Objectives

All objectiveds are located inside src/cp/objectives/*.py. Each objective is implemented as a function that takes a CpModel¹ object and adds the necessary constraints to it, while returning a returning a linear expression that represents the objective to be minimized. Objectives are considered as soft constraints as they should be satisfied in the best way possible for a valid schedule. For hard constraints, see the Constraints chapter.

Free days near weekends
Minimize consecutive night shifts
Minimize overtime/undertime
Not too many consecutive shifts
Forward rotation of shifts

All Objectives¶

Free days near weekends ⁴¶

Employees should have free days near weekends to ensure a better work-life balance. This is a soft constraint that should be satisfied as much as possible. Therefore, if an employee has a free day on a Friday to Monday, it is rewarded with a positive score in the objective function. A bonus is given when two or more consecutive free days are scheduled near the weekend.

src/cp/objectives/free_days_near_weekends.py

if day.isoweekday() in [5, 6, 7]:
    model.add(day_today_variable == 0).only_enforce_if(
        free_today_day_variable
    )
    model.add(day_today_variable == 1).only_enforce_if(
        free_today_day_variable.Not()
    )
    if day + timedelta(1) in self._days:
        model.add(day_tomorrow_variable == 0).only_enforce_if(
            free_tomorrow_day_variable
        )
        model.add(day_tomorrow_variable != 0).only_enforce_if(
            free_tomorrow_day_variable.Not()
        )

        model.add_bool_and(
            [free_today_day_variable, free_tomorrow_day_variable]
        ).only_enforce_if(free_both_days_variable)
        model.add_bool_or(
            [
                free_today_day_variable.Not(),
                free_tomorrow_day_variable.Not(),
            ]
        ).only_enforce_if(free_both_days_variable.Not())

Minimize consecutive night shifts¶

Minimize overtime/undertime ¹¶

Overtime and undertime are possible and acceptable, but they should be minimized as much as possible. Therefore, the each minute of overtime or undertime is punished with a negative score in the objective function.

src/cp/objectives/minimize_overtime.py

model.add_abs_equality(
    possible_overtime_variable,
    sum(possible_working_time) - target_working_time,
)

Not too many consecutive shifts¶

Forward rotation of shifts ⁴¶

Shifts should be rotated in a forward direction, meaning that the order of shifts should be from early to late, and not the other way around. This is a soft constraint that should be satisfied as much as possible. Therefore, rotating the shifts forward is rewarded with a positive score in the objective function.

src/cp/objectives/rotate_shifts_forward.py

model.add_bool_and(
    [current_shift_variable, next_desired_shift_variable]
).only_enforce_if(rotation_variable)
model.add_bool_or(
    [
        current_shift_variable.Not(),
        next_desired_shift_variable.Not(),
    ]
).only_enforce_if(rotation_variable.Not())

OR Tools Documentation ↩↩
Problem definition (PDF file from Moodle) ↩
Occupational Health and Safety Law (Arbeitsschutzgesetz) (PDF file from Moodle) ↩
Guidelines for shift work ↩↩