So far, we worked with deterministic mathematical programs where all model parameters (e.g. coefficients, bounds, etc.) are known constants. A stochastic program (SP) is a mathematical program (linear, nonlinear or mixed-integer) in which some of the model parameters are not known with certainty, and the uncertainty can be expressed with known probability distributions. Applications arise in a variety of industries:
| • | Financial portfolio planning over multiple periods for insurance and other financial companies, in face of uncertain prices, interest rates, and exchange rates |
| • | Exploration planning for petroleum companies, |
| • | Fuel purchasing when facing uncertain future fuel demand, |
| • | Fleet assignment: vehicle type to route assignment in face of uncertain route demand, |
| • | Electricity generator unit commitment in face of uncertain demand, |
| • | Hydro management and flood control in face of uncertain rainfall, |
| • | Optimal time to exercise for options in face of uncertain prices, |
| • | Capacity and Production planning in face of uncertain future demands and prices, |
| • | Foundry metal blending in face of uncertain input scrap qualities, |
| • | Product planning in face of future technology uncertainty, |
| • | Revenue management in the hospitality and transport industries. |
Stochastic programs fall into two major categories: a) multistage stochastic programs with recourse, and b) chance-constrained programs.
