to solve a work scheduling problem to assign
workers to shifts. Here are notes about doing that. This is a common use case,
but isn't explicitly covered in the
The tool is supposed to allocate workers to the shifts to try to cover all the
shifts, give everybody work, and try to match their preferences. I implemented
the tool:
#!/usr/bin/python3
import sys
import os
import re
def report_solution_to_console(vars):
for w in days_of_week:
annotation = ''
if human_annotate is not None:
for s in shifts.keys():
m = re.match(rf' w - ', s)
if not m: continue
if vars[human_annotate][s].value():
annotation = f" ( human_annotate SCHEDULED)"
break
if not len(annotation):
annotation = f" ( human_annotate OFF)"
print(f" w annotation ")
for s in shifts.keys():
m = re.match(rf' w - ', s)
if not m: continue
annotation = ''
if human_annotate is not None:
annotation = f" ( human_annotate shifts[s][human_annotate] )"
print(f" ---- s[m.end():] annotation ")
for h in humans:
if vars[h][s].value():
print(f" h ( shifts[s][h] )")
def report_solution_summary_to_console(vars):
print("\nSUMMARY")
for h in humans:
print(f"-- h ")
print(f" benefit: benefits[h].value():.3f ")
counts = dict()
for a in availabilities:
counts[a] = 0
for s in shifts.keys():
if vars[h][s].value():
counts[shifts[s][h]] += 1
for a in availabilities:
print(f" counts[a] a ")
human_annotate = None
days_of_week = ('SUNDAY',
'MONDAY',
'TUESDAY',
'WEDNESDAY',
'THURSDAY',
'FRIDAY',
'SATURDAY')
humans = ['ALICE', 'BOB',
'CAROL', 'DAVID', 'EVE', 'FRANK', 'GRACE', 'HEIDI', 'IVAN', 'JUDY']
shifts = 'SUNDAY - SANDING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'DISFAVORED',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'JUDY': 'NEUTRAL' ,
'WEDNESDAY - SAWING 7:30 AM - 2:30 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'NEUTRAL',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'EVE': 'REFUSED',
'JUDY': 'REFUSED' ,
'THURSDAY - SANDING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'PREFERRED',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED' ,
'SATURDAY - SAWING 7:30 AM - 2:30 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'FRANK': 'PREFERRED',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'EVE': 'REFUSED',
'JUDY': 'REFUSED',
'GRACE': 'REFUSED' ,
'SUNDAY - SAWING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'DISFAVORED',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED' ,
'MONDAY - SAWING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'PREFERRED',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED' ,
'TUESDAY - SAWING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'NEUTRAL',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED' ,
'WEDNESDAY - PAINTING 7:30 AM - 2:30 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'NEUTRAL',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'EVE': 'REFUSED',
'JUDY': 'REFUSED',
'DAVID': 'REFUSED' ,
'THURSDAY - SAWING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'PREFERRED',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED' ,
'FRIDAY - SAWING 9:00 AM - 4:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'DAVID': 'PREFERRED',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'PREFERRED',
'IVAN': 'PREFERRED',
'JUDY': 'DISFAVORED',
'HEIDI': 'REFUSED' ,
'SATURDAY - PAINTING 7:30 AM - 2:30 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'FRANK': 'PREFERRED',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'EVE': 'REFUSED',
'JUDY': 'REFUSED',
'GRACE': 'REFUSED',
'DAVID': 'REFUSED' ,
'SUNDAY - PAINTING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'DISFAVORED',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'MONDAY - PAINTING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'PREFERRED',
'IVAN': 'PREFERRED',
'JUDY': 'NEUTRAL',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'TUESDAY - PAINTING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'NEUTRAL',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'WEDNESDAY - SANDING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'DAVID': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'NEUTRAL',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'JUDY': 'NEUTRAL',
'EVE': 'REFUSED' ,
'THURSDAY - PAINTING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'NEUTRAL',
'IVAN': 'PREFERRED',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'FRIDAY - PAINTING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'PREFERRED',
'FRANK': 'PREFERRED',
'GRACE': 'PREFERRED',
'IVAN': 'PREFERRED',
'JUDY': 'DISFAVORED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'SATURDAY - SANDING 9:45 AM - 4:45 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'DAVID': 'PREFERRED',
'FRANK': 'PREFERRED',
'HEIDI': 'DISFAVORED',
'IVAN': 'PREFERRED',
'EVE': 'REFUSED',
'JUDY': 'REFUSED',
'GRACE': 'REFUSED' ,
'SUNDAY - PAINTING 11:00 AM - 6:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'PREFERRED',
'IVAN': 'NEUTRAL',
'JUDY': 'NEUTRAL',
'DAVID': 'REFUSED' ,
'MONDAY - PAINTING 12:00 PM - 7:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'PREFERRED',
'IVAN': 'NEUTRAL',
'JUDY': 'NEUTRAL',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'TUESDAY - PAINTING 12:00 PM - 7:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'NEUTRAL',
'HEIDI': 'REFUSED',
'JUDY': 'REFUSED',
'DAVID': 'REFUSED' ,
'WEDNESDAY - PAINTING 12:00 PM - 7:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'NEUTRAL',
'JUDY': 'PREFERRED',
'EVE': 'REFUSED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'THURSDAY - PAINTING 12:00 PM - 7:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'NEUTRAL',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'FRIDAY - PAINTING 12:00 PM - 7:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'NEUTRAL',
'JUDY': 'DISFAVORED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'SATURDAY - PAINTING 12:00 PM - 7:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'NEUTRAL',
'FRANK': 'NEUTRAL',
'IVAN': 'NEUTRAL',
'JUDY': 'DISFAVORED',
'EVE': 'REFUSED',
'HEIDI': 'REFUSED',
'GRACE': 'REFUSED',
'DAVID': 'REFUSED' ,
'SUNDAY - SAWING 12:00 PM - 7:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'NEUTRAL',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'NEUTRAL',
'JUDY': 'PREFERRED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'MONDAY - SAWING 2:00 PM - 9:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'TUESDAY - SAWING 2:00 PM - 9:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'HEIDI': 'REFUSED',
'JUDY': 'REFUSED',
'DAVID': 'REFUSED' ,
'WEDNESDAY - SAWING 2:00 PM - 9:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'EVE': 'REFUSED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'THURSDAY - SAWING 2:00 PM - 9:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'HEIDI': 'REFUSED',
'DAVID': 'REFUSED' ,
'FRIDAY - SAWING 2:00 PM - 9:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'HEIDI': 'REFUSED',
'JUDY': 'REFUSED',
'DAVID': 'REFUSED' ,
'SATURDAY - SAWING 2:00 PM - 9:00 PM':
'ALICE': 'PREFERRED',
'BOB': 'PREFERRED',
'CAROL': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'EVE': 'REFUSED',
'HEIDI': 'REFUSED',
'GRACE': 'REFUSED',
'DAVID': 'REFUSED' ,
'SUNDAY - PAINTING 12:15 PM - 7:15 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'PREFERRED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'NEUTRAL',
'DAVID': 'REFUSED' ,
'MONDAY - PAINTING 2:00 PM - 9:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'DAVID': 'REFUSED' ,
'TUESDAY - PAINTING 2:00 PM - 9:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'REFUSED',
'DAVID': 'REFUSED' ,
'WEDNESDAY - PAINTING 2:00 PM - 9:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'EVE': 'REFUSED',
'DAVID': 'REFUSED' ,
'THURSDAY - PAINTING 2:00 PM - 9:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'DAVID': 'REFUSED' ,
'FRIDAY - PAINTING 2:00 PM - 9:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'DISFAVORED',
'EVE': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'GRACE': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'REFUSED',
'DAVID': 'REFUSED' ,
'SATURDAY - PAINTING 2:00 PM - 9:00 PM':
'ALICE': 'NEUTRAL',
'BOB': 'NEUTRAL',
'CAROL': 'DISFAVORED',
'FRANK': 'NEUTRAL',
'HEIDI': 'NEUTRAL',
'IVAN': 'DISFAVORED',
'JUDY': 'DISFAVORED',
'EVE': 'REFUSED',
'GRACE': 'REFUSED',
'DAVID': 'REFUSED'
availabilities = ['PREFERRED', 'NEUTRAL', 'DISFAVORED']
import pulp
prob = pulp.LpProblem("Scheduling", pulp.LpMaximize)
vars = pulp.LpVariable.dicts("Assignments",
(humans, shifts.keys()),
None,None, # bounds; unused, since these are binary variables
pulp.LpBinary)
# Everyone works at least 2 shifts
Nshifts_min = 2
for h in humans:
prob += (
pulp.lpSum([vars[h][s] for s in shifts.keys()]) >= Nshifts_min,
f" h works at least Nshifts_min shifts",
)
# each shift is ~ 8 hours, so I limit everyone to 40/8 = 5 shifts
Nshifts_max = 5
for h in humans:
prob += (
pulp.lpSum([vars[h][s] for s in shifts.keys()]) <= Nshifts_max,
f" h works at most Nshifts_max shifts",
)
# all shifts staffed and not double-staffed
for s in shifts.keys():
prob += (
pulp.lpSum([vars[h][s] for h in humans]) == 1,
f" s is staffed",
)
# each human can work at most one shift on any given day
for w in days_of_week:
for h in humans:
prob += (
pulp.lpSum([vars[h][s] for s in shifts.keys() if re.match(rf' w ',s)]) <= 1,
f" h cannot be double-booked on w "
)
#### Some explicit constraints; as an example
# DAVID can't work any PAINTING shift and is off on Thu and Sun
h = 'DAVID'
prob += (
pulp.lpSum([vars[h][s] for s in shifts.keys() if re.search(r'- PAINTING',s)]) == 0,
f" h can't work any PAINTING shift"
)
prob += (
pulp.lpSum([vars[h][s] for s in shifts.keys() if re.match(r'THURSDAY SUNDAY',s)]) == 0,
f" h is off on Thursday and Sunday"
)
# Do not assign any "REFUSED" shifts
for s in shifts.keys():
for h in humans:
if shifts[s][h] == 'REFUSED':
prob += (
vars[h][s] == 0,
f" h is not available for s "
)
# Objective. I try to maximize the "happiness". Each human sees each shift as
# one of:
#
# PREFERRED
# NEUTRAL
# DISFAVORED
# REFUSED
#
# I set a hard constraint to handle "REFUSED", and arbitrarily, I set these
# benefit values for the others
benefit_availability = dict()
benefit_availability['PREFERRED'] = 3
benefit_availability['NEUTRAL'] = 2
benefit_availability['DISFAVORED'] = 1
# Not used, since this is a hard constraint. But the code needs this to be a
# part of the benefit. I can ignore these in the code, but let's keep this
# simple
benefit_availability['REFUSED' ] = -1000
benefits = dict()
for h in humans:
benefits[h] = \
pulp.lpSum([vars[h][s] * benefit_availability[shifts[s][h]] \
for s in shifts.keys()])
benefit_total = \
pulp.lpSum([benefits[h] \
for h in humans])
prob += (
benefit_total,
"happiness",
)
prob.solve()
if pulp.LpStatus[prob.status] == "Optimal":
report_solution_to_console(vars)
report_solution_summary_to_console(vars)
variable, and the shift schedule and the
workers' preferences are encoded in the
dict. The problem is defined by
a
dict of dicts, each a boolean variable indicating whether a particular
worker is scheduled for a particular shift. We define a set of constraints to
these worker allocations to restrict ourselves to valid solutions. And among
these valid solutions, we try to find the one that maximizes some benefit
function, defined here as:
So for instance each shift that was scheduled as somebody's PREFERRED shift
gives us 3 benefit points. And if all the shifts ended up being PREFERRED, we'd
have a total benefit value of 3*Nshifts. This is impossible, however, because
that would violate some constraints in the problem.
The exact trade-off between the different preferences is set in the
dict. With the above numbers, it's equally good for
somebody to have a NEUTRAL shift and a day off as it is for them to have
DISFAVORED shifts. If we really want to encourage the program to work people as
much as possible (days off discouraged), we'd want to raise the DISFAVORED
threshold.
I run this program and I get:
So we have a solution! We have 108 total benefit points. But it looks a bit
uneven: Judy only works 2 days, while some people work many more: David works 5
for instance. Why is that? I update the program with =human_annotate = 'JUDY'=,
run it again, and it tells me more about Judy's preferences:
This tells us that on Monday Judy does not work, although she marked the SAWING
shift as PREFERRED. Instead David got that shift. What would happen if David
gave that shift to Judy? He would lose 3 points, she would gain 3 points, and
the total would remain exactly the same at 108.
How would we favor a more even distribution? We need some sort of tie-break. I
want to add a nonlinearity to strongly disfavor people getting a low number of
shifts. But PuLP is very explicitly a linear programming solver, and cannot
solve nonlinear problems. Here we can get around this by enumerating each
specific case, and assigning it a nonlinear benefit function. The most obvious
approach is to define another set of boolean variables:
. And then using them to add extra benefit terms, with
values nonlinearly related to
. Something like this:
So in the previous example we considered giving David's 5th shift to Judy, for
her 3rd shift. In that scenario, David's extra benefit would change from -0.2 to
-0.3 (a shift of -0.1), while Judy's would change from -0.8 to -0.5 (a shift of
+0.3). So the balancing out the shifts in this way would work: the solver would
favor the solution with the higher benefit function.
Great. In order for this to work, we need the
variables
to function as intended: they need to be binary indicators of whether a specific
person has that many shifts or not. That would need to be implemented with
constraints. Let's plot it like this:
variable (plotted on the x axis of this
plot) would need to be defined by a set of linear AND constraints to
the true (red) values of this variable from the false (black) values.
As can be seen in this plot, this isn't possible. So this representation does
not work.
How do we fix it? We can use inequality variables instead. I define a different
set of variables
.
The equality variable from before can be expressed as a difference of these
inequality variables:
So we can use two linear constraints to make each of these variables work
properly. To use these in the benefit function we can use the equality
constraint expression from above, or we can use these directly:
In this scenario, David would get a boost of 0.4 from giving up his 5th shift,
while Judy would lose a boost of 0.2 from getting her 3rd, for a net gain of 0.2
benefit points. The exact numbers will need to be adjusted on a case by case
basis, but this works.
The full program, with this and other extra features is available
Like each month, have a look at the work funded by Freexian s Debian LTS offering.
(Edit: Twitter could improve this significantly with very few changes - I wrote about that 
This web of nodes and edges represents every module and its relationship during the compilation process of 
Here s what the data tells us:
Don t knock the fence down before you know why it s up. I repeat this phrase over and over again, yet the (metaphorical) Homeowner s Association still decides my fence is the wrong color.Well, now you get to know why the fence is up. If anyone s actually willing to challenge me on this level, I d welcome it.The four ideas I d like to discuss are this: quantum physics, Lutheranism, mental resilience, and psychology. I ve been studying these topics intensely for the past decade as a passion project. I m just going to let my thoughts flow, but I d like to hear other opinions on this.Can the mysteries of the mind, the subatomic world, and faith converge to reveal deeper truths?When it comes to self-taught knowledge on analysis, I m mostly learned on Freud, with some hints of Jung and Peterson. I ve read much of the original source material, and watched countless presentations on it. This all being said, I m both learned on Rothbard and Marx, so if there is a major flaw in the way of Freud is frowned upon, I d genuinely like to know so I can update my research and juxtapose the two schools of thought.Alongside this, although probably not directly relevant, I m learned on John Locke and transcendentalism. What I d like to focus on here is this the Id.The Id is the pleasure-seeking, instinctual part of the psyche. Jung further extends this into the idea of the shadow self, and Peterson maps the meanings of these texts into a combined work (at least in my rudimentary understanding).In my research, the Id represents the part of your psyche that deals with religious values. As an example, if you re an impulsive person, turning to a spiritual or religious outlet can be highly beneficial. I ve been using references from the foundational text of the Judaeo-Christian value system this entire time, feel free to re-read my other blog posts (instead of claiming they don t exist).Let s tie this into quantum physics. This is the part where I ll struggle most. I ve watched several movies about this, read several books, and even learned about it academically, but quantum physics is likely to be my weak spot here.I did some research, and here are the elements I m looking for: uncertainty principle, wave-particle duality, quantum entanglement, and the observer effect.I already know about the cat in the box. And the Cat in the Hat, for that matter. I know about wave-particle duality from an incredibly intelligent high school physics teacher of mine. I know about the uncertainty principle purely in a colloquial sense. The remaining element I need to wrap my head around is quantum entanglement, but it feels like I m almost there.These concepts do actually challenge the idea of pure free will. It s almost like we re coming full circle. Some theologians (including myself, if you can call me a self-taught one) do believe the idea of quantum indeterminacy can be a space where divine action may take place. You could also liken the unpredictable nature of the Id to quantum indeterminacy as well. These are ones to think about, because in all reality, they re subjective opinions. I do believe they re interconnected.In terms of Lutheranism, I ll be short on this one. Please do go read the full history behind Martin Luther and his turbulent relationship with Catholicism. I m not a Bible thumper, and I actually think this is the first time I ve mentioned religion publicly at all. This being said, now I m actually ready to defend the points on an academic level.The Id represents hidden psychological forces, quantum physics reveals subatomic mysteries, and Lutheranism emphasizes faith in the unseen God. Okay, so we have the baseline. Now, time for some mental resilience. When I think of mental resilience, the first people I think of are David Goggins and Jocko Willink. I ve also enjoyed Dr. Andrew Huberman s podcast.The idea there is simple if you understand exactly how to learn, you know your fundamentals well enough to draw them and explain them vividly on a whiteboard, and you can make it a habit, at that point you re ready to work on your mental resilience. Little by little, gradually, how far can you push the bar towards the ceiling?There s obviously limits. People sometimes get scared when I mention mental resilience, but obviously that s a bit of a catch 22. There are plenty of satirical videos out there, and of course, I don t believe in Goggins or Jocko wholeheartedly. They re just tools in the toolbox when times get tough.I wish you all well, and I hope this gets you thinking about those people who just insist there is no God or higher being, and think you re stupid for believing there is one. Those people obviously haven t read analysis, in my own opinion.Have a great night!
On the way to Trixie, polkitd (Policy Kit Daemon) has lost the functionality to evaluate its .pkla (Polkit Local Authority) files.
On 26th and 27th April we held a Debian bug-squashing party near
Leuven, Belgium. Several longstanding and new Debian contributors
gathered to work through some of the highest priority bugs affecting
the upcoming release of Debian 13 trixie .
We were hosted by the 
Dear Debian community,
this is bits from DPL for March (sorry for the delay, I was waiting
for some additional input).
Conferences
In March, I attended two conferences, each with a distinct motivation.
I joined FOSSASIA to address the imbalance in geographical developer
representation. Encouraging more developers from Asia to contribute to
Free Software is an important goal for me, and FOSSASIA provided a
valuable opportunity to work towards this.
I also attended Chemnitzer Linux-Tage, a conference I have been part of
for over 20 years. To me, it remains a key gathering for the German Free
Software community a place where contributors meet, collaborate, and
exchange ideas.
I have a remark about submitting an event proposal to both FOSDEM and
FOSSASIA:
Cross distribution experience exchange
A new release 0.1.8 of 
A few months ago 
Update 20250309 13:20-03:00 - How to help
A friend of mine living in the USA sent me this link to help the flood victims: 
The "real" thing
Let's get to the heavy, heartbreaker part. I did go to downtown Bah a Blanca, but during night, so let me share some links, most of them in Spanish, but images are images:
