Be completed for or be completed on

In those contexts, "for" would imply that the work is needed in order to continue on to the next step, which will happen on the date mentioned.

Example: "Have your worksheet completed for January 20. On that date, we will use the information on that worksheet as the starting point of the next project."

"On," on the other hand, does not imply that there is a next step starting right away.

Example: "Have your worksheet completed on January 20. I will collect it. We may use the worksheet on a later date, but not on January 20."