I know one true thing about your situation: If you are able to come to an understanding and improve teamwork, that will count for more with the big bosses than if you actually improve efficiency.
Although you are not their boss, getting things done quickly seems to have been your original goal. But, they were doing fine on their slower pace all along and have no reason to work faster/harder.
So you are at crossed purposes with them because the newbie bounced in and wants to run things differently. They are of the opinion that things were just fine the way they were, and the newbie is stepping on their toes.
Now for the big question: Why is it so important to you to have every job finished right away?
Next question: What harm is there in you doing your thing, passing along the jobs to the others' inboxes, and trusting their professionalism to complete jobs as they always did in the past?
Kris, I love you, but if you came into my office trying to change things like you went into theirs, we would eat you for lunch and poop you out by dinner. Don't be mad, but I think maybe you should chill out a bit. It's just a job.
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