Chance Constraints and Normal Deviates
作者:
A. Charnes,
W.W. Cooper,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1962)
卷期:
Volume 57,
issue 297
页码: 134-148
ISSN:0162-1459
年代: 1962
DOI:10.1080/01621459.1962.10482155
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Linear programming as a problem in optimizing a linear functional subject to linear inequality constraints is first discussed along with possible uses of the resulting duality relations. Various approaches to dealing with such problems when parts of the data are subject to error are briefly reviewed. Chance constrained programming refers to the class of such cases in which contraint violations are admissible up to pre- assigned probability levels. This topic is elaborated in the context of a ship-chartering problem in which independent normally distributed deviates from the (known) average demands may occur in any of the periods to be considered. Certain additional assumptions (including the use of a specified class of linear decision rules) make it possible to effect reductions first to a nonlinear (mathematical) programming and then to a linear programming problem. The use of the resulting duality relations for evaluating risk and quality levels of planned performance are then briefly examined.
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