ensure a shift cannot have two simillar shifts either side - shift_scheduling_sat.py

[braindeaf]

Following the example of shift_scheduling_sat.py, how could I create a constraint that ensures that a shift on the preceding day is present and/or a shift on the following day is present.

e.g.
D L D D D
O L D D D
D L O D D
O L O D D <--- this is not valid as there is a day off either side of this L(ong) shift..

I had initially thought I could use similar logic to the penalized transitions, and it took me a while to work out how the penalized transitions blocked a transition with two .Not(). Which I understand now, but applying this to more than two variables gets awkward..

    # Penalized transitions
    for previous_shift, next_shift, cost in penalized_transitions:
        for e in range(num_employees):
            for d in range(num_days - 1):
                transition = [
                    work[e, previous_shift, d].Not(), work[e, next_shift,
                                                           d + 1].Not()
                ]
                model.AddBoolOr(transition)

I appreciate it's a logic puzzle, and it's a question of saying....say

when work[2] is true
work[1] can be true or false
work[3] can be true or false
work[1] and work[3] cannot be false

I'm just struggling to turn that into code. Many thanks in advance :)

[lperron]

You can use implications:

D at day i imply O at day i + 1 is false (if the day exists)
D at day i imply O at day i - 1 is false (if the day exists)

[braindeaf]

I think maybe my question is just not very clear. I want to say that if

shift 2 is a L(ong) day, that is must have either a preceding or following D(ay) shift so the following would be valid

D L D
O L D
D L O

so it's something like

shifts = ['O', 'D', 'L', 'N']
days = [1,2,3,4,5]

model.addBoolOr([work[1, 1, 1], work[1, 1, 3]])  # if work[1, 3, 2]

so if the if work[1,3,2] should be an implication. What would that look like?

[lperron]

model.AddBoolOr([work[1, 3, 2].Not(), work[1, 1, 1], work[1, 1, 3]])

[braindeaf]

Thank you, this is just what I needed. I'm getting there slowly :)