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The Optimum Reject Allowance Problem


  • R. E. Levitan

    (International Business Machines Corporation, Research Center, Yorktown Heights, New York)


The problem of specifying an allowance for defects in a production lot is that of balancing the cost of producing too many items against the risk of not having enough to meet requirements. A model of these costs is here proposed. Sufficient conditions are developed on the probability distribution of defectives for total cost to have a single minimum with respect to the allowance. A sequential algorithm is investigated and shown to produce an optimum allowance if certain further conditions on the probability are met. Next, it is shown for a special class of probability distributions that the above conditions are satisfied. This class is that for which the probability of an item being defective is independent of previous defects in the lot, and includes the binomial distribution. Finally some computational aspects of this algorithm are discussed, and an easily computable starting value is given.

Suggested Citation

  • R. E. Levitan, 1960. "The Optimum Reject Allowance Problem," Management Science, INFORMS, vol. 6(2), pages 172-186, January.
  • Handle: RePEc:inm:ormnsc:v:6:y:1960:i:2:p:172-186
    DOI: 10.1287/mnsc.6.2.172

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    Cited by:

    1. Nasr, Walid W. & Jaber, Mohamad Y., 2019. "Supplier development in a two-level lot sizing problem with non-conforming items and learning," International Journal of Production Economics, Elsevier, vol. 216(C), pages 349-363.
    2. Shoshana Anily & Avraham Beja & Amit Mendel, 2002. "Optimal Lot Sizes with Geometric Production Yield and Rigid Demand," Operations Research, INFORMS, vol. 50(3), pages 424-432, June.
    3. Nasr, Walid W. & Maddah, Bacel & Salameh, Moueen K., 2013. "EOQ with a correlated binomial supply," International Journal of Production Economics, Elsevier, vol. 144(1), pages 248-255.
    4. Yimin Wang, 2013. "Specification vagueness and supply quality risk," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(3), pages 222-236, April.
    5. 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.
    6. Liu, John J. & Yang, Ping, 1996. "Optimal lot-sizing in an imperfect production system with homogeneous reworkable jobs," European Journal of Operational Research, Elsevier, vol. 91(3), pages 517-527, June.

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