Hi Asokan
can you please let us know which DB you are using . If you are using DB2 , then you can use the index analyzer to see the cost of the query and what is the SAP Recommendation of the same.
If you re using Oracle , then you need to check manually the explain plan and the cost associated with the same.
from your ST05 trace - are you able to see the explain plan of the query. Can you paste the same here.
Also try to replicate in your QA Environment and see the query performance. If the issue is due to a bad query logic , then you might get the same performance in QA although due to less data , the behavior is often different.
Ensure that all the indexes have statistics updated in the PROD environment.
Thanks
Rishi