By Alan J. King, Stein W. Wallace
Whereas there are a number of texts on the right way to resolve and study stochastic courses, this can be the 1st textual content to deal with easy questions about how one can version uncertainty, and the way to reformulate a deterministic version in order that it may be analyzed in a stochastic atmosphere. this article will be compatible as a stand-alone or complement for a moment direction in OR/MS or in optimization-oriented engineering disciplines the place the teacher desires to clarify the place versions come from and what the elemental matters are. The publication is easy-to-read, hugely illustrated with plenty of examples and discussions. it will likely be appropriate for graduate scholars and researchers operating in operations examine, arithmetic, engineering and comparable departments the place there's curiosity in studying how you can version uncertainty. Alan King is a learn employees Member at IBM's Thomas J. Watson learn heart in ny. Stein W. Wallace is a Professor of Operational examine at Lancaster collage administration university in England
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Example text
We then ask what we should do. We are not asking what to do in all possible situations, just what to do based on our present state. If there is no memory in a model, then there is no essential difference between steady-state and transient modeling. But if there is memory, which is normally the case for important decisions, stochastic programming is primarily about transient modeling. We are where we are, be that good or bad, and we want to know what to do. Even optimal decisions might leave us worse off than we had been before we made the decisions if constraints are tough and resources limited.
If you were considering some major changes in procedures or some major investment that would change the whole portfolio, this problem might be inherently two-stage. Random variables: Market developments and success of individual projects. Objective function: Here you wish to model risk aversion probably caused by some of the projects having correlated profits. If all divisions and projects had uncorrelated profits, there would be no risk management problem to attend to. Why not deterministic? Risk management makes little sense in a deterministic world.
1 Building an Oil Platform For a concrete example, assume you are consulting on the construction of an oil platform. One of the issues relates to the size of the platform deck. 8 Alternative Approaches 25 The bigger the deck, the larger the platform legs, and the more expensive the platform. By adding extra deck space, you buy an option, however: you make it possible later on to add more equipment. Should the field produce more sand than expected, you could add an extra unit for sand removal. Should the platform produce more oil than expected, you could add a production unit, and maybe you would end up producing so much water that you would need an extra unit for that.