Dealing with late assignments as a teacher assistant I am a graduate student and I'm T.A. of a graduate course. The professor asked us to give some assignments to the students. I have done so and a homework assignment, which contains an optional part for gaining extra marks, I designed.

Moreover, I have set a policy for late assignment being as follows:


One day: Losing 25%
Two days: Losing 50%
Three days: Losing 75%
Further outlasting ones: 100%


My intention was turning in both mandatory and optional parts together in one single written document. However a couple of students turned in that mandatory part by its due date, and optional parts after the due date.

Now, I am in a dilemma whether should I penalize their assignment or not. Also how about that optional part? Should I award extra marks or not?
Follow your stated policy, and follow it to the letter.

An important aspect of teaching, particularly with regards to assessment policies is that you have to be consistent in how you assign your grades. A main reason for this is that if questioned, you can draw upon the stated policy (especially if this was made clear to the students prior to the assessment).

In the case you described, as @ff524 stated in the comment, grade the mandatory part as normal, and apply the lateness penalty to the optional part of the assessment.

Essentially:

Mandatory part mark + (Optional part mark - lateness penalty applied to the optional part only) = Overall mark

(Note in the equation above, the equation in the parentheses has a minimum value of zero)