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Nested Benders decomposition and dynamic programming for reservoir optimisation

Author

Listed:
  • T W Archibald

    (University of Edinburgh)

  • C S Buchanan

    (University of Edinburgh)

  • K I M McKinnon

    (University of Edinburgh)

  • L C Thomas

    (University of Edinburgh)

Abstract

This paper presents a computational comparison of nested Benders decomposition and dynamic programming (DP) for stochastic optimisation problems arising from the optimisation of hydro-electric generation from hydraulically linked reservoirs. The examples considered have between 3 and 17 reservoirs, two weather states, three runoff patterns and five periods. The examples are solved exactly by the simplex method and nested Benders decomposition and solved approximately by discrete dynamic programming (DP). A full version of DP is used for examples with 3 and 4 reservoirs, and a decomposition method is used for all examples. The full DP results are within 1% of optimal and the DP decomposition results are within 3.2% of optimal. Timings are given for serial and parallel versions of the algorithms. An analysis is given of how the different methods scale with the number of periods, reservoirs, weather states and runoff patterns, and also how applicable they are to more general problems.

Suggested Citation

  • T W Archibald & C S Buchanan & K I M McKinnon & L C Thomas, 1999. "Nested Benders decomposition and dynamic programming for reservoir optimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(5), pages 468-479, May.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:5:d:10.1057_palgrave.jors.2600727
    DOI: 10.1057/palgrave.jors.2600727
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    Citations

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    Cited by:

    1. T.W. Archibald & K.I.M. McKinnon & L.C. Thomas, 2006. "Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 217-225, April.
    2. Xie, Fei & Huang, Yongxi, 2018. "A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 130-148.
    3. Fengqi You & Ignacio Grossmann, 2013. "Multicut Benders decomposition algorithm for process supply chain planning under uncertainty," Annals of Operations Research, Springer, vol. 210(1), pages 191-211, November.
    4. Li, Xiaohong & Yang, Dong & Hu, Mengqi, 2018. "A scenario-based stochastic programming approach for the product configuration problem under uncertainties and carbon emission regulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 126-146.

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