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An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand

Author

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  • Shoshana Anily

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

  • Abraham Grosfeld-Nir

    (Academic College of Tel-Aviv-Yaffo, Tel Aviv, Israel)

Abstract

A batch production process that is initially in the in-control state can fail with constant failure rate to the out-of-control state. The probability that a unit is conforming if produced while the process is in control is constant and higher than the respective constant conformance probability while the process is out of control. When production ends, the units are inspected in the order they have been produced. The objective is to design a production and inspection policy that guarantees a zero defective delivery in minimum expected total cost.The inspection problem is formulated as a partially observable Markov decision process (POMDP): Given the observations about the quality of the items that have already been inspected, the inspector should determine whether to inspect the next unit or stop inspection and possibly pay shortage costs. We show that the optimal policy is of the control limit threshold (CLT) type: The observations are used to update the probability that the production process was still in control while producing the candidate unit for inspection. The optimal policy is to continue inspection if and only if this probability exceeds a CLT value that may depend on the outstanding demand and the number of uninspected items. Structural properties satisfied by the various CLT values are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:2:p:311-323
    DOI: 10.1287/opre.1050.0258
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    References listed on IDEAS

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    3. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
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    5. Chernonog, Tatyana & Avinadav, Tal, 2016. "A two-state partially observable Markov decision process with three actionsAuthor-Name: Ben-Zvi, Tal," European Journal of Operational Research, Elsevier, vol. 254(3), pages 957-967.
    6. 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.

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