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Abstract:
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We review in this paper techniques to apply mathematical optimization to business problems where some data is predicted. The process we follow is: 1. Model some data via a statistical distribution 2. Optimize the expected value of a objective given the data distribution. For instance, from data about past equipment failure, we can infer a statistical distribution of when a given equipment will fail. We can then use this time of failure distribution to schedule maintenance operations in order to minimize expected failures while meeting various capacity constraints (availability of technician skills, availability of repair tools, etc). More generally, we need to use optimization methods where some of the input data are random variables following some statistical distribution. These optimization techniques are called stochastic optimization methods.
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