Online optimization with gradual look-ahead

We extend the setting of online optimization with look-ahead to online optimization with gradual look-ahead. While look-ahead as considered so far refers to a deterministic outlook on future data, gradual look-ahead only allows for an uncertain outlook on future data which becomes more and more precise as an input element's release time is approached. After a discussion of related concepts, we formally introduce the class of online optimization problems with gradual look-ahead. Since the course of look-ahead information of a single input element is tied to a corresponding uncertainty set trajectory, we examine how different forecasting methods and different algorithmic approaches for dealing with gradual look-ahead can be instantiated and compared to each other with respect to the optimization output. We exemplify the introduced concepts by numerical experiments for the two applications of lot sizing and vehicle routing under gradual look-ahead.