"on schedule," "behind schedule," and "ahead (of) the schedule"
"I am sorry Mr. president, we are running behind ___ schedule."
"The airplane has to take off now, we are already running behind ___ schedule."
What should go in there, if anything. Dose it depend on the situation?

I guess my question is about the usage of "the" with respect to the phrases
"on schedule," "behind schedule," and "ahead (of) the schedule."

Would you shed some light on this for me please?

Question

"on schedule," "behind schedule," and "ahead (of) the schedule"
"I am sorry Mr. president, we are running behind ___ schedule."
"The airplane has to take off now, we are already running behind ___ schedule."
What should go in there, if anything. Dose it depend on the situation?

I guess my question is about the usage of "the" with respect to the phrases
"on schedule," "behind schedule," and "ahead (of) the schedule."

Would you shed some light on this for me please?

Answer

"on schedule" is "just in time".  As scheduled. Not too soon nor too late.

"behind schedule" is "(too) late"

"ahead of schedule" is "too soon (/(too) early)"

As you can already read "behind ___ schedule" you could fill in "our". "behind our schedule".

1. "I am sorry Mr. president, we are running behind _your/our_ schedule."

2. "The airplane has to take off now, we are already running behind _our_ schedule."

I would not use "the".