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Inventory models with a mixture of backorders and lost sales

Author

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  • Douglas C. Montgomery
  • M. S. Bazaraa
  • Ajit K. Keswani

Abstract

This article presents several single‐echelon, single‐item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 ‐ b is lost forever. Both deterministic and stochastic demand are considered. although the case of stochastic demand is treated heuristically. In each situation, a mathematical model representing the average annual cost of operating the inventory system is developed. and an optimum operating policy derived. At the extremes b=1 and b=0 the models presented reduce to the usual backorders and lost sales cases, respectively.

Suggested Citation

  • Douglas C. Montgomery & M. S. Bazaraa & Ajit K. Keswani, 1973. "Inventory models with a mixture of backorders and lost sales," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 255-263, June.
    • Handle: RePEc:wly:navlog:v:20:y:1973:i:2:p:255-263
    DOI: 10.1002/nav.3800200205
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    Cited by:

    1. Xiaoqing Liu & Felix T. S. Chan & Xinsheng Xu, 2019. "Hedging Risks in the Loss-Averse Newsvendor Problem with Backlogging," Mathematics, MDPI, vol. 7(5), pages 1-23, May.
    2. Rabin Kumar Mallick & Kartik Patra & Shyamal Kumar Mondal, 2020. "Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments," Annals of Operations Research, Springer, vol. 292(1), pages 341-369, September.
    3. Achin Srivastav & Sunil Agrawal, 2020. "On a single item single stage mixture inventory models with independent stochastic lead times," Operational Research, Springer, vol. 20(4), pages 2189-2227, December.
    4. Li, Yanhai & Ou, Jinwen, 2020. "Optimal ordering policy for complementary components with partial backordering and emergency replenishment under spectral risk measure," European Journal of Operational Research, Elsevier, vol. 284(2), pages 538-549.
    5. Wang, Fong-Fan, 2023. "An efficient optimization procedure for location-inventory problems with (S-1, S) policy and retrial demands," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 664-688.
    6. Achin Srivastav & Sunil Agrawal, 2020. "Multi-objective optimization of mixture inventory system experiencing order crossover," Annals of Operations Research, Springer, vol. 290(1), pages 943-960, July.
    7. Haider Ali & Reshma Nasreen & Neetu Arneja & Chandra K. Jaggi, 2023. "Optimization of a periodically assessing model with manageable lead time under SLC with back order rebate for deteriorating items," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 241-266, February.
    8. Joaquín Sicilia & Luis San-José & Juan García-Laguna, 2012. "An inventory model where backordered demand ratio is exponentially decreasing with the waiting time," Annals of Operations Research, Springer, vol. 199(1), pages 137-155, October.
    9. Antonio Arreola‐Risa & Gregory A. DeCroix, 1998. "Inventory management under random supply disruptions and partial backorders," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 687-703, October.
    10. Behnam Vahdani & Elham Ahmadzadeh, 2021. "Incorporating Price-Dependent Demands into a Multi-Echelon Closed-Loop Network Considering the Lost Sales and Backorders: a Case Study of Wireless Network," Networks and Spatial Economics, Springer, vol. 21(3), pages 639-680, September.
    11. Yonit Barron, 2024. "Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment," Mathematics, MDPI, vol. 12(9), pages 1-30, April.
    12. S. Sarkar & B. C. Giri, 2020. "A vendor–buyer integrated inventory system with variable lead time and uncertain market demand," Operational Research, Springer, vol. 20(1), pages 491-515, March.
    13. Yanyi Xu & Doğan A. Serel & Arnab Bisi & Maqbool Dada, 2022. "Coping with Demand Uncertainty: The Interplay between Dual Sourcing and Endogenous Partial Backordering," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1560-1575, April.
    14. Wee, Hui-Ming & Huang, Yen-Deng & Wang, Wan-Tsu & Cheng, Yung-Lung, 2014. "An EPQ model with partial backorders considering two backordering costs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 898-907.

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