Google OR-Tools consecutive shifts

Question

I'm learning OR-Tools and started adding onto the nurse scheduling problem. I'm trying to add a constraint that if a nurse is working that they can only work consecutive shifts (i.e can't work shifts 1 and 3, but can work shift 2 and 3).

I'm not entirely certain what is wrong with my code. When the nurses have to ability to work at least (num_of_shifts - 1) shifts per day it works, but if they cannot it does not (e.g. works if there are 5 shifts in a day each nurse can work 4 shifts in a day).

Here is an example output, there are 3 shifts, 3 nurses and every nurse can work a max of 2 shifts (ignore the not requested part, I got rid of the code for it):

Day 0 Nurse 0 works shift 1 (not requested).
Nurse 0 works shift 2 (not requested).
Nurse 1 works shift 0 (not requested).
Nurse 1 works shift 1 (not requested).
Nurse 2 works shift 0 (not requested).

Day 1 Nurse 0 works shift 1 (not requested).
Nurse 0 works shift 2 (not requested).
Nurse 2 works shift 0 (not requested).

Day 2 Nurse 0 works shift 1 (not requested).
Nurse 0 works shift 2 (not requested).
Nurse 2 works shift 0 (not requested).
Nurse 2 works shift 1 (not requested).

Day 3 Nurse 0 works shift 0 (not requested).
Nurse 0 works shift 1 (not requested).
Nurse 1 works shift 1 (not requested).
Nurse 1 works shift 2 (not requested).

Day 4 Nurse 0 works shift 0 (not requested).
Nurse 1 works shift 1 (not requested).
Nurse 1 works shift 2 (not requested).
Nurse 2 works shift 1 (not requested).

---

This is the code that isn't working

has_started_shifts = {}
for n in all_nurses:
    for d in all_days:
        has_started_shifts[(n, d)] = model.NewBoolVar(f"has_started_shifts_n{n}_d{d}")

# consecutive shifts constraint
for n in all_nurses:
    for d in all_days:
        # If a nurse works a shift, mark that they have started shifts for the day
        for s in all_shifts:
            model.Add(has_started_shifts[(n, d)] == True).OnlyEnforceIf(shifts[(n, d, s)])

        # If a nurse works a shift, they can work any subsequent shift
            if s > 1:
                model.Add(shifts[(n, d, s)] <= shifts[(n, d, s - 1)]).OnlyEnforceIf(has_started_shifts[(n, d)])

I have tried creating auxiliary variable that keep track of if the first shift has happened yet but that didn't work either.

I have studied https://github.com/google/or-tools/blob/stable/examples/python/shift_scheduling_sat.py but it doesn't implement what I want.

Thanks for any help you can provide.

Answer 1

I figured a solution out. The way I fixed it was by finding the first and last shift for a person, then subtracting those values to find the difference, then making a constraint that a nurse must work exactly the difference in the amount of shifts for the day

first_shifts = {}
last_shifts = {}
shift_differences = {}
for n in all_nurses:
    for d in all_days:
        first_shifts[(n, d)] = model.NewIntVar(0, num_shifts - 1, f"first_shift_n{n}_d{d}")
        last_shifts[(n, d)] = model.NewIntVar(0, num_shifts - 1, f"last_shift_n{n}_d{d}")
        shift_differences[(n, d)] = model.NewIntVar(0, num_shifts - 1, f"shift_diff_n{n}_d{d}")

        # Make shift differance the differnace betweent the first and last shift
        model.Add(shift_differences[(n, d)] == last_shifts[(n, d)] - first_shifts[(n, d)])

        for s in all_shifts:
            model.Add(first_shifts[(n, d)] <= s).OnlyEnforceIf(shifts[(n, d, s)])
            model.Add(last_shifts[(n, d)] >= s).OnlyEnforceIf(shifts[(n, d, s)])


# Each nurse works at least and at most some number of shifts
for n in all_nurses:
    for d in all_days:
        model.Add(sum(shifts[(n, d, s)] for s in all_shifts) >= 1)
        model.Add(sum(shifts[(n, d, s)] for s in all_shifts) <= 8)
        # Make the number of shifts a nurse work for the day == to the shfit differance
        model.Add(sum(shifts[(n, d, s)] for s in all_shifts) == (shift_differences[(n, d)]+1))