My syllabus clearly lists the day the assignment is due. I make it very clear to the students that I do not accept late assignment, but I would willingly accept early assignment. I also put all this in their syllabi. I take assignments as part of their participation, so the student has to be present to get the assignment/participation points. Since I have made these changes I have noticed that the student attendance has gone up. I do explain to them the reason why I have attached assignment with participation and that is if they are present for the lecture they have heard the information I am covering and that is half the battle in preparing for the upcoming test or a quiz.