Shift schedule: excluding a certain type of shift when and other has been done

[techhead2]

I found out the answer to my previous question but now I stumbled upon a new one. I have diferent types of shifts. In case a nurse has already taken any of the two STEMI shifts then she can't be assigned to any other shifts. I have 2 lists of shift types. created two list of variables for each set and (hopefully) created the first condition: which does not allow to have more that one STEMO on a single day. My piece of code looks as follows:

    stemi_shifts = [ShiftType.STEMI_NIGHT, ShiftType.STEMI_MORNING]
    other_shifts = [ShiftType.MORNING,
                    ShiftType.AFTERNOON,
                    ShiftType.PHONE_FROM_HOME,
                    ShiftType.PHONE_LOCAL,
                    ShiftType.PHONE_WEEKEND]
    for e in range(num_employees):
        for w in range(num_weeks):
            for d in range(num_days):
                # Shifts for this day
                stemis = [shifts[e, s.value, w * 7 + d] for s in stemi_shifts]
                other = [shifts[e, s.value, w * 7 + d] for s in other_shifts]

                stemis_worked = model.NewIntVar(0, 1, 'max_stemi_per_day')
                model.Add(sum(stemis) <= stemis_worked)

                other_worked = model.NewIntVar(0, len(other_shifts), 'max_ohter_per_day')
                # if other == 0:
                #     sum(stemi) <= 1
                # else:
                #     sum(stemi) == 0

This is how far I got. Basicaly my problem is that I don't know how can I sum the number of other shifts together to compare it against the sum of STEMIs.

[techhead2]

I've come up with something like this, but can't prove if it is really the solution:

for e in range(num_employees):
    for d in range(num_days):
        b = model.NewBoolVar(f'constr_{e}_{d}')
        model.add(sum(shifts[(e, s.value, d)] for s in other_shifts) == 0).OnlyEnforceIf(b)
        model.add(sum(shifts[(e, s.value, d)] for s in other_shifts) > 0).OnlyEnforceIf(b.Not())

        model.add(sum(shifts[(e, s.value, d)] for s in stemi_shifts) <= 1).OnlyEnforceIf(b)

[techhead2]

Unfortunately not! I've tested it.

[sschnug]

Context seems to be missing here.

If your underlying decision-variables are of boolean type, consider going for a conflict-graph:

worker_w@shift_s_a IMPLIES !worker_w@shift s_b

Don't be scared about the size of such a graph (at least in most use-cases). It's basically the native-language of the solver and there are some clique-table/merging-actions designed to reason about this stuff.

[techhead2]

Taking you idea I modified the code as follows:

    # On any single day only 1 STEMI is allowed!
    stemi_shifts = [ShiftType.STEMI_NIGHT, ShiftType.STEMI_MORNING]
    other_shifts = [ShiftType.MORNING,
                    ShiftType.AFTERNOON,
                    ShiftType.PHONE_FROM_HOME,
                    ShiftType.PHONE_LOCAL,
                    ShiftType.PHONE_WEEKEND]
    for e in range(num_employees):
        for d in range(num_days):
            # STEMI hifts for this day
            stemis = [shifts[e, s.value, d] for s in stemi_shifts]
            stemis_worked = model.NewIntVar(0, 1, 'max_stemi_per_day')
            # This ensured that no two STEMIs are done on the same day
            model.Add(sum(stemis) <= stemis_worked)

    # No other type of shift is allowed when we aredy had a STEMI
    for e in range(num_employees):
        for d in range(num_days):
            # Implement the contraint
            b = model.NewBoolVar(f'otherc_{e}_{d}')
            # b is True if at least one other type of shift has been done
            model.add(sum(shifts[(e, s.value, d)] for s in other_shifts) > 0).OnlyEnforceIf(b)
            model.add(sum(shifts[(e, s.value, d)] for s in other_shifts) == 0).OnlyEnforceIf(b.Not())

            s = model.NewBoolVar(f'stemic_{e}_{d}')
            # s is True if at least one STEMI shift has been done
            model.add(sum(shifts[(e, s.value, d)] for s in stemi_shifts) > 0).OnlyEnforceIf(s)
            model.add(sum(shifts[(e, s.value, d)] for s in stemi_shifts) == 0).OnlyEnforceIf(s.Not())

            model.AddImplication(b, s.Not())

It seems to work but I need an expert eye for a check.