Drop Index takes longer in Prod than in Test

We have a DW nightly load that drops indexes as part of the load. 
The index drops can sometimes take minutes in prod -- whereas as test of
the same drop, in the test environment, takes seconds. Now minutes might
not seem like much, but there are many indexes so the times add up.
I can't easily enable tracing on the Oracle side (prod server,
multi-tiered env, etc...) so I'm looking for some tips for where/what
else I can look for.
Oh, the other constraint is that I can't modify the DW load process --
so I'm restricted solely to looking at the Oracle side.
Your help is much appreciated.
Thank you!

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