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Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment

Author

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  • G. Alon
  • D. Kroese
  • T. Raviv
  • R. Rubinstein

Abstract

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • G. Alon & D. Kroese & T. Raviv & R. Rubinstein, 2005. "Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment," Annals of Operations Research, Springer, vol. 134(1), pages 137-151, February.
    • Handle: RePEc:spr:annopr:v:134:y:2005:i:1:p:137-151:10.1007/s10479-005-5728-8
    DOI: 10.1007/s10479-005-5728-8
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    References listed on IDEAS

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    1. Stanley Gershwin & James Schor, 2000. "Efficient algorithms for buffer space allocation," Annals of Operations Research, Springer, vol. 93(1), pages 117-144, January.
    2. Leyuan Shi & Sigurdur Ólafsson, 2000. "Nested Partitions Method for Global Optimization," Operations Research, INFORMS, vol. 48(3), pages 390-407, June.
    3. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    4. Heavey, C. & Papadopoulos, H. T. & Browne, J., 1993. "The throughput rate of multistation unreliable production lines," European Journal of Operational Research, Elsevier, vol. 68(1), pages 69-89, July.
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    Cited by:

    1. Fahimnia, Behnam & Sarkis, Joseph & Eshragh, Ali, 2015. "A tradeoff model for green supply chain planning:A leanness-versus-greenness analysis," Omega, Elsevier, vol. 54(C), pages 173-190.
    2. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    3. Illana Bendavid & Boaz Golany, 2009. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 172(1), pages 259-276, November.
    4. Illana Bendavid & Boaz Golany, 2011. "Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology," Annals of Operations Research, Springer, vol. 189(1), pages 25-42, September.
    5. Benham, Tim & Duan, Qibin & Kroese, Dirk P. & Liquet, Benoît, 2017. "CEoptim: Cross-Entropy R Package for Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i08).
    6. K.-P. Hui & N. Bean & M. Kraetzl & Dirk Kroese, 2005. "The Cross-Entropy Method for Network Reliability Estimation," Annals of Operations Research, Springer, vol. 134(1), pages 101-118, February.
    7. Ishai Menache & Shie Mannor & Nahum Shimkin, 2005. "Basis Function Adaptation in Temporal Difference Reinforcement Learning," Annals of Operations Research, Springer, vol. 134(1), pages 215-238, February.
    8. Fahimnia, Behnam & Sarkis, Joseph & Choudhary, Alok & Eshragh, Ali, 2015. "Tactical supply chain planning under a carbon tax policy scheme: A case study," International Journal of Production Economics, Elsevier, vol. 164(C), pages 206-215.
    9. Illana Bendavid & Boaz Golany, 2011. "Predetermined intervals for start times of activities in the stochastic project scheduling problem," Annals of Operations Research, Springer, vol. 186(1), pages 429-442, June.
    10. Altiparmak, Fulya & Dengiz, Berna, 2009. "A cross entropy approach to design of reliable networks," European Journal of Operational Research, Elsevier, vol. 199(2), pages 542-552, December.
    11. Douek-Pinkovich, Yifat & Ben-Gal, Irad & Raviv, Tal, 2022. "The stochastic test collection problem: Models, exact and heuristic solution approaches," European Journal of Operational Research, Elsevier, vol. 299(3), pages 945-959.
    12. Krishna Chepuri & Tito Homem-de-Mello, 2005. "Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 153-181, February.
    13. Sagron, Ruth & Pugatch, Rami, 2021. "Universal distribution of batch completion times and time-cost tradeoff in a production line with arbitrary buffer size," European Journal of Operational Research, Elsevier, vol. 293(3), pages 980-989.
    14. Ad Ridder, 2005. "Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy," Annals of Operations Research, Springer, vol. 134(1), pages 119-136, February.

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