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# stochastic optimization

Contributor(s): Stan Gibilisco

Stochastic optimization is the process of maximizing or minimizing the value of a mathematical or statistical function when one or more of the input parameters is subject to randomness. The word stochastic means involving chance or probability.

Stochastic processes are commonly involved in business analytics (BA), sales, service, manufacturing, finance and communications. Stochastic processes always involve probability, such as trying to predict the water level in a reservoir at a certain time based on random distribution of rainfall and water usage, or estimating the number of dropped connections in a communications network based on randomly variable traffic but constant available bandwidth. In contrast, deterministic processes never involve probability; outcomes occur (or fail to occur) based on predictable and exact input values.

Stochastic optimization lends itself to real-life situations because many phenomena in the physical world involve uncertainty, imprecision or randomness. Consider the following example: A computer repair shop wants to order exactly the right number of spare parts of several different types every month to keep pace with customer demand. If the shop orders too many parts of any type from the wholesalers, money will be spent needlessly; if the shop does not order enough parts of any type, it will lose business when customers go elsewhere for service. Determining the ideal number of parts of each type to order involves stochastic optimization, because the number of customers who come in with component failures of various sorts cannot be precisely predicted. The objective is to maximize the function's output value (the shop's profit) in the face of numerous random input variables.

This was last updated in July 2012

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