Scalable and explainable stochastic programming with applications in sustainable systems engineering

Abstract

Over the years, stochastic programming (SP) has become one of the key frameworks for solving optimization problems under uncertainty in applications such as supply chain network design and routing, expansion of renewable energy systems, and environmental and disaster response planning, to name a few. However, despite significant progress in developing SP formulations and improving the tractability of such models, certain aspects have remained largely unexplored or overlooked, preventing the full potential of SP from being realized, particularly with respect to scalability and explainability. To that end, this thesis focuses on addressing the following: modeling endogeneity (i.e. dependence on decisions) in uncertain parameters, specifically the future cost of a technology in an energy systems expansion problem, and efficiently solving the resulting large-scale SP model; developing effective solution strategies for a challenging class of multistage SP problems with nonlinearity and discrete decisions; and improving the explainability of SP solutions to encourage their adoption in industry. The main contributions of this thesis are as follows: 1. We propose a multistage SP framework to model a long-term capacity planning problem with endogenous uncertainty in technology learning (i.e. reduction in the cost of a technology). We further develop a novel algorithm to evaluate the value of multistage stochastic solution, implement a column generation decomposition scheme to improve the tractability of the large-scale SP model, and discuss a case study on a network of renewable and non-renewable power-generation technologies. 2. We develop a tailored column generation (CG) algorithm for a special class of multistage stochastic mixed-integer nonlinear programs with discrete state variables, which are sparingly discussed in the literature despite their ability to model various practical real-world problems. Specifically, we integrate a column-sharing procedure into the regular CG approach, which helps ensure nonanticipativity and improves the algorithm's convergence. We showcase the effectiveness of the proposed algorithm in producing optimal or near-optimal solutions through case studies on a multistage blending problem and a mobile generator routing problem. 3. We present the first study, to the best of our knowledge, aimed at improving the explainability of solutions to large SP problems. Specifically, we develop scenario and recourse reduction techniques to derive simplified/reduced models whose solutions are nearly identical to those of the original but are significantly easier to explain. We demonstrate the applicability of our techniques in explaining solutions to supply chain and electricity procurement scheduling case studies. 4. We propose an optimization framework that redesigns conventional chemical supply chains by integrating traceability methods, also known as chain of custody models, which are expected to become increasingly important as low-carbon products penetrate the market. The vastly different investment and operational decisions resulting from the choice of chain of custody models are demonstrated through an extensive case study of a low-carbon ammonia supply chain expansion problem. Though the focus of this work has been on laying the foundations for integrating chain of custody models into future sustainable supply chain planning, going forward, additional benefits can be attained from the application of SP to model uncertainties.