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Aggregation in Dynamic Programming

Author

Listed:
  • James C. Bean

    (University of Michigan, Ann Arbor, Michigan)

  • John R. Birge

    (University of Michigan, Ann Arbor, Michigan)

  • Robert L. Smith

    (University of Michigan, Ann Arbor, Michigan)

Abstract

Reducing the size of a dynamic program through state aggregation can significantly reduce both the data and the computation time required to solve a problem. We develop a new algorithm that combines state aggregation and disaggregation steps within a single-pass procedure. The solution obtained is automatically feasible for the original problem. By exploiting general conditions on the aggregate structure, we develop bounds for assessing the error from optimality introduced by the aggregation, and we illustrate with an application in infinite horizon optimization.

Suggested Citation

  • James C. Bean & John R. Birge & Robert L. Smith, 1987. "Aggregation in Dynamic Programming," Operations Research, INFORMS, vol. 35(2), pages 215-220, April.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:2:p:215-220
    DOI: 10.1287/opre.35.2.215
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    Citations

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    Cited by:

    1. Benjamin Van Roy, 2006. "Performance Loss Bounds for Approximate Value Iteration with State Aggregation," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 234-244, May.
    2. Torpong Cheevaprawatdomrong & Irwin E. Schochetman & Robert L. Smith & Alfredo Garcia, 2007. "Solution and Forecast Horizons for Infinite-Horizon Nonhomogeneous Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 51-72, February.
    3. Chevalier, Philippe & Lamas, Alejandro & Lu, Liang & Mlinar, Tanja, 2015. "Revenue management for operations with urgent orders," European Journal of Operational Research, Elsevier, vol. 240(2), pages 476-487.
    4. Ryan, Sarah M., 1998. "Forecast frequency in rolling horizon hedging heuristics for capacity expansion," European Journal of Operational Research, Elsevier, vol. 109(3), pages 550-558, September.
    5. Murwan Siddig & Yongjia Song, 2022. "Adaptive partition-based SDDP algorithms for multistage stochastic linear programming with fixed recourse," Computational Optimization and Applications, Springer, vol. 81(1), pages 201-250, January.
    6. Ali Fattahi & Sriram Dasu & Reza Ahmadi, 2023. "Peak-Load Energy Management by Direct Load Control Contracts," Management Science, INFORMS, vol. 69(5), pages 2788-2813, May.
    7. James C. Bean & Jack R. Lohmann & Robert L. Smith, 1994. "Equipment replacement under technological change," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 117-128, February.
    8. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    9. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    10. Selvaprabu Nadarajah & Andre A. Cire, 2020. "Network-Based Approximate Linear Programming for Discrete Optimization," Operations Research, INFORMS, vol. 68(6), pages 1767-1786, November.

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