Abstract
In this chapter, after overviewing elementary probability, two-stage programming and chance constrained programming are explained in detail. In two-stage programming, a shortage or an excess arising from the violation of the constraints is penalized, and then the expectation of the amount of the penalties for the constraint violation is minimized. In contrast, chance constrained programming admits random data variations and permits constraint violations up to specified probability limits, and its formulation is somewhat variable, including the expectation model, the variance model, the probability model, and the fractile model.
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Notes
- 1.
Although the term random variable is somewhat confusing, it is well established and so it will be used in this book. However, a random function would be more appropriate, since a random variable is really a real-valued function whose domain is a sample space.
- 2.
VBA (visual basic for applications) is a programming language for Excel, and then one can code a procedure in Excel.
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Sakawa, M., Yano, H., Nishizaki, I. (2013). Stochastic Linear Programming. In: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions. International Series in Operations Research & Management Science, vol 203. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9399-0_5
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