Based on the information you provided:
How does one actually accomplish this?
In context of projects I suggest to start with optimizing the schedule for lead time (as opposed to minimum cost). Minimizing the lead time is a "regular scheduling objective" and as such can be scheduled using rule-based approach (simply put - easier).
Based on simple priority rules you can create resource-feasible schedules, here is a simple video with "boxes" to illustrate the process.
What does one measure?
Since the main optimization criterion is the lead time, I would measure:
- Time between project/task/order etc. start and end - as the main metric to optimize.
- "Wait time" vs. "Work time" - to get a better understanding of the optimization potential.
- Depending on the nature of projects/tasks/orders I would get a more deep dive into "wait" and "work" to understand their structure, reasons etc.
What does one avoid?
With overoptimizing for lead time, costs might get out of control. Having this risk I would make sure I establish some sort of control over costs to keep them reasonable.