How to add a max sequence of days working with ORTools when having multiple shifts per day

Question

I am trying to solve the shift scheduling problem according to https://github.com/google/or-tools/blob/39f44709bba203f5ff3bc18fab8098739f189a6d/examples/python/shift_scheduling_sat.py, but since my problem has multiple 30m shift slots rather than 3, aka shift1-shift22 for 06:00am till 19:00pm allocation, I can't understand or workout how the soft_sum_constraint would work on my scenario when I need for example max of 5 working days in total per week per person.

Here is a sample of my code:

for e in range(num_employees):
    if db['conthoursperweek'][(e)]>0:
        max_cont_shifts=round(int(db['conthoursperweek'][e] / 5)*2)
        for d in range(7):
            if d==6:
                if db['optedinsundays'][e]==0:
                    for s in range(num_of_shifts):
                                     model.Add(work[e, s, 6]==0)
                else:
                    model.Add(sum(work[e, s, d] 
                                                  for s in range(num_of_shifts)) >= max_cont_shifts)
                    model.Add(sum(work[e, s, d] 
                                                  for s in range(num_of_shifts)) < max_cont_shifts + 4)
                   
            else:
                model.Add(sum(work[e, s, d] 
                                                  for s in range(num_of_shifts)) >= max_cont_shifts)
                model.Add(sum(work[e, s, d] 
                                                  for s in range(num_of_shifts)) < max_cont_shifts + 4)

for d in range(num_days):
    for e in range(num_employees):
        for s in range(num_of_shifts-1):
            for x in range(s+1,num_of_shifts):
                model.Add(work[e,x,d] == 0).OnlyEnforceIf([work[e,s-1,d],work[e,s,d].Not()])

This satisfies my need for shifts per day constraints and them being continuous. I need to do the same for days but nothing I have tried so far works.

Things like below do not work:

for e in range(num_employees):
       model.Add(sum(work[e, s, d] for d in range(7) for s in range(num_of_shifts))<=80) #for max shifts per week

#or
work_days=[]
for e in range(num_employees):
       for d in range(7):
            working=sum(work[e, s, d] for s in range(num_of_shifts))
            work_days.append(working)
       model.Add(work_days<=5)

#or
for e in range(num_employees):
       for d in range(7):
            model.Add(sum(work[e, s, d])<=5)

I know the above code is wrong but I can't figure it out. Any help would be greatly appreciated.

Answer 1

Just create one boolean that is true if at least one shift of this day is true. And use it you inter-day constraints.

For the record:

a <=> or(b1, .., bn)

is encoded as

for all i: bi implies a
bool_or(a.Not(), b1, .., bn)