I'm of the mind that creative production is absolutely the most important aspect of success in modern mobile marketing. I considered merging this question with How do you test new creatives on Facebook properly?, but since this question is specifically about process, I'll leave it as a standalone thread. That said, here are some other good, relevant threads on this topic:
Background aside, here are some broad tips on building an effective creative production process:
1) First, the process part is actually very important. You need to be operating on a regular schedule, with the team being assigned specific roles and tasked with a defined number of deliverables. Ambiguity is bad here: you want very clear requirements with well-defined production volumes, eg. Person A will deliver 10 new creative concept storyboards each week, Person B will deliver 20 new static interstitial variants of an approved concept each week, Person C will deliver 3 new video variants of an approved concept each week, etc. Everyone needs to know exactly what is expected of them;
2) Someone needs to own it. One person needs to be responsible for the process -- they need authority to assign tasks and must have accountability for results. Creative production doesn't work when it is run by committee: it has to be one person's responsibility. Maybe that's a Creative Director, maybe that's a Director of Ad Creative, maybe that's the Head of Marketing, whatever -- someone needs to fully own the process and have the ability to assign work, engage outsourcers, and demand results.
3) It needs to be weekly. Creative is a volume game and the cadence needs to run on a weekly basis in order to produce the number of variants needed to create a competitive advantage on the basis of ad creative. Monthly is too slow -- even bi-weekly is too slow.
4) Be mindful of the funnel. Creative can't be turned within a week, especially not video creative. The team needs to be mindful of the funnel, which can span an entire month in order to produce one outperforming video ad creative: concept generation goes to storyboarding goes to production goes to testing. Coming up with a great concept for a video ad on January 1 means that ad isn't being exposed to potential users until February 1, so enough concepts need to be pushed through the funnel every week to ensure delivery of a sufficient number of ad creatives on a rolling basis.
5) Don't stop. It's tempting to stop the creative process after a big wave of outperforming creatives has been delivered -- don't. Creative production is a regular, ongoing process, and it's a critical part of doing mobile user acquisition efficiently at scale. Creative production never stops.
6) Invest in the test. Testing new ad creatives should account for 5-10% of your budget at scale. You need to make an investment into testing new creatives; it's just part of running a modern user acquisition function. Don't skimp on testing -- you'll gain far more from an outperforming creative than you'll lose in testing the 99% that perform at par or worse.