Abstract
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.
Highlights
Stochastic programming, known as stochastic optimization (Birge and Louveaux, 2011), is a mathematical framework to model decision-making under uncertainty
We have provided an overview of stochastic programming in process systems engineering
There are two major types of uncertainties that can be modeled using stochastic programming, exogenous uncertainty, which is the most commonly one considered, and endogenous uncertainty where realizations of the uncertainties depend on the decisions taken
Summary
Stochastic programming, known as stochastic optimization (Birge and Louveaux, 2011), is a mathematical framework to model decision-making under uncertainty. Dantzig, recognized as the father of the simplex algorithm for linear programming, wrote the pioneer paper “Linear Programming under Uncertainty” (Dantzig, 1955) In this pioneering paper, Dantzig described one of the motivations of developing the stochastic programming modeling framework as “to include the case of uncertain demands for the problem of optimal allocation of a carrier fleet to airline routes to meet an anticipated demand distribution”. Dantzig described one of the motivations of developing the stochastic programming modeling framework as “to include the case of uncertain demands for the problem of optimal allocation of a carrier fleet to airline routes to meet an anticipated demand distribution” Another early work on stochastic programming can be found in Beale (1955). With the increase in the maturity of algorithmic and computational methods, stochastic programming has been applied to a broad spectrum of problems (Wallace and Ziemba, 2005) including financial planning, electricity generation, supply chain management, mitigation of climate change, and pollution control, among many others
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