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The multiple lot sizing problem of a serial production system with interrupted geometric yields, rigid demand and Pentico’s heuristic

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  • Sy-Ming Guu

    (Chang Gung University
    Chang Gung Memorial Hospital)

  • Chun-Yi Lin

    (Chang Gung University)

Abstract

We consider the optimal lot sizing decision problem for a serial production system with the interrupted geometric yields and rigid demand. Such decisions are well-known for analytical difficulty due to often complicated cost expressions and necessity of deciding optimal lotsizes to stages/machines in the system. Pentico proposed a simple and effective heuristic that all usable items exiting a stage will be processed at the next stage till the end of the system. Pentico’s heuristic requires only the decision on the initial lot size. Based on Pentico’s heuristic, Bez-Zvi and Grosfeld-Nir considered the optimal “P-policies” to yield an optimal initial lot size so as to minimize the expected cost of the system while fulfilling the order. They showed the optimal initial lot size is always smaller than or equal to the outstanding demand. In this paper, we provide a finite upper bound and narrow searching range for the optimal initial lot sizes. It is well known that the worst case for minimizing the expected cost is to have an optimal initial lotsize equal to 1 for any outstanding demand. We characterize conditions in terms of the average expected costs for the worst case of the production system. An efficient algorithm for finding the optimal initial lot size is given which utilizes the recursive feature among the expected cost elements. For intellectual curiosity, we study a two-stage serial production system with a uniform yield in stage 1 and an interrupted geometric yield in stage 2. We propose an algorithm to derive an optimal initial lot size to enter this two-stage problem under Pentico’s heuristic. We show that for small outstanding demands (equal to 1 or 2) the optimal initial lot sizes are often greater than the outstanding demands. We prove that for large outstanding demands the optimal initial lot sizes are smaller than or equal to the outstanding demands. We also prove the existence of a finite upper bound for all optimal initial lot sizes. Our numerical example illustrates the existence of a threshold such that if the demand is smaller (greater) than it then the optimal lot size is larger (smaller) than the demand. Our analysis and numerical observation are very interesting to contrast with the most commonly seen binomial or uniform yield settings that the optimal lot size is always larger than the outstanding demand while for interrupted geometric yield the optimal lot size is always smaller than the outstanding demand.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2558-4
    DOI: 10.1007/s10479-017-2558-4
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    References listed on IDEAS

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    1. 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.
    2. Abraham Grosfeld-Nir & Boaz Ronen, 1993. "A Single Bottleneck System with Binomial Yields and Rigid Demand," Management Science, INFORMS, vol. 39(5), pages 650-653, May.
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    4. Guu, Sy-Ming & Zhang, Alex X., 2003. "The finite multiple lot sizing problem with interrupted geometric yield and holding costs," European Journal of Operational Research, Elsevier, vol. 145(3), pages 635-644, March.
    5. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
    6. 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.
    7. Sheldon M. Ross, 1971. "Quality Control under Markovian Deterioration," Management Science, INFORMS, vol. 17(9), pages 587-596, May.
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    1. Mahmood Vahdani & Zeinab Sazvar & Kannan Govindan, 2022. "An integrated economic disposal and lot-sizing problem for perishable inventories with batch production and corrupt stock-dependent holding cost," Annals of Operations Research, Springer, vol. 315(2), pages 2135-2167, August.

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