Fair Shift Distribution

问题

I have a slightly modified version of nurse_sat
https://github.com/google/or-tools/blob/master/examples/python/nurses_sat.py
where I have a dictionary of key - value pares of (day, nurse, shift) = BoolVar I want to make it so all nurses have same amount of each shift.

E.G: Let's assume that we have 30 days, and there are 3 shifts per day {0, 1, 2} and we have 3 nurses {a, b, c}
I would like to have all nurses do 10 of shift 0, 10 of shift 2 and 10 of shift 3.

The way I am trying to achieve this is:

fairshift = {}
for j in range(num_nurses):
 for k in range(num_shifts):
  fairshift[(j,k)] = sum(shifts[(i, j, k)] for i in range(num_days))

In theory, that should give me how many particular shift a nurse had. E.G: fairshift[(0, 0)] should have the number of the 0 shifts Nurse A had throughout the week. And then to make them equal, I did something like this:

for k in range(num_shifts):
 solver.Add(min([fairshift[(j, k)] for j in range(num_nurses)]) == max([fairshift[(j,k)] for j in range(num_nurses)]))

So that max number of k shifts a nurse had would be equal to the min one and if num_days is 30 they all should have 10 shifts of shift k.

However, I can't get it to work and I am unsure of why. To have IntVar instead of _SumArray, I did something like this:

for j in range(num_nurses):
 for k in range(num_shifts):
  fairshift[(j,k)] = solver.NewIntVar(0, num_days, "%i,%i" % (j,k))
  solver.Add(fairshift[(j,k)] == sum(shifts[(i, j, k)] for i in range(num_days)))

In the case of min .== max, it works but gives wrong results. I think I'm summing something wrong, but I am unsure what it is.

回答1:

fairshift = {}
for n in range(num_nurses):
  for s in range(num_shifts):
    sum_of_shifts[(n, s)] = model.NewIntVar(0, num_days, 'sum_of_shifts_%i_%i' % (n, s))
    model.Add(sum_of_shifts[(n, s)] == sum(shifts[(d, n, s)] for d in range(num_days)))


for s in range(num_shifts):
  min_fair_shift = model.NewIntVar(0, num_days, 'min_fair_shift_%i' % s)
  max_fair_shift = model.NewIntVar(0, num_days, 'max_fair_shift_%i' % s)
  model.AddMinEquality(min_fair_shift, [sum_of_shifts[(n, s)] for n in range(num_nurses)])
  model.AddMaxEquality(max_fair_shift, [sum_of_shifts[(n, s)] for n in range(num_nurses)]) 

  model.Add(max_fair_shift - min_fair_shift <= 1)

来源：https://stackoverflow.com/questions/53356121/fair-shift-distribution

标签

python

or-tools