Optimization Under Uncertainty

Uncertainty is omnipresent, 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 optimization approaches that appropriately quantify and account for uncertainty.

Multistage Optimization Under Uncertainty

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 proceeds. Each time point at which an uncertainty is realized and a reactive (recourse) decision can be taken is referred to as a decision stage. To address optimization problems involving multiple stages, we apply stochastic optimization, which provides a framework for adequately modeling this decision-making process.

Multistage stochastic optimization problems are notoriously challenging as uncertainty is difficult to model and the resulting models are often computationally complex. We strive to develop efficient modeling and solution methods for multistage problems, using concepts from both stochastic programming and adjustable robust optimization. We put a strong focus on developing methods for generating realistic model input using real data and demonstrating the value of stochastic optimization in real-world applications.

Selected Publications

Zhang, Q., Lima, R. M., & Grossmann, I. E. (2016). On the relation between flexibility analysis and robust optimization for linear systems. AIChE Journal, 62(9), 3109-3123. Invited article for Tribute to Founders: Roger Sargent.

Grossmann, I. E., Apap, R. M., Calfa, B. A., Garcia-Herreros, P., & Zhang, Q. (2016). Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty. Computers & Chemical Engineering, 91, 3-14.

Zhang, Q., Morari, M. F., Grossmann, I. E., Sundaramoorthy, A., & Pinto, J. M. (2016). An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load. Computers & Chemical Engineering, 86, 106-119.

Zhang, Q., Cremer, J. L., Grossmann, I. E., Sundaramoorthy, A., & Pinto, J. M. (2016). Risk-based integrated production scheduling and electricity procurement for power-intensive continuous processes. Computers & Chemical Engineering, 86, 90-105.