Research, INFORMS, vol. 28(2), pages 365-374, April.
    9. Steven Nahmias, 1982. "Perishable Inventory Theory: A Review," Operations Research, INFORMS, vol. 30(4), pages 680-708, August.
    10. 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.
    11. Steven Nahmias, 1976. "Myopic Approximations for the Perishable Inventory Problem," Management Science, INFORMS, vol. 22(9), pages 1002-1008, May.
    12. Brant E. Fries, 1975. "Optimal Ordering Policy for a Perishable Commodity with Fixed Lifetime," Operations Research, INFORMS, vol. 23(1), pages 46-61, February.
    13. Gregory P. Prastacos, 1984. "Blood Inventory Management: An Overview of Theory and Practice," Management Science, INFORMS, vol. 30(7), pages 777-800, July.
    14. Charles P. Schmidt & Steven Nahmias, 1985. "(S - 1, S) Policies for Perishable Inventory," Management Science, INFORMS, vol. 31(6), pages 719-728, June.
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    Cited by:

    1. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    2. 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.
    3. Tomoaki Yamazaki & Keisuke Shida & Takashi Kanazawa, 2016. "An approach to establishing a method for calculating inventory," International Journal of Production Research, Taylor & Francis Journals, vol. 54(8), pages 2320-2331, April.
    4. Kouki, Chaaben & Jemaï, Zied & Minner, Stefan, 2015. "A lost sales (r, Q) inventory control model for perishables with fixed lifetime and lead time," International Journal of Production Economics, Elsevier, vol. 168(C), pages 143-157.
    5. 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.
    6. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
    7. Avi Herbon & Uriel Spiegel & Joseph Templeman, 2012. "Simulation study of the price differentiation effect in a stochastic deteriorating inventory with heterogeneous consumers -- freshness sensitivity," Applied Economics, Taylor & Francis Journals, vol. 44(24), pages 3101-3119, August.
    8. Deming Zhou & Lawrence C. Leung & William P. Pierskalla, 2011. "Inventory Management of Platelets in Hospitals: Optimal Inventory Policy for Perishable Products with Regular and Optional Expedited Replenishments," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 420-438, October.
    9. Herbon, Avi & Levner, Eugene & Cheng, T.C.E., 2014. "Perishable inventory management with dynamic pricing using time–temperature indicators linked to automatic detecting devices," International Journal of Production Economics, Elsevier, vol. 147(PC), pages 605-613.
    10. Önal, Mehmet & Romeijn, H.Edwin & Sapra, Amar & van den Heuvel, Wilco, 2015. "The economic lot-sizing problem with perishable items and consumption order preference," European Journal of Operational Research, Elsevier, vol. 244(3), pages 881-891.
    11. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    12. Kanchanasuntorn, Kanchana & Techanitisawad, Anulark, 2006. "An approximate periodic model for fixed-life perishable products in a two-echelon inventory-distribution system," International Journal of Production Economics, Elsevier, vol. 100(1), pages 101-115, March.
    13. Gong, Min & Lian, Zhaotong & Xiao, Hua, 2022. "Inventory control policy for perishable products under a buyback contract and Brownian demands," International Journal of Production Economics, Elsevier, vol. 251(C).
    14. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2016. "A coordinated multi-item inventory system for perishables with random lifetime," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 226-237.
    15. Zahra Azadi & Harsha Gangammanavar & Sandra Eksioglu, 2020. "Developing childhood vaccine administration and inventory replenishment policies that minimize open vial wastage," Annals of Operations Research, Springer, vol. 292(1), pages 215-247, September.
    16. Xiuli Chao & Xiting Gong & Cong Shi & Huanan Zhang, 2015. "Approximation Algorithms for Perishable Inventory Systems," Operations Research, INFORMS, vol. 63(3), pages 585-601, June.
    17. 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.
    18. Goyal, S. K. & Giri, B. C., 2001. "Recent trends in modeling of deteriorating inventory," European Journal of Operational Research, Elsevier, vol. 134(1), pages 1-16, October.
    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. Umay Uzunoglu Kocer & Bahar Yalcin, 2020. "Continuous review (s, Q) inventory system with random lifetime and two demand classes," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 104-118, March.
    21. Aswin Dhamodharan & Ruben Proano, 2012. "Determining the optimal vaccine vial size in developing countries: a Monte Carlo simulation approach," Health Care Management Science, Springer, vol. 15(3), pages 188-196, September.
    22. 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.
    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.
    24. 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.
    25. Ruibin Bai & Graham Kendall, 2008. "A Model for Fresh Produce Shelf-Space Allocation and Inventory Management with Freshness-Condition-Dependent Demand," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 78-85, February.

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