Dispatching without becoming the dispatcher
If you're the only one who can route the day, the shop doesn't run without you. Fix that first.
Document the routing rules
Who goes to which type of job, which territory, which customer. Write it down once. Now anyone with the list can dispatch.
Set a daily cutoff
A hard time (say, 3:00 p.m.) past which tomorrow's schedule is locked. Last-minute shuffles eat your evening and the team's morning. The cutoff protects both.
Use one map, not five
Whether it's a job board, a software tool, or a whiteboard, one shared view of the day prevents the 'I didn't know that was today' problem. Pick a tool and stick with it.
Take your version of this question further
This is one operator-tested angle on the question. Your shop, your size, your trade, and your team change the answer. Ask your specific version inside Ask a Shop Owner to get a response grounded in how owners like you actually handled it.