A scheduler for things that must step out of service to be replenished - a
battery that recharges, an aircraft pulled for maintenance, a player who sleeps
- and then return to work.
It treats the whole repeating schedule as a single closed route. Every stint of
service and every recharge is an edge in a graph, and a valid schedule is one walk
that uses each edge exactly once and ends where it began. Hierholzer's algorithm
(1873) constructs that walk in time proportional to the number of activities, and
the walk is then cut back into one rotation per entity.
The reason such a route exists is the same reason the schedule holds together: at
every point you enter, you must also leave. For the fleet that means every entity
which goes off to recharge is obliged to come back into service - the
structure carries the guarantee, so nothing is stranded.
Each activity has a cost, and the fleet's condition at any moment is a vector of
“health.” Target profiles are kept as vectors in a hosted database; the
planner shapes the schedule so aggregate health settles as close as it can to a
chosen target, for the least cost.
Day/5-year are small instances. Crew is the real one: an
N-friend fleet scheduled by Hierholzer under capacity-limited recharge windows,
fit to a hosted vector DB of target profiles, trading cost against fit.