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Manufacturing to Order with Random Yield and Costly Inspection

Author

Listed:
  • Abraham Grosfeld-Nir

    (Faculty of Management, Tel-Aviv University, Tel Aviv, Israel, 69978)

  • Yigal Gerchak

    (Department of Management Sciences, University of Waterloo, Ontario, Canada N2L 3G1)

  • Qi-Ming He

    (Department of Industrial Engineering, DalTech, Nova Scotia, Canada B3J 2X4)

Abstract

This study considers a situation where a contractor receives an order that it commits to satisfy in full. The fulfillment of the contract requires manufacturing and inspection. Because the number of defective units within a produced lot is not known in advance, it is possible that after examining the lot, it is learned that the number of conforming units is short of the demand. If so, further manufacturing and inspection are required. Once enough conforming units are found, the inspection terminates, and the remaining uninspected units, as well as all defectives, are scrapped.Whereas previous “multiple production runs” studies implicitly assumed that inspection costs are negligible, we include these costs as a key part of the problem. It turns out that the optimal production lot size depends on the inspection cost. Our model is very general: We provide a framework to calculate the optimal batch and the expected number of inspections for any yield pattern, as well as for any inspection procedure. We also provide results and numerical examples concerning specific yield patterns that are common in practice.

Suggested Citation

  • Abraham Grosfeld-Nir & Yigal Gerchak & Qi-Ming He, 2000. "Manufacturing to Order with Random Yield and Costly Inspection," Operations Research, INFORMS, vol. 48(5), pages 761-767, October.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:5:p:761-767
    DOI: 10.1287/opre.48.5.761.12406
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    References listed on IDEAS

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    1. Evan L. Porteus, 1990. "Note---The Impact of Inspection Delay on Process and Inspection Lot Sizing," Management Science, INFORMS, vol. 36(8), pages 999-1007, August.
    2. Evan L. Porteus & Alexandar Angelus, 1997. "Opportunities for Improved Statistical Process Control," Management Science, INFORMS, vol. 43(9), pages 1214-1228, September.
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    4. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
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    1. Abdel-Malek, Layek & Montanari, Roberto & Meneghetti, Diego, 2008. "The capacitated newsboy problem with random yield: The Gardener Problem," International Journal of Production Economics, Elsevier, vol. 115(1), pages 113-127, September.
    2. Muhammad Babar Ramzan & Shehreyar Mohsin Qureshi & Sonia Irshad Mari & Muhammad Saad Memon & Mandeep Mittal & Muhammad Imran & Muhammad Waqas Iqbal, 2019. "Effect of Time-Varying Factors on Optimal Combination of Quality Inspectors for Offline Inspection Station," Mathematics, MDPI, vol. 7(1), pages 1-18, January.
    3. Kulkarni, Shailesh S., 2008. "Loss-based quality costs and inventory planning: General models and insights," European Journal of Operational Research, Elsevier, vol. 188(2), pages 428-449, July.
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    5. Zare, Marjan & Esmaeili, Maryam & He, Yuanjie, 2019. "Implications of risk-sharing strategies on supply chains with multiple retailers and under random yield," International Journal of Production Economics, Elsevier, vol. 216(C), pages 413-424.
    6. Xie, Gang & Yue, Wuyi & Wang, Shouyang & Lai, Kin Keung, 2011. "Quality investment and price decision in a risk-averse supply chain," European Journal of Operational Research, Elsevier, vol. 214(2), pages 403-410, October.
    7. Choi, Sungyong & Jeon, Sumin & Kim, Jinmin & Park, Kwangtae, 2019. "A newsvendor analysis of a binomial yield production process," European Journal of Operational Research, Elsevier, vol. 273(3), pages 983-991.
    8. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    9. Wen-Ya Wang & Diwakar Gupta, 2014. "Nurse Absenteeism and Staffing Strategies for Hospital Inpatient Units," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 439-454, July.
    10. Xu, He, 2010. "Managing production and procurement through option contracts in supply chains with random yield," International Journal of Production Economics, Elsevier, vol. 126(2), pages 306-313, August.
    11. Kutzner, Sarah C. & Kiesmüller, Gudrun P., 2013. "Optimal control of an inventory-production system with state-dependent random yield," European Journal of Operational Research, Elsevier, vol. 227(3), pages 444-452.
    12. Mart, Turgut & Duran, Serhan & Bakal, İsmail Serdar, 2013. "Tactical inventory and backorder decisions for systems with predictable production yield," International Journal of Production Economics, Elsevier, vol. 143(2), pages 294-303.
    13. D. K. Choudhury, 2020. "Modelling of Materials Management System for Cross-country Pipeline Project from Client’s Perspective," Metamorphosis: A Journal of Management Research, , vol. 19(2), pages 106-120, December.
    14. Abraham Grosfeld‐Nir & Eyal Cohen & Yigal Gerchak, 2007. "Production to order and off‐line inspection when the production process is partially observable," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 845-858, December.
    15. Kaijie Zhu & Rachel Q. Zhang & Fugee Tsung, 2007. "Pushing Quality Improvement Along Supply Chains," Management Science, INFORMS, vol. 53(3), pages 421-436, March.
    16. Shaofu Du & Yujiao Zhu & Tengfei Nie & Haisuo Yu, 2018. "Loss-averse preferences in a two-echelon supply chain with yield risk and demand uncertainty," Operational Research, Springer, vol. 18(2), pages 361-388, July.
    17. Chongfeng Lan & Zhongzhen Miao & Huanyong Ji, 2021. "Strategic Analysis of Dual-Channel Green Supply Chain with an Unreliable and Competitive Supplier," Sustainability, MDPI, vol. 13(10), pages 1-22, May.
    18. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2013. "The risk-averse newsvendor problem with random capacity," European Journal of Operational Research, Elsevier, vol. 231(2), pages 328-336.

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