The most important thing is: You need to not be bothered all day by salesmen requests, phone and other distractions. If you work with a team, one of the team has to be the manager and take care of all these things.
Not only distractions cause waste of time but they also cause mistakes because they take your and your team's attention away. From my experience, this is a huge factor that affects productivity. If you need to answer phone a lot, that needs to be changed; people will need to get used to write to you instead, talk to the manager or use the folder system I mention in the next point. That's really important.
Each project should have a folder with a number. All files should be named accordingly for fast retrieving when archived or when you need to work on a it.
Each folder should be filled by the salesman with clear instructions; there should be a place for size, colors, date received, date of delivery and notes about the files that are already provided. If there is a rush, this should be approved by the estimation department or whoever is fixing the prices for the projects. Otherwise you'll end up doing rush that aren't really rush.
When you receive a folder, if these instructions are not clear or are incomplete, the manager (or you) should send it back to the salesperson with a note about what's missing. This folder goes back at the end of the line! Over time, sales people end up being more careful as they suffer from their lack of care and attention; but you will save a great amount of time this way and your workflow will not stop or slow down because of this.
What's also convenient about instructions is that you can verify your own work more easily. The instructions should be written in the way of bullet points, like 22.214.171.124.... Once you've done one line of instruction, you can put a check mark next to it. This way you don't forget anything. The instructions need to not be written in big paragraph or it will be confusing.
The way you can create these "folders" is by using normal brown envelop or create oversize ones that you can re-use; and in each of them use a 17x11" printed sheets folded in 2, and print fields and lines on them as a brochure that will be filled by your sales people. Each set of proof should have its own folder to avoid confusion. And all these sheets should be easily found in the envelop; this way you always have references if you need to verify something from the previous proofs/requests.
Filling papers might seem annoying sometimes but when you have stuff written, you have proofs and you also have references you can trust if your memory fails you. Especially with a lot of stress, it really helps to use a system with a paper trail like this. It also forces the other departments to do their jobs properly so you don't have to waste time doing "puzzles" or spending time on stuff you shouldn't. You don't need to stand up to change a board, you simply fill your folders and put them with the proof.
There's no way you can stop it and some companies make big money simply because they can deliver rush that others can't. It's possible you work for one of them! So the only thing you can do is make sure you have an efficient workflow and that no project slows it down.
But there's some limits to what can be done. What needs to be done first is to evaluate how many projects can be done in a day and how many rush in average need to be done too.
Usually, your estimation department or the people who have set the prices for the jobs should KNOW how many hours are supposed to be spent on each project and you should also be told about it. Logically, if you work 8hr a day, they have to plan for about 5-6hr max of normal projects and leave you 2-3hr for the rush. Even less if you count your lunch time and pauses. This way you'll have time for a certain number of projects that need to be done that day and will still have extra time for unpredictable emergencies. And if you have no rush one day, you'll simply start the projects of the next day! That's how you will always get everything done on time.
Your managers cannot give you 14hr of work in a day and add rush, and expect you to be on time; at some point, the quality will decrease and/or you'll burn out! And anyway, it doesn't make sense; you can't create time, you can only use it better! If they want this, they'll need to hire more designers or a manager so you can work in peace and full time on the projects.
If your boss asks you special requests, you do them but they should fit in that kind of system mentioned above anyway. It's totally normal he does this and should simply be considered as a rush; but if you can freely talk to him and ask him if it can be done as a normal project, he will be happy to let you more time for these requests. It's his business and he's there for the money after all.
As explained above, each project should have a precise period of time calculated for each of them. You can use a Gantt chart if it can help you visualize the workflow better but frankly, that's something the departments who prepare the work for you should use. With a fast workflow of 2 days, it's almost useless to waste time fixing the chart.
One thing: Don't promise too much to please others. Be realistic. I don't know how is the environment where you work but usually all departments end up begging the designers for extra requests or more attention to their own project. You need to be careful about this and keep following your own folders' schedules and respect the dates of delivery for the projects that were planned to be done and the real rush. Otherwise you will end up penalizing yourself and the other co-workers who are well organized.
This is a system that works very well:
What is your file naming convention you use for version control?