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Optimal disposal policies for a single‐item inventory system with returns

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  • Daniel P. Heyman

Abstract

We consider a single‐item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur. Returned items can be repaired and then used to satisfy future demand, or they can be disposed of. We identify those inventory levels where disposal is the best policy. It is shown that this problem is equivalent to a problem of controlling a single‐server queue. When the return and demand processes are both Poisson, we find the optimal policy exactly. When the demand and return processes are more general, we use diffusion approximations to obtain an approximate model, which is then solved. The approximate model requires only mean and variance data. Besides the optimal policy, the output of the models includes such characteristics as the operating costs, the purchase rate for new items, the disposal rate for returned items and the average inventory level. Several numerical examples are given. An interesting by‐product of our investigation is an approximation for the steady‐state behavior of the bulk GI/G/1 queue with a queue limit.

Suggested Citation

  • Daniel P. Heyman, 1977. "Optimal disposal policies for a single‐item inventory system with returns," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(3), pages 385-405, September.
    • Handle: RePEc:wly:navlog:v:24:y:1977:i:3:p:385-405
    DOI: 10.1002/nav.3800240302
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    Cited by:

    1. Ruud H. Teunter, 2001. "Economic ordering quantities for recoverable item inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 484-495, September.
    2. Hsien-Jen Lin, 2015. "Two-echelon stochastic inventory system with returns and partial backlogging," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 966-975, April.
    3. Gökbayrak, Esra & Kayış, Enis, 2023. "Single item periodic review inventory control with sales dependent stochastic return flows," International Journal of Production Economics, Elsevier, vol. 255(C).
    4. Ki Ling Cheung & Alex X. Zhang, 1999. "The impact of inventory information distortion due to customer order cancellations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 213-231, March.
    5. Andre P. Calmon & Stephen C. Graves, 2017. "Inventory Management in a Consumer Electronics Closed-Loop Supply Chain," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 568-585, October.
    6. Yonit Barron, 2022. "A probabilistic approach to the stochastic fluid cash management balance problem," Annals of Operations Research, Springer, vol. 312(2), pages 607-645, May.
    7. Zamanzad Gavidel, Saeed & Rickli, Jeremy L., 2019. "Normal to extreme Operation Transition Threshold analysis for remanufacturing systems," International Journal of Production Economics, Elsevier, vol. 213(C), pages 46-54.

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