Chance Constrained Models
Chance Constrained Models
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DOI：
10.1007/978-3-662-53785-5_7
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
D. Olson;D. Wu
中科院分区：
文献类型：
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作者：
D. Olson;D. Wu
机会约束规划是作为一种以概率达到水平的形式描述数学规划模型中的约束的手段而发展起来的。考虑机会约束允许决策者考虑数学规划目标的实现概率。如果α是决策者期望的预定置信水平，则意味着在所有可能的情况中，最多有（1-α）个约束会被违反。第一种形式是在达到特定目标的特定概率下，最大化线性预期收益。第二是最小化方差。第二种形式并没有那么有用，因为最低的方差实际上是不投资。在这里，我们强迫投资的1000资本假设。第三种形式是最大化达到某个目标的概率，为了有用，它必须是不可行的。机会约束模型已经在许多应用中使用。在这里，我们重点讨论了财务规划，但在优化问题中，只要有统计数据，就有应用。
Chance constrained programming was developed as a means of describing constraints in mathematical programming models in the form of probability levels of attainment. Consideration of chance constraints allows decision makers to consider mathematical programming objectives in terms of the probability of their attainment. Ifαis a predetermined confidence level desired by a decision maker, the implication is that a constraint will be violated at most (1–α) of all possible cases.A number of different types of models can be built using chance constraints. The first form is to maximize the linear expected return subject to attaining specified probabilities of reaching specified targets. The second is to minimize variance. This second form is not that useful, in that the lowest variance is actually to not invest. Here we forced investment of the 1000 capital assumed. The third form is to maximize probability of attaining some target, which in order to be useful, has to be infeasible.Chance constrained models have been used in many applications. Here we have focused on financial planning, but there have been applications whenever statistical data is available in an optimization problem.