resident_shift.py

#!/usr/bin/env python3
"""Creates a shift scheduling problem and solves it."""

from absl import app
from absl import flags

from ortools.sat.python import cp_model
from google.protobuf import text_format

FLAGS = flags.FLAGS

flags.DEFINE_string("params", "max_time_in_seconds:10.0", "Sat solver parameters.")


def negated_bounded_span(works, start, length):
    """Filters an isolated sub-sequence of variables assined to True.
    Extract the span of Boolean variables [start, start + length), negate them,
    and if there is variables to the left/right of this span, surround the span by
    them in non negated form.
    Args:
      works: a list of variables to extract the span from.
      start: the start to the span.
      length: the length of the span.
    Returns:
      a list of variables which conjunction will be false if the sub-list is
      assigned to True, and correctly bounded by variables assigned to False,
      or by the start or end of works.
    """
    sequence = []
    # Left border (start of works, or works[start - 1])
    if start > 0:
        sequence.append(works[start - 1])
    for i in range(length):
        sequence.append(works[start + i].Not())
    # Right border (end of works or works[start + length])
    if start + length < len(works):
        sequence.append(works[start + length])
    return sequence


def add_soft_sequence_constraint(
    model, works, hard_min, soft_min, min_cost, soft_max, hard_max, max_cost, prefix
):
    """Sequence constraint on true variables with soft and hard bounds.
    This constraint look at every maximal contiguous sequence of variables
    assigned to true. If forbids sequence of length < hard_min or > hard_max.
    Then it creates penalty terms if the length is < soft_min or > soft_max.
    Args:
      model: the sequence constraint is built on this model.
      works: a list of Boolean variables.
      hard_min: any sequence of true variables must have a length of at least
        hard_min.
      soft_min: any sequence should have a length of at least soft_min, or a
        linear penalty on the delta will be added to the objective.
      min_cost: the coefficient of the linear penalty if the length is less than
        soft_min.
      soft_max: any sequence should have a length of at most soft_max, or a linear
        penalty on the delta will be added to the objective.
      hard_max: any sequence of true variables must have a length of at most
        hard_max.
      max_cost: the coefficient of the linear penalty if the length is more than
        soft_max.
      prefix: a base name for penalty literals.
    Returns:
      a tuple (variables_list, coefficient_list) containing the different
      penalties created by the sequence constraint.
    """
    cost_literals = []
    cost_coefficients = []

    # Forbid sequences that are too short.
    for length in range(1, hard_min):
        for start in range(len(works) - length + 1):
            model.AddBoolOr(negated_bounded_span(works, start, length))

    # Penalize sequences that are below the soft limit.
    if min_cost > 0:
        for length in range(hard_min, soft_min):
            for start in range(len(works) - length + 1):
                span = negated_bounded_span(works, start, length)
                name = ": under_span(start=%i, length=%i)" % (start, length)
                lit = model.NewBoolVar(prefix + name)
                span.append(lit)
                model.AddBoolOr(span)
                cost_literals.append(lit)
                # We filter exactly the sequence with a short length.
                # The penalty is proportional to the delta with soft_min.
                cost_coefficients.append(min_cost * (soft_min - length))

    # Penalize sequences that are above the soft limit.
    if max_cost > 0:
        for length in range(soft_max + 1, hard_max + 1):
            for start in range(len(works) - length + 1):
                span = negated_bounded_span(works, start, length)
                name = ": over_span(start=%i, length=%i)" % (start, length)
                lit = model.NewBoolVar(prefix + name)
                span.append(lit)
                model.AddBoolOr(span)
                cost_literals.append(lit)
                # Cost paid is max_cost * excess length.
                cost_coefficients.append(max_cost * (length - soft_max))

    # Just forbid any sequence of true variables with length hard_max + 1
    for start in range(len(works) - hard_max):
        model.AddBoolOr([works[i].Not() for i in range(start, start + hard_max + 1)])
    return cost_literals, cost_coefficients


def add_soft_sum_constraint(
    model, works, hard_min, soft_min, min_cost, soft_max, hard_max, max_cost, prefix
):
    """Sum constraint with soft and hard bounds.
    This constraint counts the variables assigned to true from works.
    If forbids sum < hard_min or > hard_max.
    Then it creates penalty terms if the sum is < soft_min or > soft_max.
    Args:
      model: the sequence constraint is built on this model.
      works: a list of Boolean variables.
      hard_min: any sequence of true variables must have a sum of at least
        hard_min.
      soft_min: any sequence should have a sum of at least soft_min, or a linear
        penalty on the delta will be added to the objective.
      min_cost: the coefficient of the linear penalty if the sum is less than
        soft_min.
      soft_max: any sequence should have a sum of at most soft_max, or a linear
        penalty on the delta will be added to the objective.
      hard_max: any sequence of true variables must have a sum of at most
        hard_max.
      max_cost: the coefficient of the linear penalty if the sum is more than
        soft_max.
      prefix: a base name for penalty variables.
    Returns:
      a tuple (variables_list, coefficient_list) containing the different
      penalties created by the sequence constraint.
    """
    cost_variables = []
    cost_coefficients = []
    sum_var = model.NewIntVar(hard_min, hard_max, "")
    # This adds the hard constraints on the sum.
    model.Add(sum_var == sum(works))

    # Penalize sums below the soft_min target.
    if soft_min > hard_min and min_cost > 0:
        delta = model.NewIntVar(-len(works), len(works), "")
        model.Add(delta == soft_min - sum_var)
        # TODO(user): Compare efficiency with only excess >= soft_min - sum_var.
        excess = model.NewIntVar(0, 7, prefix + ": under_sum")
        model.AddMaxEquality(excess, [delta, 0])
        cost_variables.append(excess)
        cost_coefficients.append(min_cost)

    # Penalize sums above the soft_max target.
    if soft_max < hard_max and max_cost > 0:
        delta = model.NewIntVar(-7, 7, "")
        model.Add(delta == sum_var - soft_max)
        excess = model.NewIntVar(0, 7, prefix + ": over_sum")
        model.AddMaxEquality(excess, [delta, 0])
        cost_variables.append(excess)
        cost_coefficients.append(max_cost)

    return cost_variables, cost_coefficients


def solve_shift_scheduling(params):
    """Solves the shift scheduling problem."""
    # Data
    spec = ["Dan", "Mic", "Gio", "Alb", "Fra"]
    num_spec = len(spec)
    num_weeks = 4
    shifts = ["Rip", "Rep", "Pom", "AmA", "AmB"]

    num_days = num_weeks * 7
    num_shifts = len(shifts)

    # Shift constraints on continuous sequence:
    #     (shift, hard_min, soft_min, min_penalty,
    #             soft_max, hard_max, max_penalty)
    shift_constraints = [
        # One or two consecutive days of rest, this is a hard constraint.
        ('Rip', 1, 1, 0, 2, 2, 0),
        # max 1 afternoon
        ('Pom', 1, 1, 0, 1, 1, 0),
        # min 1 max 5 days of reparto
        ('Rep', 1, 2, 2, 4, 5, 2),
    ]

    # Weekly sum constraints on shifts days:
    #     (shift, hard_min, soft_min, min_penalty,
    #             soft_max, hard_max, max_penalty)
    weekly_sum_constraints = [
        # Constraints on rests per week.
        ("Rip", 1, 2, 7, 2, 2, 4),
    ]

    # daily demands for work shifts (morning, afternon, night) for each day
    # of the week starting on Monday.
    weekly_cover_demands = [
        (2, 1, 1, 0),  # Monday
        (2, 1, 1, 0),  # Tuesday
        (2, 1, 1, 0),  # Wednesday
        (2, 1, 1, 0),  # Thursday
        (2, 1, 1, 0),  # Friday
        (1, 0, 0, 0),  # Saturday
        (1, 0, 0, 0),  # Sunday
    ]
    # Penalty for exceeding the cover constraint per shift type.
    excess_cover_penalties = (5, 5, 5, 0)

    model = cp_model.CpModel()

    work = {}
    for e in spec:
        for s in shifts:
            for d in range(num_days):
                work[e, s, d] = model.NewBoolVar(f"work_{e}_{s}_{d}")


    # Linear terms of the objective in a minimization context.
    obj_int_vars = []
    obj_int_coeffs = []
    obj_bool_vars = []
    obj_bool_coeffs = []

    # Exactly one shift per day.
    for e in spec:
        for d in range(num_days):
            model.Add(sum(work[e, s, d] for s in shifts) == 1)

    # Shift constraints
    for ct in shift_constraints:
        shift, hard_min, soft_min, min_cost, soft_max, hard_max, max_cost = ct
        for e in spec:
            works = [work[e, shift, d] for d in range(num_days)]
            variables, coeffs = add_soft_sequence_constraint(
                model,
                works,
                hard_min,
                soft_min,
                min_cost,
                soft_max,
                hard_max,
                max_cost,
                f"shift_constraint(employee {e}, shift {shift})",
            )
            obj_bool_vars.extend(variables)
            obj_bool_coeffs.extend(coeffs)

    # Assign saturdays and sundays together
    for d in range(num_days):
        if d % 7 == 5:
            for e in spec:
                model.AddImplication(work[e, shift, d], work[e, shift, d + 1])
            for s in shifts:
                model.Add(sum(work[e, s, d] for e in spec) == 1)

    # Weekly sum constraints
    for ct in weekly_sum_constraints:
        shift, hard_min, soft_min, min_cost, soft_max, hard_max, max_cost = ct
        for e in spec:
            for w in range(num_weeks):
                works = [work[e, shift, d + w * 7] for d in range(7)]
                variables, coeffs = add_soft_sum_constraint(
                    model,
                    works,
                    hard_min,
                    soft_min,
                    min_cost,
                    soft_max,
                    hard_max,
                    max_cost,
                    f"weekly_sum_constraint(employee {e}, shift {shift}, week {w:d})"
                )
                obj_int_vars.extend(variables)
                obj_int_coeffs.extend(coeffs)

    # domains for weekend?


    # missing bans on employee assignments
    for e in ["Gio", "Alb", "Fra"]:
        for s in ["AmA", "AmB"]:
            works = [work[e, s, d] for d in range(num_days)]
            model.AddForbiddenAssignments(works, tuple([1 for x in range(num_days)]))

    # Cover constraints
    for s in shifts[1:]:
        for w in range(num_weeks):
            for d in range(7):
                works = [work[e, s, w * 7 + d] for e in spec]
                min_demand = weekly_cover_demands[d][shifts.index(s) - 1]  # Ignore Off shift.
                worked = model.NewIntVar(min_demand, num_spec, "")
                model.Add(worked == sum(works))
                over_penalty = excess_cover_penalties[shifts.index(s) - 1]
                if over_penalty > 0:
                    name = f"excess_demand(shift={s}, week={w:d}, day={d:d})"
                    excess = model.NewIntVar(0, num_spec - min_demand, name)
                    model.Add(excess == worked - min_demand)
                    obj_int_vars.append(excess)
                    obj_int_coeffs.append(over_penalty)

    # Objective
    model.Minimize(
        sum(obj_bool_vars[i] * obj_bool_coeffs[i] for i in range(len(obj_bool_vars)))
        + sum(obj_int_vars[i] * obj_int_coeffs[i] for i in range(len(obj_int_vars)))
    )

    # Solve the model.
    solver = cp_model.CpSolver()
    if params:
        text_format.Parse(params, solver.parameters)
    solution_printer = cp_model.ObjectiveSolutionPrinter()
    status = solver.Solve(model, solution_printer)

    # Print solution.
    if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:
        print()
        print(f"            {'Mon Tue Wed Thu Fri Sat Sun ' * num_weeks}")
        for e in spec:
            schedule = ""
            for d in range(num_days):
                for s in shifts:
                    if solver.BooleanValue(work[e, s, d]):
                        schedule += shifts[shifts.index(s)] + " "
            print(f"worker {e}: {schedule}")
        print()
        print("Penalties:")
        for i, var in enumerate(obj_bool_vars):
            if solver.BooleanValue(var):
                penalty = obj_bool_coeffs[i]
                if penalty > 0:
                    print("  %s violated, penalty=%i" % (var.Name(), penalty))
                else:
                    print("  %s fulfilled, gain=%i" % (var.Name(), -penalty))

        for i, var in enumerate(obj_int_vars):
            if solver.Value(var) > 0:
                print(
                    "  %s violated by %i, linear penalty=%i"
                    % (var.Name(), solver.Value(var), obj_int_coeffs[i])
                )

    print()
    print("Statistics")
    print("  - status          : %s" % solver.StatusName(status))
    print("  - conflicts       : %i" % solver.NumConflicts())
    print("  - branches        : %i" % solver.NumBranches())
    print("  - wall time       : %f s" % solver.WallTime())


def main(_):
    solve_shift_scheduling(FLAGS.params)


if __name__ == "__main__":
    app.run(main)