Or-tools护士排班问题：添加连续至少工作2天约束报错求助

Hey there! Let's break down why your current code is throwing errors and how to fix the constraint properly.

Why Your Attempts Failed #

Both of your tries hit issues because OR-Tools doesn't support using Python's native and operator directly in constraint conditions. Here's the breakdown:

1. First try: shifts[(n, d-1, s)]==0 and shifts[(n, d, s)]==1 gets evaluated as a plain Python boolean expression (not an OR-Tools constraint object), which AddImplication can't process—hence the TypeError.
2. Second try: The and here returns a BoundedLinearExpression instead of a valid boolean variable/index that OnlyEnforceIf expects, leading to the AttributeError.

Correct Implementation #

To enforce "if a nurse works shift s on day d and didn't work it on day d-1, they must work it on day d+1", you need to use OR-Tools' built-in logical constraint helpers like AddBoolAnd to combine your conditions properly.

Here's the revised code:

for n in all_nurses:
    # Adjust the date range to avoid index out-of-bounds (d-1 and d+1 must be valid days)
    # Assuming your days are indexed from 0 to 6 (7 days total), use d from 1 to 5
    for d in range(1, len(all_days) - 1):
        for s in all_shifts:
            # Define the two conditions as OR-Tools expressions
            prev_day_off = shifts[(n, d-1, s)] == 0
            today_on = shifts[(n, d, s)] == 1
            
            # Combine conditions with AddBoolAnd to create a valid boolean constraint
            must_work_next_day = model.AddBoolAnd([prev_day_off, today_on])
            
            # Enforce: if the combined condition is true, next day must be on shift s
            model.AddImplication(must_work_next_day, shifts[(n, d+1, s)] == 1)

Handling Edge Cases #

Don't forget the last day of your schedule! The above code doesn't cover if a nurse works the final day but didn't work the day before. Add this extra constraint to close that gap:

last_day = len(all_days) - 1
for n in all_nurses:
    for s in all_shifts:
        # If nurse works last day, they must have worked the previous day
        model.Add(shifts[(n, last_day - 1, s)] == 1).OnlyEnforceIf(shifts[(n, last_day, s)] == 1)

How This Works #

• AddBoolAnd([prev_day_off, today_on]) creates a boolean variable that's only True when both conditions are met.
• AddImplication(condition, consequence) ensures that if the condition is True, the consequence (working the next day) must also be True.
• The edge case constraint prevents a single shift on the final day, fully enforcing your "at least 2 consecutive work days" rule.

内容的提问来源于stack exchange，提问作者Przemek