Turnaround times for graphic design work/projects can vary depending on the type of job. There are a number of variables at play that influence how long a job will take.
Is your project a complex logo or a simple one page marketing PDF? The more complicated the project the longer it will typically take.
The turnaround times for design jobs that are part of your unlimited graphic design subscription is often 1 business day for single jobs. Many companies including Design Pickle offer this - It's one thing that sets them apart from individual freelancers who can sometimes take longer to complete requests. If you're dealing with an unlimited graphic design company there can sometimes be designers working in multiple time zones on your design jobs thus speeding up the process.
The client must be able to clearly communicate their vision for what they want. This includes the look and feel (colors, fonts, images, icons and logos to use) and any examples the designer can use inspiration (e.g. mood boards, collages or images that convey the desired aesthetic).
If for some reason there is a gap in understanding there amy be wasted effort by the designer as they won't be producing the correct look and feel, and work will need to be redone. The less guessing by the designer, the better.
It pays to spend extra time explaining what you're looking for design-wise in the earliest parts of the process. This investment of time and effort can pay tremendous dividends down the road.
Throughout the design process decisions must be made, and feedback given. If either the designer or client is slow to respond this will increase turnaround times.
The more experienced a designer or agency is the better their turnaround times will be. The best designers and agencies can take an incomplete or incoherent brief, gaze into a crystal ball and just know what needs to be done.
When they present work to the client the client is relieved to know that the designer just 'gets it'. Designer ability is a key variable in the types of turnaround times you can expect for outsourced design jobs.
Turnaround times for graphic design jobs - whether done in-house or in an outsourcing arrangement can vary tremendously. As long as you have taken the time to properly evaluate your designer's ability you should expect the process to go smoothly.
Prompt, clear communication can help reduce turnaround times to ensure that good design is produced quickly, and that is the goal of any client/designer relationship.