Polynomial time sensitivity analysis of task schedules

By performing sensitivity analysis on an optimal task schedule, this paper derives a polynomial time method to determine whether the task schedule remains optimal after arbitrary changes to task costs occur. We consider fast reactive mission planning for unmanned aircraft in changing environments. Changing external conditions such as weather or threats may alter task costs, which can render an initially optimal task schedule suboptimal. Instead of optimizing the task schedule every time task costs change, stability criteria allow for fast evaluation of whether schedules remain optimal. This paper develops a method to compute stability regions for a set of schedules in a prototypical mission for unmanned aircraft, the traveling salesman problem, where the alternative schedules are part of a pre-approved mission plan. As the traveling salesman problem is NP-hard, heuristic methods are frequently used to solve it. The presented approach is also applicable to analyze stability regions for a tour obtained through application of the k-opt heuristic with respect to the k-neighborhood and is demonstrated with an example problem.