Kamiński Bogumił, Jakubczyk Michał, Szufel Przemysław
SGH Warsaw School of Economics, Al. Niepodległości 162, 02-554 Warsaw, Poland.
Cent Eur J Oper Res. 2018;26(1):135-159. doi: 10.1007/s10100-017-0479-6. Epub 2017 May 24.
In the paper, we consider sequential decision problems with uncertainty, represented as decision trees. Sensitivity analysis is always a crucial element of decision making and in decision trees it often focuses on probabilities. In the stochastic model considered, the user often has only limited information about the true values of probabilities. We develop a framework for performing sensitivity analysis of optimal strategies accounting for this distributional uncertainty. We design this robust optimization approach in an intuitive and not overly technical way, to make it simple to apply in daily managerial practice. The proposed framework allows for (1) analysis of the stability of the expected-value-maximizing strategy and (2) identification of strategies which are robust with respect to pessimistic/optimistic/mode-favoring perturbations of probabilities. We verify the properties of our approach in two cases: (a) probabilities in a tree are the primitives of the model and can be modified independently; (b) probabilities in a tree reflect some underlying, structural probabilities, and are interrelated. We provide a free software tool implementing the methods described.
在本文中，我们考虑具有不确定性的序贯决策问题，其以决策树的形式呈现。敏感性分析始终是决策的关键要素，在决策树中它通常聚焦于概率。在所考虑的随机模型中，用户通常对概率的真实值仅有有限的信息。我们开发了一个框架，用于对考虑这种分布不确定性的最优策略进行敏感性分析。我们以直观且不过于技术化的方式设计这种鲁棒优化方法，以便于在日常管理实践中应用。所提出的框架允许：（1）分析期望值最大化策略的稳定性；（2）识别对于概率的悲观/乐观/模式偏好扰动具有鲁棒性的策略。我们在两种情况下验证了我们方法的性质：（a）树中的概率是模型的原始数据，可以独立修改；（b）树中的概率反映一些潜在的结构概率，并且相互关联。我们提供了一个实现所述方法的免费软件工具。
