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The recent successes of emerging photovoltaics (PVs) are largely driven by innovations in material science. However, closing the gap to commercialization still requires significant progress to match contradicting requirements, such as performance, longevity, and recyclability. In this perspective, we envision the layout of a digital twin for PV materials able to provide the necessary acceleration of innovation.

Recent developments in the field of data analysis offer enormous potential to derive predictions of future aircraft maintenance necessities from observable aircraft attributes. This procedure is called Predictive Maintenance. The Predictive Maintenance generates considerable business benefits compared to alternatives like reactive or preventive maintenance for various reasons. Nevertheless, recognizing a maintenance necessity is only the first step, since the execution of the maintenance action has to fit into the airlines operational schedule. An essential step to realize financial benefits is to integrate Predictive Maintenance into the airlines optimization processes. To contribute to this task, we expand a well-known Tail Assignment model for the assignment of a potentially heterogeneous fleet of aircraft to a schedule of flights by a number of part failure scenarios. This results in a stochastic mixed integer linear optimization program, for which an optimization algorithm with solution guarantees is developed. This optimization algorithm is based on Benders Decomposition, which is concretized for the Tail Assignment problem and optimized for this task. Using this algorithm, a large proportion of the recovery costs for almost all instances tested is saved. The algorithm solves all instances in a reasonable amount of time. The algorithm uses a state-of-the-art mixed-integer linear solver, implementing a decomposition-based solution procedure for stochastic programs, called the L-shaped method. To demonstrate the potential of the approach, we benchmark our results using four strategies, motivated by commonly used preventive, reactive and passive approaches. Our approach leads to considerable cost savings when compared to each of the four benchmark approaches. The algorithms are tested on a set of instances with up to 80 flights based on a pre-pandemic schedule of a larger German airline. To the best of our knowledge, this article presents the first attempt to implement an exact optimization approach integrating malfunction predictions of the form presented into a Tail Assignment model.

Optimization problems under uncertain conditions abound in many real-life applications. While solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually applied in case solutions are sought that are feasible for all realizations of uncertainties within some predefined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we deal with a class of joint probabilistic/robust constraints. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for finding their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in determining controls such that a certain robustness measure remains below some given upper bound with high probability.