These variables can be as simple as 1 location, 1 skill requirement, 1 shift of work and 1 set roster of people.
Add numerous locations to the equation and Collective Bargaining and Federal labor laws and these become new considerations for the problem solving method.
Finding the most efficient route and staffing it with properly qualified personnel is a critical financial consideration.
Although not easy to describe in one sentence, the goal is essentially the same for any method of attacking the problem: "Within a set of constraints and rules, move a set roster of people with certain qualifications, from place to place with the fewest personnel and aircraft or vehicles in the least amount of time."
Lowest cost has traditionally been the major driver for any crew scheduling solution.
These are awarded based on seniority and modified only when their selections have already been taken by a more senior crew member (bidlines) or their trip and day off selections (preferential bidding) do not make up a complete line (hours, days off, etc.
Before assigning a single trip, the schedulers put all planned absences (vacation, training, etc.)
Slowly over the last thirty years, foreign airlines using the "no seniority" rostering system have allowed some measure of seniority to creep into the allocation process from pilots who may now ask for a specific day off or trip once a quarter or make multiple requests within a schedule period.