Approximation of multistage stochastic programming problems by smoothed quantization

IF 7.8 3区管理学 Q1 MANAGEMENT

Review of Managerial Science Pub Date : 2024-02-28 DOI:10.1007/s11846-024-00733-5

引用次数: 0

Abstract

We present an approximation technique for solving multistage stochastic programming problems with an underlying Markov stochastic process. This process is approximated by a discrete skeleton process, which is consequently smoothed down by means of the original unconditional distribution. Approximated in this way, the problem is solvable by means of Markov Stochastic Dual Dynamic Programming. We state an upper bound for the nested distance between the exact process and its approximation and discuss its convergence in the one-dimensional case. We further propose an adjustment of the approximation, which guarantees that the approximate problem is bounded. Finally, we apply our technique to a real-life production-emission trading problem and demonstrate the performance of its approximation given the “true” distribution of the random parameters.

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通过平滑量化逼近多阶段随机程序设计问题

摘要我们提出了一种近似技术，用于解决带有马尔可夫随机过程的多阶段随机程序设计问题。该过程由离散骨架过程近似，然后通过原始无条件分布对其进行平滑处理。通过这种近似方法，问题可以通过马尔可夫随机双动态编程法求解。我们提出了精确过程与其近似值之间嵌套距离的上限，并讨论了其在一维情况下的收敛性。我们进一步提出了一种近似调整方法，它能保证近似问题是有界的。最后，我们将我们的技术应用于现实生活中的生产-排放交易问题，并证明了在随机参数 "真实 "分布的情况下，其近似值的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Review of Managerial Science MANAGEMENT-

CiteScore

11.30

自引率

14.50%

发文量

期刊介绍： Review of Managerial Science (RMS) provides a forum for innovative research from all scientific areas of business administration. The journal publishes original research of high quality and is open to various methodological approaches (analytical modeling, empirical research, experimental work, methodological reasoning etc.). The scope of RMS encompasses – but is not limited to – accounting, auditing, banking, business strategy, corporate governance, entrepreneurship, financial structure and capital markets, health economics, human resources management, information systems, innovation management, insurance, marketing, organization, production and logistics, risk management and taxation. RMS also encourages the submission of papers combining ideas and/or approaches from different areas in an innovative way. Review papers presenting the state of the art of a research area and pointing out new directions for further research are also welcome. The scientific standards of RMS are guaranteed by a rigorous, double-blind peer review process with ad hoc referees and the journal´s internationally composed editorial board.