One system keeps the whole department at a Target of 80% or better billable. Engineers and other production staff need to carry the overhead staff; admin, business development, management. The holidays can be forecasted with reduced billability, annual leave is managed to comply with target.
Requires each department to be accounted for as a unit, having all roles on the books together.
Whatever your target billability is, your fee multiplier is adjusted to meet your target profit.