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Production to order and off‐line inspection when the production process is partially observable

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  • Abraham Grosfeld‐Nir
  • Eyal Cohen
  • Yigal Gerchak

Abstract

This study combines inspection and lot‐sizing decisions. The issue is whether to INSPECT another unit or PRODUCE a new lot. A unit produced is either conforming or defective. Demand need to be satisfied in full, by conforming units only. The production process may switch from a “good” state to a “bad” state, at constant rate. The proportion of conforming units in the good state is higher than in the bad state. The true state is unobservable and can only be inferred from the quality of units inspected. We thus update, after each inspection, the probability that the unit, next candidate for inspection, was produced while the production process was in the good state. That “good‐state‐probability” is the basis for our decision to INSPECT or PRODUCE. We prove that the optimal policy has a simple form: INSPECT only if the good‐state‐probability exceeds a control limit. We provide a methodology to calculate the optimal lot size and the expected costs associated with INSPECT and PRODUCE. Surprisingly, we find that the control limit, as a function of the demand (and other problem parameters) is not necessarily monotone. Also, counter to intuition, it is possible that the optimal action is PRODUCE, after revealing a conforming unit. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:8:p:845-858
    DOI: 10.1002/nav.20256
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    1. Joel M. Calabrese, 1995. "Bayesian Process Control for Attributes," Management Science, INFORMS, vol. 41(4), pages 637-645, April.
    2. William S. Lovejoy, 1991. "Computationally Feasible Bounds for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 39(1), pages 162-175, February.
    3. Steffen L. Lauritzen & Dennis Nilsson, 2001. "Representing and Solving Decision Problems with Limited Information," Management Science, INFORMS, vol. 47(9), pages 1235-1251, September.
    4. Abraham Grosfeld-Nir & Yigal Gerchak, 2004. "Multiple Lotsizing in Production to Order with Random Yields: Review of Recent Advances," Annals of Operations Research, Springer, vol. 126(1), pages 43-69, February.
    5. White, Chelsea C. & White, Douglas J., 1989. "Markov decision processes," European Journal of Operational Research, Elsevier, vol. 39(1), pages 1-16, March.
    6. Givon, Moshe & Grosfeld-Nir, Abraham, 2008. "Using partially observed Markov processes to select optimal termination time of TV shows," Omega, Elsevier, vol. 36(3), pages 477-485, June.
    7. 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.
    8. Evan L. Porteus & Alexandar Angelus, 1997. "Opportunities for Improved Statistical Process Control," Management Science, INFORMS, vol. 43(9), pages 1214-1228, September.
    9. William S. Lovejoy, 1987. "Ordered Solutions for Dynamic Programs," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 269-276, May.
    10. S. Christian Albright, 1979. "Structural Results for Partially Observable Markov Decision Processes," Operations Research, INFORMS, vol. 27(5), pages 1041-1053, October.
    11. 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.
    12. Chelsea C. White & William T. Scherer, 1989. "Solution Procedures for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 37(5), pages 791-797, October.
    13. Chelsea C. White, 1977. "A Markov Quality Control Process Subject to Partial Observation," Management Science, INFORMS, vol. 23(8), pages 843-852, April.
    14. George E. Monahan, 1982. "State of the Art---A Survey of Partially Observable Markov Decision Processes: Theory, Models, and Algorithms," Management Science, INFORMS, vol. 28(1), pages 1-16, January.
    15. 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.
    16. Candace Arai Yano & Hau L. Lee, 1995. "Lot Sizing with Random Yields: A Review," Operations Research, INFORMS, vol. 43(2), pages 311-334, April.
    17. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
    18. Refael Hassin, 1984. "A Dichotomous Search for a Geometric Random Variable," Operations Research, INFORMS, vol. 32(2), pages 423-439, April.
    19. Daniel E. Lane, 1989. "A Partially Observable Model of Decision Making by Fishermen," Operations Research, INFORMS, vol. 37(2), pages 240-254, April.
    20. Avraham Beja, 1977. "Optimal reject allowance with constant marginal production efficiency," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(1), pages 21-33, March.
    21. Ali E. Abbas & Susan P. Holmes, 2004. "Bioinformatics and Management Science: Some Common Tools and Techniques," Operations Research, INFORMS, vol. 52(2), pages 165-190, April.
    22. 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.
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