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Lot Sizing with Randomly Graded Yields

Author

Listed:
  • Steven Nahmias

    (Santa Clara University, Santa Clara, California)

  • Kamran Moinzadeh

    (University of Washington, Seattle, Washington)

Abstract

We consider a single inventory item that is graded into one of two quality levels after production. The proportion of grade one units produced in a lot is a random variable assumed to follow the lognormal distribution. Demands for grade 2 may be filled with grade 1 product, but not vice versa. Assuming that demands for the two grades are known and constant, we develop a continuous review model in which cycles are defined as times when total inventory equals zero. Since grade 1 inventory may be depleted before total stock and shortages are not permitted, cycles may consist of multiple set-ups. We show that the optimal order-to-point, S , has a form similar to the EOQ. Tables of the CDF of an appropriately defined unit normal multivariate distribution are incorporated into a spreadsheet to facilitate calculations for any parameter setting.

Suggested Citation

  • Steven Nahmias & Kamran Moinzadeh, 1997. "Lot Sizing with Randomly Graded Yields," Operations Research, INFORMS, vol. 45(6), pages 974-989, December.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:6:p:974-989
    DOI: 10.1287/opre.45.6.974
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    Citations

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    Cited by:

    1. Narendra Agrawal & Steven Nahmias, 1997. "Rationalization Of The Supplier Base In The Presence Of Yield Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 6(3), pages 291-308, September.
    2. Yang Dong & Kefeng Xu & Sining Song, 2014. "Contracting for Quality in a Multiple-Level Global Supply Chain," Working Papers 0205mss, College of Business, University of Texas at San Antonio.
    3. Hsieh, Chung-Chi & Lai, Hsing-Hua, 2017. "Capacity allocation with differentiated product demands under dual sourcing," International Journal of Production Economics, Elsevier, vol. 193(C), pages 757-769.
    4. Ying-Ju Chen & Brian Tomlin & Yimin Wang, 2017. "Dual Coproduct Technologies: Implications for Process Development and Adoption," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 692-712, October.
    5. Peter Berling & Danja R. Sonntag, 2022. "Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2628-2645, June.
    6. 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.
    7. Saurabh Bansal & Mahesh Nagarajan, 2017. "Product Portfolio Management with Production Flexibility in Agribusiness," Operations Research, INFORMS, vol. 65(4), pages 914-930, August.
    8. Tim Noparumpa & Burak Kazaz & Scott Webster, 2015. "Wine Futures and Advance Selling Under Quality Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 411-426, July.
    9. Kaijie Zhu & Rachel Q. Zhang & Fugee Tsung, 2007. "Pushing Quality Improvement Along Supply Chains," Management Science, INFORMS, vol. 53(3), pages 421-436, March.
    10. Ying-Ju Chen & Brian Tomlin & Yimin Wang, 2013. "Coproduct Technologies: Product Line Design and Process Innovation," Management Science, INFORMS, vol. 59(12), pages 2772-2789, December.
    11. Brian Downs & Richard Metters & John Semple, 2001. "Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach," Management Science, INFORMS, vol. 47(3), pages 464-479, March.
    12. Yangyang Peng & Xiaolin Xu & Xue Liang & Weili Xue, 2020. "Mismatch risk allocation in a coproduct supply chain," Annals of Operations Research, Springer, vol. 291(1), pages 707-730, August.
    13. Vidal-Carreras, Pilar I. & Garcia-Sabater, Jose P. & Coronado-Hernandez, Jairo R., 2012. "Economic lot scheduling with deliberated and controlled coproduction," European Journal of Operational Research, Elsevier, vol. 219(2), pages 396-404.
    14. Tao Lu & Ying‐Ju Chen & Brian Tomlin & Yimin Wang, 2019. "Selling Co‐Products through a Distributor: The Impact on Product Line Design," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 1010-1032, April.

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