Interactions of Uncertainty and Optimization: Theory, Algorithms, and Applications to Chemical Site Operations
This thesis explores different paradigms for incorporating uncertainty with optimization frameworks for applications in chemical engineering and site-wide operations. First, we address the simulation optimization problem, which deals with the search for optimal input parameters to black-box stochastic simulations which are potentially expensive to evaluate. We include a comprehensive literature survey of the state-of-the-art in the area, propose a new provably convergent trust region-based algorithm, and discuss implementation details along with extensive computational experience, including examples for chemical engineering applications. Next, we look at the problem of long-term site-wide maintenance turnaround planning. Turnarounds involve the disruption of production for significant periods of time, and may incur enormous costs in terms of maintenance manpower as well as lost sales. The problem involves (1) the simulation of profit deterioration due to wear and tear followed by the determination of how frequently a particular turnaround should take place; and (2) the consideration of site network structure and turnaround frequencies to determine how turnarounds of different plants may be coordinated over a long-term horizon. We investigate two mixed-integer models, the first of which determines optimal frequencies of individual plant turnarounds, while the second considers maximizing long-term profit through coordination of turnarounds across the site. We then turn to more conventional methods of dealing with optimization under uncertainty, and make use of a combined robust optimization and stochastic programming approach to medium-term maintenance planning in integrated chemical sites. The nature of the uncertainty considered affects two aspects of maintenance planning, one of which is most suitably addressed through a robust optimization framework, while the other is better handled with stochastic programming models. In summary, we highlight the importance of considering uncertainty in optimization as well as the choice of approach or paradigm used through chemical engineering applications that span varied domains and time scales.