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Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging

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  • Ouyang, Liang-Yuh
  • Chang, Chun-Tao

Abstract

The traditional economic production quantity (EPQ) model assumes that the production products are all perfect. It is not always true in the real production system, due to imperfect production process or other factors, imperfect quality items may be produced. Furthermore, it is well-known that the total production-inventory costs can be reduced by reworking the imperfect quality items produced with a relatively smaller additional reworking and holding costs. In addition, the permissible delay in payments offered by the supplier is widely adopted in the practical business market. In this study, we explore the effects of the reworking imperfect quality items and trade credit on the EPQ model with imperfect production processes and complete backlogging. A mathematical model which includes the reworking and shortage costs, interest earned and interest charged is presented. Besides, an arithmetic-geometric mean inequality approach is employed and an algorithm is developed to find the optimal production policy. Furthermore, some numerical examples and sensitivity analysis are provided to demonstrate the proposed model.

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  • Ouyang, Liang-Yuh & Chang, Chun-Tao, 2013. "Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging," International Journal of Production Economics, Elsevier, vol. 144(2), pages 610-617.
    • Handle: RePEc:eee:proeco:v:144:y:2013:i:2:p:610-617
    DOI: 10.1016/j.ijpe.2013.04.027
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    2. Soosan Moradi & Mohammad Reza Gholamian & Arash Sepehri, 2023. "An inventory model for imperfect quality items considering learning effects and partial trade credit policy," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 276-325, March.
    3. Mohsen Lashgari & Ata Allah Taleizadeh & Abbas Ahmadi, 2016. "Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain," Annals of Operations Research, Springer, vol. 238(1), pages 329-354, March.
    4. Wu, Jiang & Ouyang, Liang-Yuh & Cárdenas-Barrón, Leopoldo Eduardo & Goyal, Suresh Kumar, 2014. "Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing," European Journal of Operational Research, Elsevier, vol. 237(3), pages 898-908.
    5. Xu, Xinhan & Chen, Xiangfeng & Jia, Fu & Brown, Steve & Gong, Yu & Xu, Yifan, 2018. "Supply chain finance: A systematic literature review and bibliometric analysis," International Journal of Production Economics, Elsevier, vol. 204(C), pages 160-173.
    6. Chun-Tao Chang & Yao-Ting Tseng, 2024. "The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain," Mathematics, MDPI, vol. 12(7), pages 1-24, March.
    7. Soni, Hardik N, 2013. "Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment," International Journal of Production Economics, Elsevier, vol. 146(1), pages 259-268.
    8. Yu-Chung Tsao, 2015. "A piecewise nonlinear optimization for a production-inventory model under maintenance, variable setup costs, and trade credits," Annals of Operations Research, Springer, vol. 233(1), pages 465-481, October.
    9. A. Thangam, 2017. "Retailer’s optimal replenishment policy in a two-echelon supply chain under two-part delay in payments and disruption in delivery," 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. 8(1), pages 26-46, January.
    10. Ata Allah Taleizadeh & Sara Tavassoli & Arijit Bhattacharya, 2020. "Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering," Annals of Operations Research, Springer, vol. 287(1), pages 403-437, April.
    11. Ping Ruan & Yung-Fu Huang & Ming-Wei Weng, 2022. "Impact of COVID-19 on Supply Chains: A Hybrid Trade Credit Policy," Mathematics, MDPI, vol. 10(8), pages 1-22, April.
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    13. Chen, Sheng-Chih & Teng, Jinn-Tsair, 2015. "Inventory and credit decisions for time-varying deteriorating items with up-stream and down-stream trade credit financing by discounted cash flow analysis," European Journal of Operational Research, Elsevier, vol. 243(2), pages 566-575.
    14. Wu, Jiang & Skouri, Konstantina & Teng, Jinn-Tsair & Ouyang, Liang-Yuh, 2014. "A note on “optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment”," International Journal of Production Economics, Elsevier, vol. 155(C), pages 324-329.
    15. Sarkar, Biswajit & Saren, Sharmila, 2016. "Product inspection policy for an imperfect production system with inspection errors and warranty cost," European Journal of Operational Research, Elsevier, vol. 248(1), pages 263-271.
    16. Chandan Mahato & Gour Chandra Mahata, 2023. "Optimal ordering policy under order-size dependent trade credit and complete backlogging derived algebraically," OPSEARCH, Springer;Operational Research Society of India, vol. 60(1), pages 420-444, March.
    17. Chen, Sheng-Chih & Teng, Jinn-Tsair & Skouri, Konstantina, 2014. "Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit," International Journal of Production Economics, Elsevier, vol. 155(C), pages 302-309.
    18. Liang-Yuh Ouyang & Cheng-Ju Chuang & Chia-Huei Ho & Chien-Wei Wu, 2014. "An integrated inventory model with quality improvement and two-part credit policy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1042-1061, October.
    19. 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.
    20. 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.
    21. Beatriz Abdul-Jalbar & Roberto Dorta-Guerra & José M. Gutiérrez & Joaquín Sicilia, 2021. "Production/Inventory Policies for a Two-Echelon System with Credit Period Incentives," Mathematics, MDPI, vol. 9(15), pages 1-25, July.
    22. Mohsen Lashgari & Ata Taleizadeh & Abbas Ahmadi, 2016. "Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain," Annals of Operations Research, Springer, vol. 238(1), pages 329-354, March.
    23. Ruihai Li & Jinn-Tsair Teng & Yingfei Zheng, 2019. "Optimal credit term, order quantity and selling price for perishable products when demand depends on selling price, expiration date, and credit period," Annals of Operations Research, Springer, vol. 280(1), pages 377-405, September.
    24. Sarkar, Biswajit & Moon, Ilkyeong, 2014. "Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process," International Journal of Production Economics, Elsevier, vol. 155(C), pages 204-213.

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