Stochastic Programming incorporates random variables to represent uncertain parameters, making it suitable for modeling real-world scenarios with inherent uncertainty.

Stochastic Programming aims to find optimal decisions that minimize risk or maximize expected utility in the presence of uncertain parameters.

Scenario analysis involves generating multiple scenarios representing possible realizations of uncertain parameters and solving the optimization problem for each scenario.

Probability distributions are used to define random variables, calculate expected values, and represent risk preferences in Stochastic Programming.

Deterministic programming is not a type of Stochastic Programming, as it assumes all parameters are known with certainty.

The recourse function allows for adjusting decisions based on new information obtained after the first stage of decision-making in Stochastic Programming.

Lagrangian relaxation is a widely used technique for solving large-scale Stochastic Programming problems, as it decomposes the problem into smaller subproblems.

Stochastic Programming problems often involve a large number of scenarios and variables, making them computationally challenging to solve, especially for large-scale problems.

Stochastic Programming is widely used in finance for portfolio optimization, risk management, and asset allocation, as it allows for incorporating uncertainty in financial markets.

In Stochastic Programming, a scenario tree represents possible realizations of uncertain parameters, while a decision tree represents the sequence of decisions made at different stages.

Value-at-Risk (VaR) is a widely used risk measure in Stochastic Programming, as it quantifies the maximum possible loss with a given probability.

Non-anticipativity constraints in Stochastic Programming ensure that decisions made at a particular stage are based only on information available at that stage, preventing information leakage between stages and maintaining consistency of decisions across scenarios.

Monte Carlo simulation, Latin hypercube sampling, and importance sampling are all commonly used techniques for approximating the expected value of a function in Stochastic Programming.

Scenario reduction techniques in Stochastic Programming aim to reduce the number of scenarios while maintaining the accuracy of the solution, leading to reduced computational complexity and improved efficiency.

GAMS, AIMMS, and CPLEX are all widely used software packages that provide capabilities for solving Stochastic Programming problems.