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The ( S − 1, S ) Inventory Model under Time Limit on Backorders

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  • Chandrasekhar Das

    (University of Saskatchewan, Saskatoon, Saskatchewan)

Abstract

Existing models of inventory control assume that when a stockout occurs customers either wait as long as necessary or not at all for the replenishment to arrive. This paper introduces a more realistic assumption—customers are assumed to wait a fixed amount of time before cancelling their orders. The new assumption is incorporated in the ( S − 1, S ) inventory model, which is appropriate for slow-moving items. Statistical and economic measures of performance for the model are developed on the basis of certain queuing results. We then use optimization techniques to derive a minimum-cost inventory policy with or without constraints on service levels. We also derive an optimal policy for trade-offs between inventory levels and replenishment rates and provide computational approaches.

Suggested Citation

  • Chandrasekhar Das, 1977. "The ( S − 1, S ) Inventory Model under Time Limit on Backorders," Operations Research, INFORMS, vol. 25(5), pages 835-850, October.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:5:p:835-850
    DOI: 10.1287/opre.25.5.835
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    Cited by:

    1. Placido dos Santos, Felipe Silva & Oliveira, Fabricio, 2019. "An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming," European Journal of Operational Research, Elsevier, vol. 275(2), pages 677-693.
    2. Ma, Weina & Hekimoğlu, Mustafa & Dekker, Rommert, 2023. "Admission control for a capacitated supply system with real-time replenishment information," International Journal of Production Economics, Elsevier, vol. 266(C).
    3. Saif Benjaafar & Mohsen ElHafsi & Tingliang Huang, 2010. "Optimal control of a production‐inventory system with both backorders and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 252-265, April.
    4. Christian Howard & Johan Marklund & Tarkan Tan & Ingrid Reijnen, 2015. "Inventory Control in a Spare Parts Distribution System with Emergency Stocks and Pipeline Information," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 142-156, May.
    5. Awi Federgruen & Ziv Katalan, 1996. "Customer waiting‐time distributions under base‐stock policies in single‐facility multi‐item production systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 533-548, June.

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