How should we manage large database
As mentioned in another answer, you should consider using a database. In the long run it will make your life easier. 

But, R can help you automate things. You can store excel files in specific folders and/or with specific names (or patterns of names ex. file1_day1, file1_day2 etc) and then create R scripts that process them and produce the report you want.

Since you are using excel files (nothing personal with excel, it is a great program) I am inclined to think that your data will fit in a decent computer running R. In any case, if you end up using R, you should check out data.table package.

Furthermore, R can help you create more complicate reports. Plus, its learning path is not too steep.