A Review of Stochastic Programming Methods for Optimization of Process Systems Under Uncertainty

Uncertainties are widespread in the optimization of process systems, such as uncertainties in process technologies, prices, and customer demands. In this paper, we review the basic concepts and recent advances of a risk-neutral mathematical framework called "stochastic programming" and its applications in solving process systems engineering problems under uncertainty. This review intends to provide both a tutorial for beginners without prior experience and a high-level overview of the current state-of-the-art developments for experts in process systems engineering and stochastic programming. The mathematical formulations and algorithms for two-stage and multistage stochastic programming are reviewed with illustrative examples from process industries. The differences between stochastic programming under exogenous uncertainty and endogenous uncertainties are discussed. The concepts and several data-driven methods for generating scenario trees are also reviewed.