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Optimal Lot Sizes with Geometric Production Yield and Rigid Demand

Author

Listed:
  • Shoshana Anily

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

  • Avraham Beja

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

  • Amit Mendel

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

Abstract

A job shop has to deliver a given number of custom-order items. Production is performed in “lots” that require costly setup, and output quality is stochastic. The size of each lot must be set before output quality is observed. We study production processes whose yield is distributed according to a generalized truncated geometric distribution: Production can randomly go “out of control,” in which case all subsequent output of that lot is defective. The “generalization” allows both hazard rates and marginal production costs to vary as production progresses. Our results characterize the optimal lot sizes. In particular, we show that for small demands the optimal lot size equals the outstanding demand, and for larger demands it is less than the outstanding demand, with all lot sizes being uniformly bounded. For sufficiently large demands, we identify conditions under which the optimal lots are precisely those that minimize the ratio of production cost to the expected number of good items. A tighter characterization is given for the standard case, where hazard rates and marginal costs are constant.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:3:p:424-432
    DOI: 10.1287/opre.50.3.424.7743
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    References listed on IDEAS

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    Cited by:

    1. Grosfeld-Nir, Abraham & Anily, Shoshana & Ben-Zvi, Tal, 2006. "Lot-sizing two-echelon assembly systems with random yields and rigid demand," European Journal of Operational Research, Elsevier, vol. 173(2), pages 600-616, September.
    2. M-C Wu & L-C Huang & H-M Hsu & T-S Su, 2011. "Multiple lot-sizing decisions in a two-stage production with an interrupted geometric yield and non-rigid demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1075-1084, June.
    3. 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.
    4. Sy-Ming Guu & Chun-Yi Lin, 2018. "The multiple lot sizing problem of a serial production system with interrupted geometric yields, rigid demand and Pentico’s heuristic," Annals of Operations Research, Springer, vol. 269(1), pages 167-183, October.

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