As I understand work, an unfilled company job has a
total normalised workload: w
c requirements: r_c(person skill_c, time)
number of positions to fill: n
where
time[now, infinity] integrated:
sum over i:= 1 to c:
involvement of person ×
r_i(person skill_i)
= w
(solving for total involvement × requirement = total normalised workload,
because it's a boundary of inequality (>=100% of w))
That is applicable to set of all living people at the moment L
finds out about posting: A subset of L
would accept: B subset of L
beta(person) := how much of required workload will this person fill after integrating their (involvement x requirement) over their time there
time: 0 to inf (now until end of the universe)
involvement(t): -inf to inf (work units)
requirement_i(t): [0, 1] (in units inverse to work units)
(a capable and willing person who's not conscious will have involvement=0,
someone who only would work on weekends for a place that's closed on weekends will have person skill_attendance>0 on weekends, but requirement_attendance>0 only on workdays, a disjoint set)
a person with beta=1 fills the position until the position ceases to exist
basically nobody has beta=1, that happens probably only if trade becomes obsolete or position is e.g. to paint a specific room)
remaining workload after parting ways (company closed, person dead and/or universe ended):
w_r = w - beta(w)
if w_r = 0 then they never have to hire anyone for this position ever again
otherwise the hiring process repeats with w=w_r
Here, there's a start to formalizing the problem if someone is willing to look into this. It's my half an hour armchair take on this, because I figured it is all I can do. even if it's not anything at all, I tried and enjoyed the process.
I think my main point is, hiring processess seem to be very far from addressing the basic parameters of actual process of working somewhere in my view.
Let's get GPT-4 onto this maybe