Before you choose a solution you should be clear what the problem is. This is a SQL Server database? What do you mean when you say they compress the DB? I'm not aware of a compress feature other that permanently turning on the page or row level compression. If you mean they keep shrinking the database and it keeps growing back, is it actually getting bigger and bigger over, say a month, or is it just growing back to the same size it was when they shrank it? If it needs to be a certain size, it's better to accept that and just leave it at that size.
Appreciate all for sharing your thoughts on the same. I investigated the issue and found that .mdf was 14 GB and out of which 1 gb was showing unused. I encountered they have issue with .ldf and same growing on weekly basis. Due to less space issue on their server,client IT used to shrink it every alternate day and wanted to fix it. I found database was in simple recovery mode. DB growth Settings was set to grow 10%. So set the DB growth settings to grow by 10 mb, kept the .mdf and .ldf files on different drive so that they will not have space issue so frequently. Created a Job for shrinking .ldf to 1Mb on weekly basis.