By Stochastic, we mean that some inputs to the problem are not single exact numbers--they are probability distributions. Many models can not reliabily handle "tail events" because they are built on a single point average of the probability distribution or similar oversimplifications.

• As any air traveler these days can tell you, for instance, the availability and transit time for each plan in an airline is not a fixed number, but a probability distribution, which includes factors such as equipment failures and weather delays.
• Daily weather also plays a factor for the regional agribusiness – not merely for eventual crop yields, but also the efficiency by which vehicles move through the fields, the urgency to harvest certain areas, and even the ultimate production costs.
• For the asset management company, demand for its assets is uncertain and must be forecasted. The standard “point” forecasts (also called “deterministic” forecasts) are much less realistic and valuable than “distributional” (or “stochastic”) forecasts, especially since the demand curve is often not a smooth, normal distribution.
• In the high frequency hedge fund case, optimization needs to understand that virtually every request to buy or sell securities is a process where prices are in constant flux. Therefore, the optimal approach to balancing portfolios and achieving other risk controls will require a probabilistic strategy.
• For the biotech innovator, the manufacturing process is highly variable, making scheduling difficult.
• For the 2020 U.S. Census, route optimization relies in part on the probablity that people in varying demographics will be home during certain day parts.