Decision-Making Under Uncertainty

Uncertainty is ubiquitous, and decisions are constantly made under uncertainty: process design with uncertain yield, production planning with uncertain demand, supply chain management with risk of disruptions, and R&D portfolio optimization with uncertain project outcomes, to just name a few examples that are relevant to the process industry. In our research, we develop decision-making approaches that appropriately account for uncertainty, employing concepts from stochastic programming and robust optimization. In addition to advancing theory and methodology, we emphasize the generation of realistic model input using real data and the demonstration of the value of stochastic optimization in real-world applications.

Decision-making under uncertainty follows a natural sequential process in which uncertainty realization (i.e. observation of the true values of previously uncertain parameters) and subsequent reactive decision-making alternate as time progresses. Each time point at which an uncertainty is realized and a reactive (recourse) decision can be taken is referred to as a decision stage. The adequate modeling of decision stages is particularly important in planning and scheduling applications, but gives rise to very large optimization problems. We address these problems by developing efficient decomposition algorithms and tractable reformulations.

Endogenous uncertainty refers to uncertainty that can be affected by our decisions. For example, product demand is often uncertain, but we may be able to shift the distribution to higher values by lowering the price. We distinguish between three types of endogenous uncertainty: type 1 where decisions alter the probability distribution of uncertain parameters; type 2a where decisions determine whether and when uncertain parameters materialize, and type 2b where decisions determine when the true values of uncertain parameters are observed. The figure below shows a purely set-based interpretation of endogenous uncertainty (particularly relevant in the context of robust optimization).

In our work, we address all types of endogenous uncertainty, which enables the modeling of a rich set of relevant optimization problems. Moreover, there is an inherent, strong connection between endogenous uncertainty and active learning, which opens up new opportunities for data-driven optimization that effectively combines optimization and machine learning.

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• Feng, W., Feng, Y., & Zhang, Q. (2021). Multistage distributionally robust optimization for integrated production and maintenance scheduling. AIChE Journal, e17329.
• Feng, W., Feng, Y., & Zhang, Q. (2021). Multistage robust mixed-integer optimization under endogenous uncertainty. European Journal of Operational Research, 294, 460-475.
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