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On Ordering Perishable Inventory when Both Demand and Lifetime are Random

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  • Steven Nahmias

    (University of Pittsburgh)

Abstract

We consider the problem of ordering perishable inventory when there is uncertainty in both the demand and the lifetime of the product. Under the assumption that units outdate in the same order in which they enter inventory, it is shown that the structure of the optimal policy is essentially the same as in the case where the lifetime is deterministic. An explicit expression for the expected outdating of any order is derived. Two different bounds on the expected outdating are then used to construct two critical number approximations. Computations for a discrete version of the problem are performed to compare the expected costs of both approximations with the optimal. One approximation appeared to give slightly better results and produced an expected cost generally within a fraction of a percent of the optimal for the cases tested.

Suggested Citation

  • Steven Nahmias, 1977. "On Ordering Perishable Inventory when Both Demand and Lifetime are Random," Management Science, INFORMS, vol. 24(1), pages 82-90, September.
    • Handle: RePEc:inm:ormnsc:v:24:y:1977:i:1:p:82-90
    DOI: 10.1287/mnsc.24.1.82
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    Cited by:

    1. Dirk Lauinger & Romain G. Billy & Felipe Vásquez & Daniel B. Müller, 2021. "A general framework for stock dynamics of populations and built and natural environments," Journal of Industrial Ecology, Yale University, vol. 25(5), pages 1136-1146, October.
    2. Jochen Schlapp & Moritz Fleischmann & Danja Sonntag, 2022. "Inventory timing: How to serve a stochastic season," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2891-2906, July.
    3. Chen, Jing & Dong, Ming & Xu, Lei, 2018. "A perishable product shipment consolidation model considering freshness-keeping effort," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 56-86.
    4. Tekin, Eylem & Gurler, Ulku & Berk, Emre, 2001. "Age-based vs. stock level control policies for a perishable inventory system," European Journal of Operational Research, Elsevier, vol. 134(2), pages 309-329, October.
    5. 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.
    6. Maloni, Michael J. & Benton, W.C., 1997. "Supply chain partnerships: Opportunities for operations research," European Journal of Operational Research, Elsevier, vol. 101(3), pages 419-429, September.
    7. Hossein Abouee‐Mehrizi & Mahdi Mirjalili & Vahid Sarhangian, 2022. "Data‐driven platelet inventory management under uncertainty in the remaining shelf life of units," Production and Operations Management, Production and Operations Management Society, vol. 31(10), pages 3914-3932, October.
    8. Lowalekar, Harshal & Ravi, R. Raghavendra, 2017. "Revolutionizing blood bank inventory management using the TOC thinking process: An Indian case study," International Journal of Production Economics, Elsevier, vol. 186(C), pages 89-122.
    9. William L. Cooper, 2001. "Pathwise Properties and Performance Bounds for a Perishable Inventory System," Operations Research, INFORMS, vol. 49(3), pages 455-466, June.
    10. Jake Clarkson & Michael A. Voelkel & Anna‐Lena Sachs & Ulrich W. Thonemann, 2023. "The periodic review model with independent age‐dependent lifetimes," Production and Operations Management, Production and Operations Management Society, vol. 32(3), pages 813-828, March.
    11. 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.
    12. Williams, Craig L. & Eddy Patuwo, B., 2004. "Analysis of the effect of various unit costs on the optimal incoming quantity in a perishable inventory model," European Journal of Operational Research, Elsevier, vol. 156(1), pages 140-147, July.
    13. Ketzenberg, Michael & Gaukler, Gary & Salin, Victoria, 2018. "Expiration dates and order quantities for perishables," European Journal of Operational Research, Elsevier, vol. 266(2), pages 569-584.
    14. Siawsolit, Chokdee & Gaukler, Gary M., 2021. "Offsetting omnichannel grocery fulfillment cost through advance ordering of perishables," International Journal of Production Economics, Elsevier, vol. 239(C).
    15. Gaukler, Gary & Ketzenberg, Michael & Salin, Victoria, 2017. "Establishing dynamic expiration dates for perishables: An application of rfid and sensor technology," International Journal of Production Economics, Elsevier, vol. 193(C), pages 617-632.
    16. Jinzhi Bu & Xiting Gong & Xiuli Chao, 2023. "Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems," Management Science, INFORMS, vol. 69(2), pages 846-864, February.
    17. Elena Katok & Andrew Lathrop & William Tarantino & Susan H. Xu, 2001. "Jeppesen Uses a Dynamic-Programming-Based DSS to Manage Inventory," Interfaces, INFORMS, vol. 31(6), pages 54-65, December.
    18. Li‐Ming Chen & Amar Sapra, 2021. "Inventory renewal for a perishable product: Economies of scale and age‐dependent demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 359-377, April.
    19. Ketzenberg, Michael & Oliva, Rogelio & Wang, Yimin & Webster, Scott, 2023. "Retailer inventory data sharing in a fresh product supply chain," European Journal of Operational Research, Elsevier, vol. 307(2), pages 680-693.

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