The phrase "tight schedule" is correct and usable in written English. You can use it when you mean a schedule that is very full or has very little time for rest or leisure activities. For example: "The students had a tight schedule of exams throughout the week and very little time for sleep.".
It's a tight schedule.
We had a tight schedule.
We're on a very tight schedule".
She keeps me on a tight schedule.
"We are on a very tight schedule," Hanophy said twice.
"He has a really tight schedule there," Mr. Hujanen said.
"It's a very complex job on a very tight schedule".
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union