Abstract
Optimization problems with both decision-dependent (endogenous) and decision-independent (exogenous) uncertainties are typical in the chemical process industry, especially in planning and scheduling. Stochastic programming is a framework for modelling optimization problems that involve uncertainty. Multistage stochastic programming (MSSP) is one approach for modelling such problems that consider decisions and recourse actions and that involve realization of uncertainties in multiple stages. However, MSSP models grow exponentially with increasing number of scenarios and time periods, and they quickly become computationally intractable for real-world problems. In this paper, we propose a general primal-bounding framework for large-scale MSSP models with both endogenous and exogenous uncertainties based on extending the concepts of expected value solution from MSSP under exogenous uncertainties. The proposed framework utilizes already known information and assumes the expected results for unrealized information to determine current state decisions. We applied the framework to solve instances of process-network-synthesis problem, which involves both uncertain process yields (endogenous uncertainty) and uncertain demand (exogenous uncertainty) with up to 1024 scenarios. The computational results reveal that proposed approach yielded feasible solutions within 22.3%, 13.4%, and 6.5% of the true solutions for the first, second and third instances, and obtained these solutions up to three order of magnitude faster than solving the original MSSP models.
