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Inventory problems with perishable items: Fixed lifetimes and backlogging

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  • Olsson, Fredrik
  • Tydesjö, Patrik

Abstract

Our model deals with a single-product and a single-stock location with Poisson demand. The replenishment leadtime from the external supplier is fixed. The lifetime of the product is also fixed, and aging is assumed to begin when the order is placed. When the age of a unit has reached its lifetime, the unit is useless and thus discarded from the system. The replenishment policy is assumed to be an order-up-to S-policy. Demand that cannot be met immediately is backordered. We consider three different cases where the service requirements are represented by: (1) backorder costs per unit, (2) a service level constraint, (3) backorder costs per unit and time unit. Cases 1 and 2 are solved exactly, while an approximation is developed for case 3. We show how the results from an earlier paper assuming lost sales can be used to solve the considered problems. Our results are compared to the results in a related paper considering (Q, r)-policies.

Suggested Citation

  • Olsson, Fredrik & Tydesjö, Patrik, 2010. "Inventory problems with perishable items: Fixed lifetimes and backlogging," European Journal of Operational Research, Elsevier, vol. 202(1), pages 131-137, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:131-137
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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.
    2. Steven Nahmias, 1982. "Perishable Inventory Theory: A Review," Operations Research, INFORMS, vol. 30(4), pages 680-708, August.
    3. 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. 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. 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.
    3. 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.
    4. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    5. Stratos Ioannidis & Oualid Jouini & Angelos Economopoulos & Vassilis Kouikoglou, 2013. "Control policies for single-stage production systems with perishable inventory and customer impatience," Annals of Operations Research, Springer, vol. 209(1), pages 115-138, October.
    6. 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.
    7. Zhou, Quan Spring & Olsen, Tava Lennon, 2017. "Inventory rotation of medical supplies for emergency response," European Journal of Operational Research, Elsevier, vol. 257(3), pages 810-821.
    8. 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.
    9. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.
    10. van Donselaar, Karel H. & Broekmeulen, Rob A.C.M., 2012. "Approximations for the relative outdating of perishable products by combining stochastic modeling, simulation and regression modeling," International Journal of Production Economics, Elsevier, vol. 140(2), pages 660-669.
    11. Broekmeulen, Rob A.C.M. & van Donselaar, Karel H., 2019. "Quantifying the potential to improve on food waste, freshness and sales for perishables in supermarkets," International Journal of Production Economics, Elsevier, vol. 209(C), pages 265-273.
    12. Fredrik Olsson, 2019. "Simple modeling techniques for base-stock inventory systems with state dependent demand rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 61-76, August.
    13. 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).
    14. Lihao Lu & Jianxiong Zhang & Wansheng Tang, 2016. "Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1480-1494, April.
    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.

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