Abstract
We consider a multistage stochastic linear program in which we aim to assess the quality of an operational policy computed by means of a stochastic dual dynamic programming algorithm. We perform policy assessment by considering two strategies to compute a confidence interval on the optimality gap: (i) using multiple scenario trees and (ii) using a single scenario tree. The first approach has already been considered in several applications, while the second approach has been discussed previously only in a two-stage framework. The second approach is useful in practical applications in order to more quickly assess the quality of a policy. We present these ideas in the context of a multistage stochastic program for Brazilian long-term hydrothermal scheduling, and use numerical instances to compare the confidence intervals on the optimality gap computed via both strategies. We further consider the relative merits of using naive Monte Carlo sampling, randomized quasi Monte Carlo sampling, and Latin hypercube sampling within our framework for assessing the quality of a policy.
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Notes
Results were obtained using a 10-processor machine with 32 GB of RAM, a high-performance 300 GB SAS 15,000 rpm disk, and Windows Server 2008 R2 Standard Edition, where each processor has two 1333 MHz Intel Xeon X5690 cores. To solve the linear programming subproblems at each stage, we use Gurobi 4.61.
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The authors thank two anonymous referees whose comments and suggestions improved this paper.
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de Matos, V.L., Morton, D.P. & Finardi, E.C. Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling. Ann Oper Res 253, 713–731 (2017). https://doi.org/10.1007/s10479-016-2107-6
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DOI: https://doi.org/10.1007/s10479-016-2107-6