Task scheduling with progress control

Tasks with long durations often face the requirement of having to periodically report their progress to process controllers. Under this requirement, working teams that simultaneously process multiple tasks need to schedule their work carefully in order to demonstrate satisfactory progress on each unfinished task. We present a single-machine scheduling model that reflects this requirement. Our model has multiple milestones at which the tasks are penalized if their progress is below a satisfactory level. We develop polynomial solution methods for the general case with convex nonlinear penalty functions and for the special case with linear penalty functions. Extensions of our model are also discussed.