I would imagine Riker would be the ultimate guy in charge of it. He probably sets the schedules of the bridge crew and senior officers. The departments schedules are probably delegated to the department heads. Riker might get the report daily and sign off on it. The military has a lot of stuff where the guys under you do the work and you hand the forms to the OIC who looks it over and signs it.
Ahh fun, where Trekbbs members try to figure out the day to day paperwork routine of the Enterprise.
Don't forget Data is Operations Manager. Which we know from O'Brien on Ds9 includes vending machines basically.
I don't think operations manager means that nor does the Ops department means he is head of all operations. I take Ops to be more of a proper noun.
Here is what memory alpha says http://memory-alpha.wikia.com/wiki/Operations_division but it's kind of confusing.
However Data is 2nd officer (third in command of the ship) so I assume he is fully trained to replace Riker if needs be and does take on some delegation of responsibility due to that. I wonder are all second officers in charge of Ops.
(well Data is an android so he can probably do almost any job on the ship but you know what I mean)
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