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Exact closed-form solutions for "optimal inventory model for items with imperfect quality and shortage backordering"

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  • Chang, Hung-Chi
  • Ho, Chia-Huei

Abstract

Wee et al. [Optimal inventory model for items with imperfect quality and shortage backordering. Omega 2007;35(1):7-11] recently contributed an optimal inventory model for items with imperfect quality and shortage backordering. This article revisits their study and applies the well-known renewal-reward theorem to obtain a new expected net profit per unit time. We derive the exact closed-form solutions to determine the optimal lot size, backordering quantity and maximum expected net profit per unit time, specifically without differential calculus. We also solve the same model algebraically from another direction, which has been mentioned, but the process has not been finished yet. The problem parameter effects upon the optimal solutions are examined analytically and numerically.

Suggested Citation

  • Chang, Hung-Chi & Ho, Chia-Huei, 2010. "Exact closed-form solutions for "optimal inventory model for items with imperfect quality and shortage backordering"," Omega, Elsevier, vol. 38(3-4), pages 233-237, June.
  • Handle: RePEc:eee:jomega:v:38:y:2010:i:3-4:p:233-237
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    References listed on IDEAS

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    2. Hsu, Jia-Tzer & Hsu, Lie-Fern, 2013. "An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns," International Journal of Production Economics, Elsevier, vol. 143(1), pages 162-170.
    3. (Ai-Chih) Chang, Jasmine & Lu, Haibing & (Junmin) Shi, Jim, 2019. "Stockout risk of production-inventory systems with compound Poisson demands," Omega, Elsevier, vol. 83(C), pages 181-198.
    4. Sebatjane, Makoena & Adetunji, Olufemi, 2019. "Economic order quantity model for growing items with imperfect quality," Operations Research Perspectives, Elsevier, vol. 6(C).
    5. Rezaei, Jafar & Salimi, Negin, 2012. "Economic order quantity and purchasing price for items with imperfect quality when inspection shifts from buyer to supplier," International Journal of Production Economics, Elsevier, vol. 137(1), pages 11-18.
    6. San-José, Luis A. & Sicilia, Joaquín & García-Laguna, Juan, 2014. "Optimal lot size for a production–inventory system with partial backlogging and mixture of dispatching policies," International Journal of Production Economics, Elsevier, vol. 155(C), pages 194-203.
    7. Zhao, Li & Tian, Peng & Xiangyong Li, 2012. "Dynamic pricing in the presence of consumer inertia," Omega, Elsevier, vol. 40(2), pages 137-148, April.
    8. Taleizadeh, Ata Allah & Khanbaglo, Mahboobeh Perak Sari & Cárdenas-Barrón, Leopoldo Eduardo, 2016. "An EOQ inventory model with partial backordering and reparation of imperfect products," International Journal of Production Economics, Elsevier, vol. 182(C), pages 418-434.
    9. Wee, Hui Ming & Widyadana, Gede Agus, 2013. "A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule," Omega, Elsevier, vol. 41(6), pages 941-954.
    10. Teng, Jinn-Tsair & Min, Jie & Pan, Qinhua, 2012. "Economic order quantity model with trade credit financing for non-decreasing demand," Omega, Elsevier, vol. 40(3), pages 328-335.
    11. Khan, M. & Jaber, M.Y. & Guiffrida, A.L. & Zolfaghari, S., 2011. "A review of the extensions of a modified EOQ model for imperfect quality items," International Journal of Production Economics, Elsevier, vol. 132(1), pages 1-12, July.
    12. Berthaut, F. & Gharbi, A. & Dhouib, K., 2011. "Joint modified block replacement and production/inventory control policy for a failure-prone manufacturing cell," Omega, Elsevier, vol. 39(6), pages 642-654, December.
    13. Lie-Fern Hsu & Jia-Tzer Hsu, 2016. "Economic production quantity (EPQ) models under an imperfect production process with shortages backordered," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(4), pages 852-867, March.
    14. Yu, Jonas C.P., 2013. "A collaborative strategy for deteriorating inventory system with imperfect items and supplier credits," International Journal of Production Economics, Elsevier, vol. 143(2), pages 403-409.

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