I would suggest a new table with a single record entered in it. It will be Record ID of 1
Create the start and end dates of your inquiry range.
Then in the travel table make a field called [Link to travel inquiry date range] with a formula of 1
Lookup the inquiry dates down to the travel dates and on the travel dates recor create a checkbox formula fi LD called [Employee is travelling]. Figure out the formula for that.
Then on the the employee record make a summary of the # of active trips during the inquiry period.
Then make a report of employees with no travel records. That will be your answer.
To be more elegant, put a report link field on the single record table and use that report you just creahave ed. When you save the inquiry date range the single record will refresh and your report will be right on that record.