By Alan J. King, Stein W. Wallace

Whereas there are a number of texts on find out how to clear up and research stochastic courses, this can be the 1st textual content to handle easy questions on tips to version uncertainty, and the way to reformulate a deterministic version in order that it may be analyzed in a stochastic surroundings. this article will be compatible as a stand-alone or complement for a moment path in OR/MS or in optimization-oriented engineering disciplines the place the trainer desires to clarify the place versions come from and what the elemental concerns are. The ebook is easy-to-read, hugely illustrated with plenty of examples and discussions. will probably be compatible for graduate scholars and researchers operating in operations learn, arithmetic, engineering and comparable departments the place there's curiosity in studying the way to version uncertainty. Alan King is a examine employees Member at IBM's Thomas J. Watson examine heart in long island. Stein W. Wallace is a Professor of Operational examine at Lancaster college administration college in England.

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**Sample text**

Are driven not by how you make scenarios, but by the actual problem formulation. 6 Distributions: Do They Exist and Can We Find Them? 2 Dependent Random Variables If you replace all random variables by their means, you end up with a deterministic optimization problem. Much of this book is about why that might not be a good idea, especially when there are opportunities to learn about the information and take action. A related sense in which expected values are misleading is the fact that they obscure dependencies among these random variables.

However, implicit in the formulations used to ﬁnd schedules we almost always ﬁnd the assumption that the world is deterministic. Of course, nobody actually thinks this is the case. But that is beside the point: The models are deterministic, hence leading to solutions with typical knife-edge properties, as discussed on p. 6. Such solutions normally do not have good expected behavior relative to surprises such as delays and breakdowns. We saw that in our news mix example on p. 4, and it is also outlined in Higle and Wallace [26] and Wallace [55].

According to NPV analysis, the well should be abandoned when the expected discounted future proﬁts equal the cost of well abandonment. This is correct if there is no uncertainty. However, the price of oil (and of electricity) is variable. NPV neglects the proﬁt that could be obtained if the price of oil shoots up faster than the cost of operations. This potential proﬁt is called the “option value” of the well; for further information on the real options approach, see Sick [51]. For us the concept of option is included in the notion of recourse actions, which embody the potential to respond when information has been observed.